Lab-on-a-Chip 시스템의 혈류 역학에 대한 검토: 엔지니어링 관점

Review on Blood Flow Dynamics in Lab-on-a-Chip Systems: An Engineering Perspective

  • Bin-Jie Lai
  • Li-Tao Zhu
  • Zhe Chen*
  • Bo Ouyang*
  • , and 
  • Zheng-Hong Luo*

Abstract

다양한 수송 메커니즘 하에서, “LOC(lab-on-a-chip)” 시스템에서 유동 전단 속도 조건과 밀접한 관련이 있는 혈류 역학은 다양한 수송 현상을 초래하는 것으로 밝혀졌습니다.

본 연구는 적혈구의 동적 혈액 점도 및 탄성 거동과 같은 점탄성 특성의 역할을 통해 LOC 시스템의 혈류 패턴을 조사합니다. 모세관 및 전기삼투압의 주요 매개변수를 통해 LOC 시스템의 혈액 수송 현상에 대한 연구는 실험적, 이론적 및 수많은 수치적 접근 방식을 통해 제공됩니다.

전기 삼투압 점탄성 흐름에 의해 유발되는 교란은 특히 향후 연구 기회를 위해 혈액 및 기타 점탄성 유체를 취급하는 LOC 장치의 혼합 및 분리 기능 향상에 논의되고 적용됩니다. 또한, 본 연구는 보다 정확하고 단순화된 혈류 모델에 대한 요구와 전기역학 효과 하에서 점탄성 유체 흐름에 대한 수치 연구에 대한 강조와 같은 LOC 시스템 하에서 혈류 역학의 수치 모델링의 문제를 식별합니다.

전기역학 현상을 연구하는 동안 제타 전위 조건에 대한 보다 실용적인 가정도 강조됩니다. 본 연구는 모세관 및 전기삼투압에 의해 구동되는 미세유체 시스템의 혈류 역학에 대한 포괄적이고 학제적인 관점을 제공하는 것을 목표로 한다.

KEYWORDS: 

1. Introduction

1.1. Microfluidic Flow in Lab-on-a-Chip (LOC) Systems

Over the past several decades, the ability to control and utilize fluid flow patterns at microscales has gained considerable interest across a myriad of scientific and engineering disciplines, leading to growing interest in scientific research of microfluidics. 

(1) Microfluidics, an interdisciplinary field that straddles physics, engineering, and biotechnology, is dedicated to the behavior, precise control, and manipulation of fluids geometrically constrained to a small, typically submillimeter, scale. 

(2) The engineering community has increasingly focused on microfluidics, exploring different driving forces to enhance working fluid transport, with the aim of accurately and efficiently describing, controlling, designing, and applying microfluidic flow principles and transport phenomena, particularly for miniaturized applications. 

(3) This attention has chiefly been fueled by the potential to revolutionize diagnostic and therapeutic techniques in the biomedical and pharmaceutical sectorsUnder various driving forces in microfluidic flows, intriguing transport phenomena have bolstered confidence in sustainable and efficient applications in fields such as pharmaceutical, biochemical, and environmental science. The “lab-on-a-chip” (LOC) system harnesses microfluidic flow to enable fluid processing and the execution of laboratory tasks on a chip-sized scale. LOC systems have played a vital role in the miniaturization of laboratory operations such as mixing, chemical reaction, separation, flow control, and detection on small devices, where a wide variety of fluids is adapted. Biological fluid flow like blood and other viscoelastic fluids are notably studied among the many working fluids commonly utilized by LOC systems, owing to the optimization in small fluid sample volumed, rapid response times, precise control, and easy manipulation of flow patterns offered by the system under various driving forces. 

(4)The driving forces in blood flow can be categorized as passive or active transport mechanisms and, in some cases, both. Under various transport mechanisms, the unique design of microchannels enables different functionalities in driving, mixing, separating, and diagnosing blood and drug delivery in the blood. 

(5) Understanding and manipulating these driving forces are crucial for optimizing the performance of a LOC system. Such knowledge presents the opportunity to achieve higher efficiency and reliability in addressing cellular level challenges in medical diagnostics, forensic studies, cancer detection, and other fundamental research areas, for applications of point-of-care (POC) devices. 

(6)

1.2. Engineering Approach of Microfluidic Transport Phenomena in LOC Systems

Different transport mechanisms exhibit unique properties at submillimeter length scales in microfluidic devices, leading to significant transport phenomena that differ from those of macroscale flows. An in-depth understanding of these unique transport phenomena under microfluidic systems is often required in fluidic mechanics to fully harness the potential functionality of a LOC system to obtain systematically designed and precisely controlled transport of microfluids under their respective driving force. Fluid mechanics is considered a vital component in chemical engineering, enabling the analysis of fluid behaviors in various unit designs, ranging from large-scale reactors to separation units. Transport phenomena in fluid mechanics provide a conceptual framework for analytically and descriptively explaining why and how experimental results and physiological phenomena occur. The Navier–Stokes (N–S) equation, along with other governing equations, is often adapted to accurately describe fluid dynamics by accounting for pressure, surface properties, velocity, and temperature variations over space and time. In addition, limiting factors and nonidealities for these governing equations should be considered to impose corrections for empirical consistency before physical models are assembled for more accurate controls and efficiency. Microfluidic flow systems often deviate from ideal conditions, requiring adjustments to the standard governing equations. These deviations could arise from factors such as viscous effects, surface interactions, and non-Newtonian fluid properties from different microfluid types and geometrical layouts of microchannels. Addressing these nonidealities supports the refining of theoretical models and prediction accuracy for microfluidic flow behaviors.

The analytical calculation of coupled nonlinear governing equations, which describes the material and energy balances of systems under ideal conditions, often requires considerable computational efforts. However, advancements in computation capabilities, cost reduction, and improved accuracy have made numerical simulations using different numerical and modeling methods a powerful tool for effectively solving these complex coupled equations and modeling various transport phenomena. Computational fluid dynamics (CFD) is a numerical technique used to investigate the spatial and temporal distribution of various flow parameters. It serves as a critical approach to provide insights and reasoning for decision-making regarding the optimal designs involving fluid dynamics, even prior to complex physical model prototyping and experimental procedures. The integration of experimental data, theoretical analysis, and reliable numerical simulations from CFD enables systematic variation of analytical parameters through quantitative analysis, where adjustment to delivery of blood flow and other working fluids in LOC systems can be achieved.

Numerical methods such as the Finite-Difference Method (FDM), Finite-Element-Method (FEM), and Finite-Volume Method (FVM) are heavily employed in CFD and offer diverse approaches to achieve discretization of Eulerian flow equations through filling a mesh of the flow domain. A more in-depth review of numerical methods in CFD and its application for blood flow simulation is provided in Section 2.2.2.

1.3. Scope of the Review

In this Review, we explore and characterize the blood flow phenomena within the LOC systems, utilizing both physiological and engineering modeling approaches. Similar approaches will be taken to discuss capillary-driven flow and electric-osmotic flow (EOF) under electrokinetic phenomena as a passive and active transport scheme, respectively, for blood transport in LOC systems. Such an analysis aims to bridge the gap between physical (experimental) and engineering (analytical) perspectives in studying and manipulating blood flow delivery by different driving forces in LOC systems. Moreover, the Review hopes to benefit the interests of not only blood flow control in LOC devices but also the transport of viscoelastic fluids, which are less studied in the literature compared to that of Newtonian fluids, in LOC systems.

Section 2 examines the complex interplay between viscoelastic properties of blood and blood flow patterns under shear flow in LOC systems, while engineering numerical modeling approaches for blood flow are presented for assistance. Sections 3 and 4 look into the theoretical principles, numerical governing equations, and modeling methodologies for capillary driven flow and EOF in LOC systems as well as their impact on blood flow dynamics through the quantification of key parameters of the two driving forces. Section 5 concludes the characterized blood flow transport processes in LOC systems under these two forces. Additionally, prospective areas of research in improving the functionality of LOC devices employing blood and other viscoelastic fluids and potentially justifying mechanisms underlying microfluidic flow patterns outside of LOC systems are presented. Finally, the challenges encountered in the numerical studies of blood flow under LOC systems are acknowledged, paving the way for further research.

2. Blood Flow Phenomena

ARTICLE SECTIONS

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2.1. Physiological Blood Flow Behavior

Blood, an essential physiological fluid in the human body, serves the vital role of transporting oxygen and nutrients throughout the body. Additionally, blood is responsible for suspending various blood cells including erythrocytes (red blood cells or RBCs), leukocytes (white blood cells), and thrombocytes (blood platelets) in a plasma medium.Among the cells mentioned above, red blood cells (RBCs) comprise approximately 40–45% of the volume of healthy blood. 

(7) An RBC possesses an inherent elastic property with a biconcave shape of an average diameter of 8 μm and a thickness of 2 μm. This biconcave shape maximizes the surface-to-volume ratio, allowing RBCs to endure significant distortion while maintaining their functionality. 

(8,9) Additionally, the biconcave shape optimizes gas exchange, facilitating efficient uptake of oxygen due to the increased surface area. The inherent elasticity of RBCs allows them to undergo substantial distortion from their original biconcave shape and exhibits high flexibility, particularly in narrow channels.RBC deformability enables the cell to deform from a biconcave shape to a parachute-like configuration, despite minor differences in RBC shape dynamics under shear flow between initial cell locations. As shown in Figure 1(a), RBCs initiating with different resting shapes and orientations displaying display a similar deformation pattern 

(10) in terms of its shape. Shear flow induces an inward bending of the cell at the rear position of the rim to the final bending position, 

(11) resulting in an alignment toward the same position of the flow direction.

Figure 1. Images of varying deformation of RBCs and different dynamic blood flow behaviors. (a) The deforming shape behavior of RBCs at four different initiating positions under the same experimental conditions of a flow from left to right, (10) (b) RBC aggregation, (13) (c) CFL region. (18) Reproduced with permission from ref (10). Copyright 2011 Elsevier. Reproduced with permission from ref (13). Copyright 2022 The Authors, under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/. Reproduced with permission from ref (18). Copyright 2019 Elsevier.

The flexible property of RBCs enables them to navigate through narrow capillaries and traverse a complex network of blood vessels. The deformability of RBCs depends on various factors, including the channel geometry, RBC concentration, and the elastic properties of the RBC membrane. 

(12) Both flexibility and deformability are vital in the process of oxygen exchange among blood and tissues throughout the body, allowing cells to flow in vessels even smaller than the original cell size prior to deforming.As RBCs serve as major components in blood, their collective dynamics also hugely affect blood rheology. RBCs exhibit an aggregation phenomenon due to cell to cell interactions, such as adhesion forces, among populated cells, inducing unique blood flow patterns and rheological behaviors in microfluidic systems. For blood flow in large vessels between a diameter of 1 and 3 cm, where shear rates are not high, a constant viscosity and Newtonian behavior for blood can be assumed. However, under low shear rate conditions (0.1 s

–1) in smaller vessels such as the arteries and venules, which are within a diameter of 0.2 mm to 1 cm, blood exhibits non-Newtonian properties, such as shear-thinning viscosity and viscoelasticity due to RBC aggregation and deformability. The nonlinear viscoelastic property of blood gives rise to a complex relationship between viscosity and shear rate, primarily influenced by the highly elastic behavior of RBCs. A wide range of research on the transient behavior of the RBC shape and aggregation characteristics under varied flow circumstances has been conducted, aiming to obtain a better understanding of the interaction between blood flow shear forces from confined flows.

For a better understanding of the unique blood flow structures and rheological behaviors in microfluidic systems, some blood flow patterns are introduced in the following section.

2.1.1. RBC Aggregation

RBC aggregation is a vital phenomenon to be considered when designing LOC devices due to its impact on the viscosity of the bulk flow. Under conditions of low shear rate, such as in stagnant or low flow rate regions, RBCs tend to aggregate, forming structures known as rouleaux, resembling stacks of coins as shown in Figure 1(b). 

(13) The aggregation of RBCs increases the viscosity at the aggregated region, 

(14) hence slowing down the overall blood flow. However, when exposed to high shear rates, RBC aggregates disaggregate. As shear rates continue to increase, RBCs tend to deform, elongating and aligning themselves with the direction of the flow. 

(15) Such a dynamic shift in behavior from the cells in response to the shear rate forms the basis of the viscoelastic properties observed in whole blood. In essence, the viscosity of the blood varies according to the shear rate conditions, which are related to the velocity gradient of the system. It is significant to take the intricate relationship between shear rate conditions and the change of blood viscosity due to RBC aggregation into account since various flow driving conditions may induce varied effects on the degree of aggregation.

2.1.2. Fåhræus-Lindqvist Effect

The Fåhræus–Lindqvist (FL) effect describes the gradual decrease in the apparent viscosity of blood as the channel diameter decreases. 

(16) This effect is attributed to the migration of RBCs toward the central region in the microchannel, where the flow rate is higher, due to the presence of higher pressure and asymmetric distribution of shear forces. This migration of RBCs, typically observed at blood vessels less than 0.3 mm, toward the higher flow rate region contributes to the change in blood viscosity, which becomes dependent on the channel size. Simultaneously, the increase of the RBC concentration in the central region of the microchannel results in the formation of a less viscous region close to the microchannel wall. This region called the Cell-Free Layer (CFL), is primarily composed of plasma. 

(17) The combination of the FL effect and the following CFL formation provides a unique phenomenon that is often utilized in passive and active plasma separation mechanisms, involving branched and constriction channels for various applications in plasma separation using microfluidic systems.

2.1.3. Cell-Free Layer Formation

In microfluidic blood flow, RBCs form aggregates at the microchannel core and result in a region that is mostly devoid of RBCs near the microchannel walls, as shown in Figure 1(c). 

(18) The region is known as the cell-free layer (CFL). The CFL region is often known to possess a lower viscosity compared to other regions within the blood flow due to the lower viscosity value of plasma when compared to that of the aggregated RBCs. Therefore, a thicker CFL region composed of plasma correlates to a reduced apparent whole blood viscosity. 

(19) A thicker CFL region is often established following the RBC aggregation at the microchannel core under conditions of decreasing the tube diameter. Apart from the dependence on the RBC concentration in the microchannel core, the CFL thickness is also affected by the volume concentration of RBCs, or hematocrit, in whole blood, as well as the deformability of RBCs. Given the influence CFL thickness has on blood flow rheological parameters such as blood flow rate, which is strongly dependent on whole blood viscosity, investigating CFL thickness under shear flow is crucial for LOC systems accounting for blood flow.

2.1.4. Plasma Skimming in Bifurcation Networks

The uneven arrangement of RBCs in bifurcating microchannels, commonly termed skimming bifurcation, arises from the axial migration of RBCs within flowing streams. This uneven distribution contributes to variations in viscosity across differing sizes of bifurcating channels but offers a stabilizing effect. Notably, higher flow rates in microchannels are associated with increased hematocrit levels, resulting in higher viscosity compared with those with lower flow rates. Parametric investigations on bifurcation angle, 

(20) thickness of the CFL, 

(21) and RBC dynamics, including aggregation and deformation, 

(22) may alter the varying viscosity of blood and its flow behavior within microchannels.

2.2. Modeling on Blood Flow Dynamics

2.2.1. Blood Properties and Mathematical Models of Blood Rheology

Under different shear rate conditions in blood flow, the elastic characteristics and dynamic changes of the RBC induce a complex velocity and stress relationship, resulting in the incompatibility of blood flow characterization through standard presumptions of constant viscosity used for Newtonian fluid flow. Blood flow is categorized as a viscoelastic non-Newtonian fluid flow where constitutive equations governing this type of flow take into consideration the nonlinear viscometric properties of blood. To mathematically characterize the evolving blood viscosity and the relationship between the elasticity of RBC and the shear blood flow, respectively, across space and time of the system, a stress tensor (τ) defined by constitutive models is often coupled in the Navier–Stokes equation to account for the collective impact of the constant dynamic viscosity (η) and the elasticity from RBCs on blood flow.The dynamic viscosity of blood is heavily dependent on the shear stress applied to the cell and various parameters from the blood such as hematocrit value, plasma viscosity, mechanical properties of the RBC membrane, and red blood cell aggregation rate. The apparent blood viscosity is considered convenient for the characterization of the relationship between the evolving blood viscosity and shear rate, which can be defined by Casson’s law, as shown in eq 1.

𝜇=𝜏0𝛾˙+2𝜂𝜏0𝛾˙⎯⎯⎯⎯⎯⎯⎯√+𝜂�=�0�˙+2��0�˙+�

(1)where τ

0 is the yield stress–stress required to initiate blood flow motion, η is the Casson rheological constant, and γ̇ is the shear rate. The value of Casson’s law parameters under blood with normal hematocrit level can be defined as τ

0 = 0.0056 Pa and η = 0.0035 Pa·s. 

(23) With the known property of blood and Casson’s law parameters, an approximation can be made to the dynamic viscosity under various flow condition domains. The Power Law model is often employed to characterize the dynamic viscosity in relation to the shear rate, since precise solutions exist for specific geometries and flow circumstances, acting as a fundamental standard for definition. The Carreau and Carreau–Yasuda models can be advantageous over the Power Law model due to their ability to evaluate the dynamic viscosity at low to zero shear rate conditions. However, none of the above-mentioned models consider the memory or other elastic behavior of blood and its RBCs. Some other commonly used mathematical models and their constants for the non-Newtonian viscosity property characterization of blood are listed in Table 1 below. 

(24−26)Table 1. Comparison of Various Non-Newtonian Models for Blood Viscosity 

(24−26)

ModelNon-Newtonian ViscosityParameters
Power Law(2)n = 0.61, k = 0.42
Carreau(3)μ0 = 0.056 Pa·s, μ = 0.00345 Pa·s, λ = 3.1736 s, m = 2.406, a = 0.254
Walburn–Schneck(4)C1 = 0.000797 Pa·s, C2 = 0.0608 Pa·s, C3 = 0.00499, C4 = 14.585 g–1, TPMA = 25 g/L
Carreau–Yasuda(5)μ0 = 0.056 Pa·s, μ = 0.00345 Pa·s, λ = 1.902 s, n = 0.22, a = 1.25
Quemada(6)μp = 0.0012 Pa·s, k = 2.07, k0 = 4.33, γ̇c = 1.88 s–1

The blood rheology is commonly known to be influenced by two key physiological factors, namely, the hematocrit value (H

t) and the fibrinogen concentration (c

f), with an average value of 42% and 0.252 gd·L

–1, respectively. Particularly in low shear conditions, the presence of varying fibrinogen concentrations affects the tendency for aggregation and rouleaux formation, while the occurrence of aggregation is contingent upon specific levels of hematocrit. 

(27) The study from Apostolidis et al. 

(28) modifies the Casson model through emphasizing its reliance on hematocrit and fibrinogen concentration parameter values, owing to the extensive knowledge of the two physiological blood parameters.The viscoelastic response of blood is heavily dependent on the elasticity of the RBC, which is defined by the relationship between the deformation and stress relaxation from RBCs under a specific location of shear flow as a function of the velocity field. The stress tensor is usually characterized by constitutive equations such as the Upper-Convected Maxwell Model 

(29) and the Oldroyd-B model 

(30) to track the molecule effects under shear from different driving forces. The prominent non-Newtonian features, such as shear thinning and yield stress, have played a vital role in the characterization of blood rheology, particularly with respect to the evaluation of yield stress under low shear conditions. The nature of stress measurement in blood, typically on the order of 1 mPa, is challenging due to its low magnitude. The occurrence of the CFL complicates the measurement further due to the significant decrease in apparent viscosity near the wall over time and a consequential disparity in viscosity compared to the bulk region.In addition to shear thinning viscosity and yield stress, the formation of aggregation (rouleaux) from RBCs under low shear rates also contributes to the viscoelasticity under transient flow 

(31) and thixotropy 

(32) of whole blood. Given the difficulty in evaluating viscoelastic behavior of blood under low strain magnitudes and limitations in generalized Newtonian models, the utilization of viscoelastic models is advocated to encompass elasticity and delineate non-shear components within the stress tensor. Extending from the Oldroyd-B model, Anand et al. 

(33) developed a viscoelastic model framework for adapting elasticity within blood samples and predicting non-shear stress components. However, to also address the thixotropic effects, the model developed by Horner et al. 

(34) serves as a more comprehensive approach than the viscoelastic model from Anand et al. Thixotropy 

(32) typically occurs from the structural change of the rouleaux, where low shear rate conditions induce rouleaux formation. Correspondingly, elasticity increases, while elasticity is more representative of the isolated RBCs, under high shear rate conditions. The model of Horner et al. 

(34) considers the contribution of rouleaux to shear stress, taking into account factors such as the characteristic time for Brownian aggregation, shear-induced aggregation, and shear-induced breakage. Subsequent advancements in the model from Horner et al. often revolve around refining the three aforementioned key terms for a more substantial characterization of rouleaux dynamics. Notably, this has led to the recently developed mHAWB model 

(35) and other model iterations to enhance the accuracy of elastic and viscoelastic contributions to blood rheology, including the recently improved model suggested by Armstrong et al. 

(36)

2.2.2. Numerical Methods (FDM, FEM, FVM)

Numerical simulation has become increasingly more significant in analyzing the geometry, boundary layers of flow, and nonlinearity of hyperbolic viscoelastic flow constitutive equations. CFD is a powerful and efficient tool utilizing numerical methods to solve the governing hydrodynamic equations, such as the Navier–Stokes (N–S) equation, continuity equation, and energy conservation equation, for qualitative evaluation of fluid motion dynamics under different parameters. CFD overcomes the challenge of analytically solving nonlinear forms of differential equations by employing numerical methods such as the Finite-Difference Method (FDM), Finite-Element Method (FEM), and Finite-Volume Method (FVM) to discretize and solve the partial differential equations (PDEs), allowing for qualitative reproduction of transport phenomena and experimental observations. Different numerical methods are chosen to cope with various transport systems for optimization of the accuracy of the result and control of error during the discretization process.FDM is a straightforward approach to discretizing PDEs, replacing the continuum representation of equations with a set of finite-difference equations, which is typically applied to structured grids for efficient implementation in CFD programs. 

(37) However, FDM is often limited to simple geometries such as rectangular or block-shaped geometries and struggles with curved boundaries. In contrast, FEM divides the fluid domain into small finite grids or elements, approximating PDEs through a local description of physics. 

(38) All elements contribute to a large, sparse matrix solver. However, FEM may not always provide accurate results for systems involving significant deformation and aggregation of particles like RBCs due to large distortion of grids. 

(39) FVM evaluates PDEs following the conservation laws and discretizes the selected flow domain into small but finite size control volumes, with each grid at the center of a finite volume. 

(40) The divergence theorem allows the conversion of volume integrals of PDEs with divergence terms into surface integrals of surface fluxes across cell boundaries. Due to its conservation property, FVM offers efficient outcomes when dealing with PDEs that embody mass, momentum, and energy conservation principles. Furthermore, widely accessible software packages like the OpenFOAM toolbox 

(41) include a viscoelastic solver, making it an attractive option for viscoelastic fluid flow modeling. 

(42)

2.2.3. Modeling Methods of Blood Flow Dynamics

The complexity in the blood flow simulation arises from deformability and aggregation that RBCs exhibit during their interaction with neighboring cells under different shear rate conditions induced by blood flow. Numerical models coupled with simulation programs have been applied as a groundbreaking method to predict such unique rheological behavior exhibited by RBCs and whole blood. The conventional approach of a single-phase flow simulation is often applied to blood flow simulations within large vessels possessing a moderate shear rate. However, such a method assumes the properties of plasma, RBCs and other cellular components to be evenly distributed as average density and viscosity in blood, resulting in the inability to simulate the mechanical dynamics, such as RBC aggregation under high-shear flow field, inherent in RBCs. To accurately describe the asymmetric distribution of RBC and blood flow, multiphase flow simulation, where numerical simulations of blood flows are often modeled as two immiscible phases, RBCs and blood plasma, is proposed. A common assumption is that RBCs exhibit non-Newtonian behavior while the plasma is treated as a continuous Newtonian phase.Numerous multiphase numerical models have been proposed to simulate the influence of RBCs on blood flow dynamics by different assumptions. In large-scale simulations (above the millimeter range), continuum-based methods are wildly used due to their lower computational demands. 

(43) Eulerian multiphase flow simulations offer the solution of a set of conservation equations for each separate phase and couple the phases through common pressure and interphase exchange coefficients. Xu et al. 

(44) utilized the combined finite-discrete element method (FDEM) to replicate the dynamic behavior and distortion of RBCs subjected to fluidic forces, utilizing the Johnson–Kendall–Roberts model 

(45) to define the adhesive forces of cell-to-cell interactions. The iterative direct-forcing immersed boundary method (IBM) is commonly employed in simulations of the fluid–cell interface of blood. This method effectively captures the intricacies of the thin and flexible RBC membranes within various external flow fields. 

(46) The study by Xu et al. 

(44) also adopts this approach to bridge the fluid dynamics and RBC deformation through IBM. Yoon and You utilized the Maxwell model to define the viscosity of the RBC membrane. 

(47) It was discovered that the Maxwell model could represent the stress relaxation and unloading processes of the cell. Furthermore, the reduced flexibility of an RBC under particular situations such as infection is specified, which was unattainable by the Kelvin–Voigt model 

(48) when compared to the Maxwell model in the literature. The Yeoh hyperplastic material model was also adapted to predict the nonlinear elasticity property of RBCs with FEM employed to discretize the RBC membrane using shell-type elements. Gracka et al. 

(49) developed a numerical CFD model with a finite-volume parallel solver for multiphase blood flow simulation, where an updated Maxwell viscoelasticity model and a Discrete Phase Model are adopted. In the study, the adapted IBM, based on unstructured grids, simulates the flow behavior and shape change of the RBCs through fluid-structure coupling. It was found that the hybrid Euler–Lagrange (E–L) approach 

(50) for the development of the multiphase model offered better results in the simulated CFL region in the microchannels.To study the dynamics of individual behaviors of RBCs and the consequent non-Newtonian blood flow, cell-shape-resolved computational models are often adapted. The use of the boundary integral method has become prevalent in minimizing computational expenses, particularly in the exclusive determination of fluid velocity on the surfaces of RBCs, incorporating the option of employing IBM or particle-based techniques. The cell-shaped-resolved method has enabled an examination of cell to cell interactions within complex ambient or pulsatile flow conditions 

(51) surrounding RBC membranes. Recently, Rydquist et al. 

(52) have looked to integrate statistical information from macroscale simulations to obtain a comprehensive overview of RBC behavior within the immediate proximity of the flow through introduction of respective models characterizing membrane shape definition, tension, bending stresses of RBC membranes.At a macroscopic scale, continuum models have conventionally been adapted for assessing blood flow dynamics through the application of elasticity theory and fluid dynamics. However, particle-based methods are known for their simplicity and adaptability in modeling complex multiscale fluid structures. Meshless methods, such as the boundary element method (BEM), smoothed particle hydrodynamics (SPH), and dissipative particle dynamics (DPD), are often used in particle-based characterization of RBCs and the surrounding fluid. By representing the fluid as discrete particles, meshless methods provide insights into the status and movement of the multiphase fluid. These methods allow for the investigation of cellular structures and microscopic interactions that affect blood rheology. Non-confronting mesh methods like IBM can also be used to couple a fluid solver such as FEM, FVM, or the Lattice Boltzmann Method (LBM) through membrane representation of RBCs. In comparison to conventional CFD methods, LBM has been viewed as a favorable numerical approach for solving the N–S equations and the simulation of multiphase flows. LBM exhibits the notable advantage of being amenable to high-performance parallel computing environments due to its inherently local dynamics. In contrast to DPD and SPH where RBC membranes are modeled as physically interconnected particles, LBM employs the IBM to account for the deformation dynamics of RBCs 

(53,54) under shear flows in complex channel geometries. 

(54,55) However, it is essential to acknowledge that the utilization of LBM in simulating RBC flows often entails a significant computational overhead, being a primary challenge in this context. Krüger et al. 

(56) proposed utilizing LBM as a fluid solver, IBM to couple the fluid and FEM to compute the response of membranes to deformation under immersed fluids. This approach decouples the fluid and membranes but necessitates significant computational effort due to the requirements of both meshes and particles.Despite the accuracy of current blood flow models, simulating complex conditions remains challenging because of the high computational load and cost. Balachandran Nair et al. 

(57) suggested a reduced order model of RBC under the framework of DEM, where the RBC is represented by overlapping constituent rigid spheres. The Morse potential force is adapted to account for the RBC aggregation exhibited by cell to cell interactions among RBCs at different distances. Based upon the IBM, the reduced-order RBC model is adapted to simulate blood flow transport for validation under both single and multiple RBCs with a resolved CFD-DEM solver. 

(58) In the resolved CFD-DEM model, particle sizes are larger than the grid size for a more accurate computation of the surrounding flow field. A continuous forcing approach is taken to describe the momentum source of the governing equation prior to discretization, which is different from a Direct Forcing Method (DFM). 

(59) As no body-conforming moving mesh is required, the continuous forcing approach offers lower complexity and reduced cost when compared to the DFM. Piquet et al. 

(60) highlighted the high complexity of the DFM due to its reliance on calculating an additional immersed boundary flux for the velocity field to ensure its divergence-free condition.The fluid–structure interaction (FSI) method has been advocated to connect the dynamic interplay of RBC membranes and fluid plasma within blood flow such as the coupling of continuum–particle interactions. However, such methodology is generally adapted for anatomical configurations such as arteries 

(61,62) and capillaries, 

(63) where both the structural components and the fluid domain undergo substantial deformation due to the moving boundaries. Due to the scope of the Review being blood flow simulation within microchannels of LOC devices without deformable boundaries, the Review of the FSI method will not be further carried out.In general, three numerical methods are broadly used: mesh-based, particle-based, and hybrid mesh–particle techniques, based on the spatial scale and the fundamental numerical approach, mesh-based methods tend to neglect the effects of individual particles, assuming a continuum and being efficient in terms of time and cost. However, the particle-based approach highlights more of the microscopic and mesoscopic level, where the influence of individual RBCs is considered. A review from Freund et al. 

(64) addressed the three numerical methodologies and their respective modeling approaches of RBC dynamics. Given the complex mechanics and the diverse levels of study concerning numerical simulations of blood and cellular flow, a broad spectrum of numerical methods for blood has been subjected to extensive review. 

(64−70) Ye at al. 

(65) offered an extensive review of the application of the DPD, SPH, and LBM for numerical simulations of RBC, while Rathnayaka et al. 

(67) conducted a review of the particle-based numerical modeling for liquid marbles through drawing parallels to the transport of RBCs in microchannels. A comparative analysis between conventional CFD methods and particle-based approaches for cellular and blood flow dynamic simulation can be found under the review by Arabghahestani et al. 

(66) Literature by Li et al. 

(68) and Beris et al. 

(69) offer an overview of both continuum-based models at micro/macroscales and multiscale particle-based models encompassing various length and temporal dimensions. Furthermore, these reviews deliberate upon the potential of coupling continuum-particle methods for blood plasma and RBC modeling. Arciero et al. 

(70) investigated various modeling approaches encompassing cellular interactions, such as cell to cell or plasma interactions and the individual cellular phases. A concise overview of the reviews is provided in Table 2 for reference.

Table 2. List of Reviews for Numerical Approaches Employed in Blood Flow Simulation

ReferenceNumerical methods
Li et al. (2013) (68)Continuum-based modeling (BIM), particle-based modeling (LBM, LB-FE, SPH, DPD)
Freund (2014) (64)RBC dynamic modeling (continuum-based modeling, complementary discrete microstructure modeling), blood flow dynamic modeling (FDM, IBM, LBM, particle-mesh methods, coupled boundary integral and mesh-based methods, DPD)
Ye et al. (2016) (65)DPD, SPH, LBM, coupled IBM-Smoothed DPD
Arciero et al. (2017) (70)LBM, IBM, DPD, conventional CFD Methods (FDM, FVM, FEM)
Arabghahestani et al. (2019) (66)Particle-based methods (LBM, DPD, direct simulation Monte Carlo, molecular dynamics), SPH, conventional CFD methods (FDM, FVM, FEM)
Beris et al. (2021) (69)DPD, smoothed DPD, IBM, LBM, BIM
Rathnayaka (2022) (67)SPH, CG, LBM

3. Capillary Driven Blood Flow in LOC Systems

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3.1. Capillary Driven Flow Phenomena

Capillary driven (CD) flow is a pivotal mechanism in passive microfluidic flow systems 

(9) such as the blood circulation system and LOC systems. 

(71) CD flow is essentially the movement of a liquid to flow against drag forces, where the capillary effect exerts a force on the liquid at the borders, causing a liquid–air meniscus to flow despite gravity or other drag forces. A capillary pressure drops across the liquid–air interface with surface tension in the capillary radius and contact angle. The capillary effect depends heavily on the interaction between the different properties of surface materials. Different values of contact angles can be manipulated and obtained under varying levels of surface wettability treatments to manipulate the surface properties, resulting in different CD blood delivery rates for medical diagnostic device microchannels. CD flow techniques are appealing for many LOC devices, because they require no external energy. However, due to the passive property of liquid propulsion by capillary forces and the long-term instability of surface treatments on channel walls, the adaptability of CD flow in geometrically complex LOC devices may be limited.

3.2. Theoretical and Numerical Modeling of Capillary Driven Blood Flow

3.2.1. Theoretical Basis and Assumptions of Microfluidic Flow

The study of transport phenomena regarding either blood flow driven by capillary forces or externally applied forces under microfluid systems all demands a comprehensive recognition of the significant differences in flow dynamics between microscale and macroscale. The fundamental assumptions and principles behind fluid transport at the microscale are discussed in this section. Such a comprehension will lay the groundwork for the following analysis of the theoretical basis of capillary forces and their role in blood transport in LOC systems.

At the macroscale, fluid dynamics are often strongly influenced by gravity due to considerable fluid mass. However, the high surface to volume ratio at the microscale shifts the balance toward surface forces (e.g., surface tension and viscous forces), much larger than the inertial force. This difference gives rise to transport phenomena unique to microscale fluid transport, such as the prevalence of laminar flow due to a very low Reynolds number (generally lower than 1). Moreover, the fluid in a microfluidic system is often assumed to be incompressible due to the small flow velocity, indicating constant fluid density in both space and time.Microfluidic flow behaviors are governed by the fundamental principles of mass and momentum conservation, which are encapsulated in the continuity equation and the Navier–Stokes (N–S) equation. The continuity equation describes the conservation of mass, while the N–S equation captures the spatial and temporal variations in velocity, pressure, and other physical parameters. Under the assumption of the negligible influence of gravity in microfluidic systems, the continuity equation and the Eulerian representation of the incompressible N–S equation can be expressed as follows:

∇·𝐮⇀=0∇·�⇀=0

(7)

−∇𝑝+𝜇∇2𝐮⇀+∇·𝝉⇀−𝐅⇀=0−∇�+�∇2�⇀+∇·�⇀−�⇀=0

(8)Here, p is the pressure, u is the fluid viscosity, 

𝝉⇀�⇀ represents the stress tensor, and F is the body force exerted by external forces if present.

3.2.2. Theoretical Basis and Modeling of Capillary Force in LOC Systems

The capillary force is often the major driving force to manipulate and transport blood without an externally applied force in LOC systems. Forces induced by the capillary effect impact the free surface of fluids and are represented not directly in the Navier–Stokes equations but through the pressure boundary conditions of the pressure term p. For hydrophilic surfaces, the liquid generally induces a contact angle between 0° and 30°, encouraging the spread and attraction of fluid under a positive cos θ condition. For this condition, the pressure drop becomes positive and generates a spontaneous flow forward. A hydrophobic solid surface repels the fluid, inducing minimal contact. Generally, hydrophobic solids exhibit a contact angle larger than 90°, inducing a negative value of cos θ. Such a value will result in a negative pressure drop and a flow in the opposite direction. The induced contact angle is often utilized to measure the wall exposure of various surface treatments on channel walls where different wettability gradients and surface tension effects for CD flows are established. Contact angles between different interfaces are obtainable through standard values or experimental methods for reference. 

(72)For the characterization of the induced force by the capillary effect, the Young–Laplace (Y–L) equation 

(73) is widely employed. In the equation, the capillary is considered a pressure boundary condition between the two interphases. Through the Y–L equation, the capillary pressure force can be determined, and subsequently, the continuity and momentum balance equations can be solved to obtain the blood filling rate. Kim et al. 

(74) studied the effects of concentration and exposure time of a nonionic surfactant, Silwet L-77, on the performance of a polydimethylsiloxane (PDMS) microchannel in terms of plasma and blood self-separation. The study characterized the capillary pressure force by incorporating the Y–L equation and further evaluated the effects of the changing contact angle due to different levels of applied channel wall surface treatments. The expression of the Y–L equation utilized by Kim et al. 

(74) is as follows:

𝑃=−𝜎(cos𝜃b+cos𝜃tℎ+cos𝜃l+cos𝜃r𝑤)�=−�(cos⁡�b+cos⁡�tℎ+cos⁡�l+cos⁡�r�)

(9)where σ is the surface tension of the liquid and θ

bθ

tθ

l, and θ

r are the contact angle values between the liquid and the bottom, top, left, and right walls, respectively. A numerical simulation through Coventor software is performed to evaluate the dynamic changes in the filling rate within the microchannel. The simulation results for the blood filling rate in the microchannel are expressed at a specific time stamp, shown in Figure 2. The results portray an increasing instantaneous filling rate of blood in the microchannel following the decrease in contact angle induced by a higher concentration of the nonionic surfactant treated to the microchannel wall.

Figure 2. Numerical simulation of filling rate of capillary driven blood flow under various contact angle conditions at a specific timestamp. (74) Reproduced with permission from ref (74). Copyright 2010 Elsevier.

When in contact with hydrophilic or hydrophobic surfaces, blood forms a meniscus with a contact angle due to surface tension. The Lucas–Washburn (L–W) equation 

(75) is one of the pioneering theoretical definitions for the position of the meniscus over time. In addition, the L–W equation provides the possibility for research to obtain the velocity of the blood formed meniscus through the derivation of the meniscus position. The L–W equation 

(75) can be shown below:

𝐿(𝑡)=𝑅𝜎cos(𝜃)𝑡2𝜇⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√�(�)=��⁡cos(�)�2�

(10)Here L(t) represents the distance of the liquid driven by the capillary forces. However, the generalized L–W equation solely assumes the constant physical properties from a Newtonian fluid rather than considering the non-Newtonian fluid behavior of blood. Cito et al. 

(76) constructed an enhanced version of the L–W equation incorporating the power law to consider the RBC aggregation and the FL effect. The non-Newtonian fluid apparent viscosity under the Power Law model is defined as

𝜇=𝑘·(𝛾˙)𝑛−1�=�·(�˙)�−1

(11)where γ̇ is the strain rate tensor defined as 

𝛾˙=12𝛾˙𝑖𝑗𝛾˙𝑗𝑖⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√�˙=12�˙���˙��. The stress tensor term τ is computed as τ = μγ̇

ij. The updated L–W equation by Cito 

(76) is expressed as

𝐿(𝑡)=𝑅[(𝑛+13𝑛+1)(𝜎cos(𝜃)𝑅𝑘)1/𝑛𝑡]𝑛/𝑛+1�(�)=�[(�+13�+1)(�⁡cos(�)��)1/��]�/�+1

(12)where k is the flow consistency index and n is the power law index, respectively. The power law index, from the Power Law model, characterizes the extent of the non-Newtonian behavior of blood. Both the consistency and power law index rely on blood properties such as hematocrit, the appearance of the FL effect, the formation of RBC aggregates, etc. The updated L–W equation computes the location and velocity of blood flow caused by capillary forces at specified time points within the LOC devices, taking into account the effects of blood flow characteristics such as RBC aggregation and the FL effect on dynamic blood viscosity.Apart from the blood flow behaviors triggered by inherent blood properties, unique flow conditions driven by capillary forces that are portrayed under different microchannel geometries also hold crucial implications for CD blood delivery. Berthier et al. 

(77) studied the spontaneous Concus–Finn condition, the condition to initiate the spontaneous capillary flow within a V-groove microchannel, as shown in Figure 3(a) both experimentally and numerically. Through experimental studies, the spontaneous Concus–Finn filament development of capillary driven blood flow is observed, as shown in Figure 3(b), while the dynamic development of blood flow is numerically simulated through CFD simulation.

Figure 3. (a) Sketch of the cross-section of Berthier’s V-groove microchannel, (b) experimental view of blood in the V-groove microchannel, (78) (c) illustration of the dynamic change of the extension of filament from FLOW 3D under capillary flow at three increasing time intervals. (78) Reproduced with permission from ref (78). Copyright 2014 Elsevier.

Berthier et al. 

(77) characterized the contact angle needed for the initiation of the capillary driving force at a zero-inlet pressure, through the half-angle (α) of the V-groove geometry layout, and its relation to the Concus–Finn filament as shown below:

𝜃<𝜋2−𝛼sin𝛼1+2(ℎ2/𝑤)sin𝛼<cos𝜃{�<�2−�sin⁡�1+2(ℎ2/�)⁡sin⁡�<cos⁡�

(13)Three possible regimes were concluded based on the contact angle value for the initiation of flow and development of Concus–Finn filament:

𝜃>𝜃1𝜃1>𝜃>𝜃0𝜃0no SCFSCF without a Concus−Finn filamentSCF without a Concus−Finn filament{�>�1no SCF�1>�>�0SCF without a Concus−Finn filament�0SCF without a Concus−Finn filament

(14)Under Newton’s Law, the force balance with low Reynolds and Capillary numbers results in the neglect of inertial terms. The force balance between the capillary forces and the viscous force induced by the channel wall is proposed to derive the analytical fluid velocity. This relation between the two forces offers insights into the average flow velocity and the penetration distance function dependent on time. The apparent blood viscosity is defined by Berthier et al. 

(78) through Casson’s law, 

(23) given in eq 1. The research used the FLOW-3D program from Flow Science Inc. software, which solves transient, free-surface problems using the FDM in multiple dimensions. The Volume of Fluid (VOF) method 

(79) is utilized to locate and track the dynamic extension of filament throughout the advancing interface within the channel ahead of the main flow at three progressing time stamps, as depicted in Figure 3(c).

4. Electro-osmotic Flow (EOF) in LOC Systems

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The utilization of external forces, such as electric fields, has significantly broadened the possibility of manipulating microfluidic flow in LOC systems. 

(80) Externally applied electric field forces induce a fluid flow from the movement of ions in fluid terms as the “electro-osmotic flow” (EOF).Unique transport phenomena, such as enhanced flow velocity and flow instability, induced by non-Newtonian fluids, particularly viscoelastic fluids, under EOF, have sparked considerable interest in microfluidic devices with simple or complicated geometries within channels. 

(81) However, compared to the study of Newtonian fluids and even other electro-osmotic viscoelastic fluid flows, the literature focusing on the theoretical and numerical modeling of electro-osmotic blood flow is limited due to the complexity of blood properties. Consequently, to obtain a more comprehensive understanding of the complex blood flow behavior under EOF, theoretical and numerical studies of the transport phenomena in the EOF section will be based on the studies of different viscoelastic fluids under EOF rather than that of blood specifically. Despite this limitation, we believe these studies offer valuable insights that can help understand the complex behavior of blood flow under EOF.

4.1. EOF Phenomena

Electro-osmotic flow occurs at the interface between the microchannel wall and bulk phase solution. When in contact with the bulk phase, solution ions are absorbed or dissociated at the solid–liquid interface, resulting in the formation of a charge layer, as shown in Figure 4. This charged channel surface wall interacts with both negative and positive ions in the bulk sample, causing repulsion and attraction forces to create a thin layer of immobilized counterions, known as the Stern layer. The induced electric potential from the wall gradually decreases with an increase in the distance from the wall. The Stern layer potential, commonly termed the zeta potential, controls the intensity of the electrostatic interactions between mobile counterions and, consequently, the drag force from the applied electric field. Next to the Stern layer is the diffuse mobile layer, mainly composed of a mobile counterion. These two layers constitute the “electrical double layer” (EDL), the thickness of which is directly proportional to the ionic strength (concentration) of the bulk fluid. The relationship between the two parameters is characterized by a Debye length (λ

D), expressed as

𝜆𝐷=𝜖𝑘B𝑇2(𝑍𝑒)2𝑐0⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√��=��B�2(��)2�0

(15)where ϵ is the permittivity of the electrolyte solution, k

B is the Boltzmann constant, T is the electron temperature, Z is the integer valence number, e is the elementary charge, and c

0 is the ionic density.

Figure 4. Schematic diagram of an electro-osmotic flow in a microchannel with negative surface charge. (82) Reproduced with permission from ref (82). Copyright 2012 Woodhead Publishing.

When an electric field is applied perpendicular to the EDL, viscous drag is generated due to the movement of excess ions in the EDL. Electro-osmotic forces can be attributed to the externally applied electric potential (ϕ) and the zeta potential, the system wall induced potential by charged walls (ψ). As illustrated in Figure 4, the majority of ions in the bulk phase have a uniform velocity profile, except for a shear rate condition confined within an extremely thin Stern layer. Therefore, EOF displays a unique characteristic of a “near flat” or plug flow velocity profile, different from the parabolic flow typically induced by pressure-driven microfluidic flow (Hagen–Poiseuille flow). The plug-shaped velocity profile of the EOF possesses a high shear rate above the Stern layer.Overall, the EOF velocity magnitude is typically proportional to the Debye Length (λ

D), zeta potential, and magnitude of the externally applied electric field, while a more viscous liquid reduces the EOF velocity.

4.2. Modeling on Electro-osmotic Viscoelastic Fluid Flow

4.2.1. Theoretical Basis of EOF Mechanisms

The EOF of an incompressible viscoelastic fluid is commonly governed by the continuity and incompressible N–S equations, as shown in eqs 7 and 8, where the stress tensor and the electrostatic force term are coupled. The electro-osmotic body force term F, representing the body force exerted by the externally applied electric force, is defined as 

𝐹⇀=𝑝𝐸𝐸⇀�⇀=���⇀, where ρ

E and 

𝐸⇀�⇀ are the net electric charge density and the applied external electric field, respectively.Numerous models are established to theoretically study the externally applied electric potential and the system wall induced potential by charged walls. The following Laplace equation, expressed as eq 16, is generally adapted and solved to calculate the externally applied potential (ϕ).

∇2𝜙=0∇2�=0

(16)Ion diffusion under applied electric fields, together with mass transport resulting from convection and diffusion, transports ionic solutions in bulk flow under electrokinetic processes. The Nernst–Planck equation can describe these transport methods, including convection, diffusion, and electro-diffusion. Therefore, the Nernst–Planck equation is used to determine the distribution of the ions within the electrolyte. The electric potential induced by the charged channel walls follows the Poisson–Nernst–Plank (PNP) equation, which can be written as eq 17.

∇·[𝐷𝑖∇𝑛𝑖−𝑢⇀𝑛𝑖+𝑛𝑖𝐷𝑖𝑧𝑖𝑒𝑘𝑏𝑇∇(𝜙+𝜓)]=0∇·[��∇��−�⇀��+����������∇(�+�)]=0

(17)where D

in

i, and z

i are the diffusion coefficient, ionic concentration, and ionic valence of the ionic species I, respectively. However, due to the high nonlinearity and numerical stiffness introduced by different lengths and time scales from the PNP equations, the Poisson–Boltzmann (PB) model is often considered the major simplified method of the PNP equation to characterize the potential distribution of the EDL region in microchannels. In the PB model, it is assumed that the ionic species in the fluid follow the Boltzmann distribution. This model is typically valid for steady-state problems where charge transport can be considered negligible, the EDLs do not overlap with each other, and the intrinsic potentials are low. It provides a simplified representation of the potential distribution in the EDL region. The PB equation governing the EDL electric potential distribution is described as

∇2𝜓=(2𝑒𝑧𝑛0𝜀𝜀0)sinh(𝑧𝑒𝜓𝑘b𝑇)∇2�=(2���0��0)⁡sinh(����b�)

(18)where n

0 is the ion bulk concentration, z is the ionic valence, and ε

0 is the electric permittivity in the vacuum. Under low electric potential conditions, an even further simplified model to illustrate the EOF phenomena is the Debye–Hückel (DH) model. The DH model is derived by obtaining a charge density term by expanding the exponential term of the Boltzmann equation in a Taylor series.

4.2.2. EOF Modeling for Viscoelastic Fluids

Many studies through numerical modeling were performed to obtain a deeper understanding of the effect exhibited by externally applied electric fields on viscoelastic flow in microchannels under various geometrical designs. Bello et al. 

(83) found that methylcellulose solution, a non-Newtonian polymer solution, resulted in stronger electro-osmotic mobility in experiments when compared to the predictions by the Helmholtz–Smoluchowski equation, which is commonly used to define the velocity of EOF of a Newtonian fluid. Being one of the pioneers to identify the discrepancies between the EOF of Newtonian and non-Newtonian fluids, Bello et al. attributed such discrepancies to the presence of a very high shear rate in the EDL, resulting in a change in the orientation of the polymer molecules. Park and Lee 

(84) utilized the FVM to solve the PB equation for the characterization of the electric field induced force. In the study, the concept of fractional calculus for the Oldroyd-B model was adapted to illustrate the elastic and memory effects of viscoelastic fluids in a straight microchannel They observed that fluid elasticity and increased ratio of viscoelastic fluid contribution to overall fluid viscosity had a significant impact on the volumetric flow rate and sensitivity of velocity to electric field strength compared to Newtonian fluids. Afonso et al. 

(85) derived an analytical expression for EOF of viscoelastic fluid between parallel plates using the DH model to account for a zeta potential condition below 25 mV. The study established the understanding of the electro-osmotic viscoelastic fluid flow under low zeta potential conditions. Apart from the electrokinetic forces, pressure forces can also be coupled with EOF to generate a unique fluid flow behavior within the microchannel. Sousa et al. 

(86) analytically studied the flow of a standard viscoelastic solution by combining the pressure gradient force with an externally applied electric force. It was found that, at a near wall skimming layer and the outer layer away from the wall, macromolecules migrating away from surface walls in viscoelastic fluids are observed. In the study, the Phan-Thien Tanner (PTT) constitutive model is utilized to characterize the viscoelastic properties of the solution. The approach is found to be valid when the EDL is much thinner than the skimming layer under an enhanced flow rate. Zhao and Yang 

(87) solved the PB equation and Carreau model for the characterization of the EOF mechanism and non-Newtonian fluid respectively through the FEM. The numerical results depict that, different from the EOF of Newtonian fluids, non-Newtonian fluids led to an increase of electro-osmotic mobility for shear thinning fluids but the opposite for shear thickening fluids.Like other fluid transport driving forces, EOF within unique geometrical layouts also portrays unique transport phenomena. Pimenta and Alves 

(88) utilized the FVM to perform numerical simulations of the EOF of viscoelastic fluids considering the PB equation and the Oldroyd-B model, in a cross-slot and flow-focusing microdevices. It was found that electroelastic instabilities are formed due to the development of large stresses inside the EDL with streamlined curvature at geometry corners. Bezerra et al. 

(89) used the FDM to numerically analyze the vortex formation and flow instability from an electro-osmotic non-Newtonian fluid flow in a microchannel with a nozzle geometry and parallel wall geometry setting. The PNP equation is utilized to characterize the charge motion in the EOF and the PTT model for non-Newtonian flow characterization. A constriction geometry is commonly utilized in blood flow adapted in LOC systems due to the change in blood flow behavior under narrow dimensions in a microchannel. Ji et al. 

(90) recently studied the EOF of viscoelastic fluid in a constriction microchannel connected by two relatively big reservoirs on both ends (as seen in Figure 5) filled with the polyacrylamide polymer solution, a viscoelastic fluid, and an incompressible monovalent binary electrolyte solution KCl.

Figure 5. Schematic diagram of a negatively charged constriction microchannel connected to two reservoirs at both ends. An electro-osmotic flow is induced in the system by the induced potential difference between the anode and cathode. (90) Reproduced with permission from ref (90). Copyright 2021 The Authors, under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

In studying the EOF of viscoelastic fluids, the Oldroyd-B model is often utilized to characterize the polymeric stress tensor and the deformation rate of the fluid. The Oldroyd-B model is expressed as follows:

𝜏=𝜂p𝜆(𝐜−𝐈)�=�p�(�−�)

(19)where η

p, λ, c, and I represent the polymer dynamic viscosity, polymer relaxation time, symmetric conformation tensor of the polymer molecules, and the identity matrix, respectively.A log-conformation tensor approach is taken to prevent convergence difficulty induced by the viscoelastic properties. The conformation tensor (c) in the polymeric stress tensor term is redefined by a new tensor (Θ) based on the natural logarithm of the c. The new tensor is defined as

Θ=ln(𝐜)=𝐑ln(𝚲)𝐑Θ=ln(�)=�⁡ln(�)�

(20)in which Λ is the diagonal matrix and R is the orthogonal matrix.Under the new conformation tensor, the induced EOF of a viscoelastic fluid is governed by the continuity and N–S equations adapting the Oldroyd-B model, which is expressed as

∂𝚯∂𝑡+𝐮·∇𝚯=𝛀Θ−ΘΩ+2𝐁+1𝜆(eΘ−𝐈)∂�∂�+�·∇�=�Θ−ΘΩ+2�+1�(eΘ−�)

(21)where Ω and B represent the anti-symmetric matrix and the symmetric traceless matrix of the decomposition of the velocity gradient tensor ∇u, respectively. The conformation tensor can be recovered by c = exp(Θ). The PB model and Laplace equation are utilized to characterize the charged channel wall induced potential and the externally applied potential.The governing equations are numerically solved through the FVM by RheoTool, 

(42) an open-source viscoelastic EOF solver on the OpenFOAM platform. A SIMPLEC (Semi-Implicit Method for Pressure Linked Equations-Consistent) algorithm was applied to solve the velocity-pressure coupling. The pressure field and velocity field were computed by the PCG (Preconditioned Conjugate Gradient) solver and the PBiCG (Preconditioned Biconjugate Gradient) solver, respectively.Ranging magnitudes of an applied electric field or fluid concentration induce both different streamlines and velocity magnitudes at various locations and times of the microchannel. In the study performed by Ji et al., 

(90) notable fluctuation of streamlines and vortex formation is formed at the upper stream entrance of the constriction as shown in Figure 6(a) and (b), respectively, due to the increase of electrokinetic effect, which is seen as a result of the increase in polymeric stress (τ

xx). 

(90) The contraction geometry enhances the EOF velocity within the constriction channel under high E

app condition (600 V/cm). Such phenomena can be attributed to the dependence of electro-osmotic viscoelastic fluid flow on the system wall surface and bulk fluid properties. 

(91)

Figure 6. Schematic diagram of vortex formation and streamlines of EOF depicting flow instability at (a) 1.71 s and (b) 1.75 s. Spatial distribution of the elastic normal stress at (c) high Eapp condition. Streamline of an electro-osmotic flow under Eapp of 600 V/cm (90) for (d) non-Newtonian and (e) Newtonian fluid through a constriction geometry. Reproduced with permission from ref (90). Copyright 2021 The Authors, under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

As elastic normal stress exceeds the local shear stress, flow instability and vortex formation occur. The induced elastic stress under EOF not only enhances the instability of the flow but often generates an irregular secondary flow leading to strong disturbance. 

(92) It is also vital to consider the effect of the constriction layout of microchannels on the alteration of the field strength within the system. The contraction geometry enhances a larger electric field strength compared with other locations of the channel outside the constriction region, resulting in a higher velocity gradient and stronger extension on the polymer within the viscoelastic solution. Following the high shear flow condition, a higher magnitude of stretch for polymer molecules in viscoelastic fluids exhibits larger elastic stresses and enhancement of vortex formation at the region. 

(93)As shown in Figure 6(c), significant elastic normal stress occurs at the inlet of the constriction microchannel. Such occurrence of a polymeric flow can be attributed to the dominating elongational flow, giving rise to high deformation of the polymers within the viscoelastic fluid flow, resulting in higher elastic stress from the polymers. Such phenomena at the entrance result in the difference in velocity streamline as circled in Figure 6(d) compared to that of the Newtonian fluid at the constriction entrance in Figure 6(e). 

(90) The difference between the Newtonian and polymer solution at the exit, as circled in Figure 6(d) and (e), can be attributed to the extrudate swell effect of polymers 

(94) within the viscoelastic fluid flow. The extrudate swell effect illustrates that, as polymers emerge from the constriction exit, they tend to contract in the flow direction and grow in the normal direction, resulting in an extrudate diameter greater than the channel size. The deformation of polymers within the polymeric flow at both the entrance and exit of the contraction channel facilitates the change in shear stress conditions of the flow, leading to the alteration in streamlines of flows for each region.

4.3. EOF Applications in LOC Systems

4.3.1. Mixing in LOC Systems

Rather than relying on the micromixing controlled by molecular diffusion under low Reynolds number conditions, active mixers actively leverage convective instability and vortex formation induced by electro-osmotic flows from alternating current (AC) or direct current (DC) electric fields. Such adaptation is recognized as significant breakthroughs for promotion of fluid mixing in chemical and biological applications such as drug delivery, medical diagnostics, chemical synthesis, and so on. 

(95)Many researchers proposed novel designs of electro-osmosis micromixers coupled with numerical simulations in conjunction with experimental findings to increase their understanding of the role of flow instability and vortex formation in the mixing process under electrokinetic phenomena. Matsubara and Narumi 

(96) numerically modeled the mixing process in a microchannel with four electrodes on each side of the microchannel wall, which generated a disruption through unstable electro-osmotic vortices. It was found that particle mixing was sensitive to both the convection effect induced by the main and secondary vortex within the micromixer and the change in oscillation frequency caused by the supplied AC voltage when the Reynolds number was varied. Qaderi et al. 

(97) adapted the PNP equation to numerically study the effect of the geometry and zeta potential configuration of the microchannel on the mixing process with a combined electro-osmotic pressure driven flow. It was reported that the application of heterogeneous zeta potential configuration enhances the mixing efficiency by around 23% while the height of the hurdles increases the mixing efficiency at most 48.1%. Cho et al. 

(98) utilized the PB model and Laplace equation to numerically simulate the electro-osmotic non-Newtonian fluid mixing process within a wavy and block layout of microchannel walls. The Power Law model is adapted to describe the fluid rheological characteristic. It was found that shear-thinning fluids possess a higher volumetric flow rate, which could result in poorer mixing efficiency compared to that of Newtonian fluids. Numerous studies have revealed that flow instability and vortex generation, in particular secondary vortices produced by barriers or greater magnitudes of heterogeneous zeta potential distribution, enhance mixing by increasing bulk flow velocity and reducing flow distance.To better understand the mechanism of disturbance formed in the system due to externally applied forces, known as electrokinetic instability, literature often utilize the Rayleigh (Ra) number, 

(1) as described below:

𝑅𝑎𝑣=𝑢ev𝑢eo=(𝛾−1𝛾+1)2𝑊𝛿2𝐸el2𝐻2𝜁𝛿Ra�=�ev�eo=(�−1�+1)2��2�el2�2��

(22)where γ is the conductivity ratio of the two streams and can be written as 

𝛾=𝜎el,H𝜎el,L�=�el,H�el,L. The Ra number characterizes the ratio between electroviscous and electro-osmotic flow. A high Ra

v value often results in good mixing. It is evident that fluid properties such as the conductivity (σ) of the two streams play a key role in the formation of disturbances to enhance mixing in microsystems. At the same time, electrokinetic parameters like the zeta potential (ζ) in the Ra number is critical in the characterization of electro-osmotic velocity and a slip boundary condition at the microchannel wall.To understand the mixing result along the channel, the concentration field can be defined and simulated under the assumption of steady state conditions and constant diffusion coefficient for each of the working fluid within the system through the convection–diffusion equation as below:

∂𝑐𝒊∂𝑡+∇⇀(𝑐𝑖𝑢⇀−𝐷𝑖∇⇀𝑐𝒊)=0∂��∂�+∇⇀(���⇀−��∇⇀��)=0

(23)where c

i is the species concentration of species i and D

i is the diffusion coefficient of the corresponding species.The standard deviation of concentration (σ

sd) can be adapted to evaluate the mixing quality of the system. 

(97) The standard deviation for concentration at a specific portion of the channel may be calculated using the equation below:

𝜎sd=∫10(𝐶∗(𝑦∗)−𝐶m)2d𝑦∗∫10d𝑦∗⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯�sd=∫01(�*(�*)−�m)2d�*∫01d�*

(24)where C*(y*) and C

m are the non-dimensional concentration profile and the mean concentration at the portion, respectively. C* is the non-dimensional concentration and can be calculated as 

𝐶∗=𝐶𝐶ref�*=��ref, where C

ref is the reference concentration defined as the bulk solution concentration. The mean concentration profile can be calculated as 

𝐶m=∫10(𝐶∗(𝑦∗)d𝑦∗∫10d𝑦∗�m=∫01(�*(�*)d�*∫01d�*. With the standard deviation of concentration, the mixing efficiency 

(97) can then be calculated as below:

𝜀𝑥=1−𝜎sd𝜎sd,0��=1−�sd�sd,0

(25)where σ

sd,0 is the standard derivation of the case of no mixing. The value of the mixing efficiency is typically utilized in conjunction with the simulated flow field and concentration field to explore the effect of geometrical and electrokinetic parameters on the optimization of the mixing results.

5. Summary

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5.1. Conclusion

Viscoelastic fluids such as blood flow in LOC systems are an essential topic to proceed with diagnostic analysis and research through microdevices in the biomedical and pharmaceutical industries. The complex blood flow behavior is tightly controlled by the viscoelastic characteristics of blood such as the dynamic viscosity and the elastic property of RBCs under various shear rate conditions. Furthermore, the flow behaviors under varied driving forces promote an array of microfluidic transport phenomena that are critical to the management of blood flow and other adapted viscoelastic fluids in LOC systems. This review addressed the blood flow phenomena, the complicated interplay between shear rate and blood flow behaviors, and their numerical modeling under LOC systems through the lens of the viscoelasticity characteristic. Furthermore, a theoretical understanding of capillary forces and externally applied electric forces leads to an in-depth investigation of the relationship between blood flow patterns and the key parameters of the two driving forces, the latter of which is introduced through the lens of viscoelastic fluids, coupling numerical modeling to improve the knowledge of blood flow manipulation in LOC systems. The flow disturbances triggered by the EOF of viscoelastic fluids and their impact on blood flow patterns have been deeply investigated due to their important role and applications in LOC devices. Continuous advancements of various numerical modeling methods with experimental findings through more efficient and less computationally heavy methods have served as an encouraging sign of establishing more accurate illustrations of the mechanisms for multiphase blood and other viscoelastic fluid flow transport phenomena driven by various forces. Such progress is fundamental for the manipulation of unique transport phenomena, such as the generated disturbances, to optimize functionalities offered by microdevices in LOC systems.

The following section will provide further insights into the employment of studied blood transport phenomena to improve the functionality of micro devices adapting LOC technology. A discussion of the novel roles that external driving forces play in microfluidic flow behaviors is also provided. Limitations in the computational modeling of blood flow and electrokinetic phenomena in LOC systems will also be emphasized, which may provide valuable insights for future research endeavors. These discussions aim to provide guidance and opportunities for new paths in the ongoing development of LOC devices that adapt blood flow.

5.2. Future Directions

5.2.1. Electro-osmosis Mixing in LOC Systems

Despite substantial research, mixing results through flow instability and vortex formation phenomena induced by electro-osmotic mixing still deviate from the effective mixing results offered by chaotic mixing results such as those seen in turbulent flows. However, recent discoveries of a mixing phenomenon that is generally observed under turbulent flows are found within electro-osmosis micromixers under low Reynolds number conditions. Zhao 

(99) experimentally discovered a rapid mixing process in an AC applied micromixer, where the power spectrum of concentration under an applied voltage of 20 V

p-p induces a −5/3 slope within a frequency range. This value of the slope is considered as the O–C spectrum in macroflows, which is often visible under relatively high Re conditions, such as the Taylor microscale Reynolds number Re > 500 in turbulent flows. 

(100) However, the Re value in the studied system is less than 1 at the specific location and applied voltage. A secondary flow is also suggested to occur close to microchannel walls, being attributed to the increase of convective instability within the system.Despite the experimental phenomenon proposed by Zhao et al., 

(99) the range of effects induced by vital parameters of an EOF mixing system on the enhanced mixing results and mechanisms of disturbance generated by the turbulent-like flow instability is not further characterized. Such a gap in knowledge may hinder the adaptability and commercialization of the discovery of micromixers. One of the parameters for further evaluation is the conductivity gradient of the fluid flow. A relatively strong conductivity gradient (5000:1) was adopted in the system due to the conductive properties of the two fluids. The high conductivity gradients may contribute to the relatively large Rayleigh number and differences in EDL layer thickness, resulting in an unusual disturbance in laminar flow conditions and enhanced mixing results. However, high conductivity gradients are not always achievable by the working fluids due to diverse fluid properties. The reliance on turbulent-like phenomena and rapid mixing results in a large conductivity gradient should be established to prevent the limited application of fluids for the mixing system. In addition, the proposed system utilizes distinct zeta potential distributions at the top and bottom walls due to their difference in material choices, which may be attributed to the flow instability phenomena. Further studies should be made on varying zeta potential magnitude and distribution to evaluate their effect on the slip boundary conditions of the flow and the large shear rate condition close to the channel wall of EOF. Such a study can potentially offer an optimized condition in zeta potential magnitude through material choices and geometrical layout of the zeta potential for better mixing results and manipulation of mixing fluid dynamics. The two vital parameters mentioned above can be varied with the aid of numerical simulation to understand the effect of parameters on the interaction between electro-osmotic forces and electroviscous forces. At the same time, the relationship of developed streamlines of the simulated velocity and concentration field, following their relationship with the mixing results, under the impact of these key parameters can foster more insight into the range of impact that the two parameters have on the proposed phenomena and the microfluidic dynamic principles of disturbances.

In addition, many of the current investigations of electrokinetic mixers commonly emphasize the fluid dynamics of mixing for Newtonian fluids, while the utilization of biofluids, primarily viscoelastic fluids such as blood, and their distinctive response under shear forces in these novel mixing processes of LOC systems are significantly less studied. To develop more compatible microdevice designs and efficient mixing outcomes for the biomedical industry, it is necessary to fill the knowledge gaps in the literature on electro-osmotic mixing for biofluids, where properties of elasticity, dynamic viscosity, and intricate relationship with shear flow from the fluid are further considered.

5.2.2. Electro-osmosis Separation in LOC Systems

Particle separation in LOC devices, particularly in biological research and diagnostics, is another area where disturbances may play a significant role in optimization. 

(101) Plasma analysis in LOC systems under precise control of blood flow phenomena and blood/plasma separation procedures can detect vital information about infectious diseases from particular antibodies and foreign nucleic acids for medical treatments, diagnostics, and research, 

(102) offering more efficient results and simple operating procedures compared to that of the traditional centrifugation method for blood and plasma separation. However, the adaptability of LOC devices for blood and plasma separation is often hindered by microchannel clogging, where flow velocity and plasma yield from LOC devices is reduced due to occasional RBC migration and aggregation at the filtration entrance of microdevices. 

(103)It is important to note that the EOF induces flow instability close to microchannel walls, which may provide further solutions to clogging for the separation process of the LOC systems. Mohammadi et al. 

(104) offered an anti-clogging effect of RBCs at the blood and plasma separating device filtration entry, adjacent to the surface wall, through RBC disaggregation under high shear rate conditions generated by a forward and reverse EOF direction.

Further theoretical and numerical research can be conducted to characterize the effect of high shear rate conditions near microchannel walls toward the detachment of binding blood cells on surfaces and the reversibility of aggregation. Through numerical modeling with varying electrokinetic parameters to induce different degrees of disturbances or shear conditions at channel walls, it may be possible to optimize and better understand the process of disrupting the forces that bind cells to surface walls and aggregated cells at filtration pores. RBCs that migrate close to microchannel walls are often attracted by the adhesion force between the RBC and the solid surface originating from the van der Waals forces. Following RBC migration and attachment by adhesive forces adjacent to the microchannel walls as shown in Figure 7, the increase in viscosity at the region causes a lower shear condition and encourages RBC aggregation (cell–cell interaction), which clogs filtering pores or microchannels and reduces flow velocity at filtration region. Both the impact that shear forces and disturbances may induce on cell binding forces with surface walls and other cells leading to aggregation may suggest further characterization. Kinetic parameters such as activation energy and the rate-determining step for cell binding composition attachment and detachment should be considered for modeling the dynamics of RBCs and blood flows under external forces in LOC separation devices.

Figure 7. Schematic representations of clogging at a microchannel pore following the sequence of RBC migration, cell attachment to channel walls, and aggregation. (105) Reproduced with permission from ref (105). Copyright 2018 The Authors under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

5.2.3. Relationship between External Forces and Microfluidic Systems

In blood flow, a thicker CFL suggests a lower blood viscosity, suggesting a complex relationship between shear stress and shear rate, affecting the blood viscosity and blood flow. Despite some experimental and numerical studies on electro-osmotic non-Newtonian fluid flow, limited literature has performed an in-depth investigation of the role that applied electric forces and other external forces could play in the process of CFL formation. Additional studies on how shear rates from external forces affect CFL formation and microfluidic flow dynamics can shed light on the mechanism of the contribution induced by external driving forces to the development of a separate phase of layer, similar to CFL, close to the microchannel walls and distinct from the surrounding fluid within the system, then influencing microfluidic flow dynamics.One of the mechanisms of phenomena to be explored is the formation of the Exclusion Zone (EZ) region following a “Self-Induced Flow” (SIF) phenomenon discovered by Li and Pollack, 

(106) as shown in Figure 8(a) and (b), respectively. A spontaneous sustained axial flow is observed when hydrophilic materials are immersed in water, resulting in the buildup of a negative layer of charges, defined as the EZ, after water molecules absorb infrared radiation (IR) energy and break down into H and OH

+.

Figure 8. Schematic representations of (a) the Exclusion Zone region and (b) the Self Induced Flow through visualization of microsphere movement within a microchannel. (106) Reproduced with permission from ref (106). Copyright 2020 The Authors under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

Despite the finding of such a phenomenon, the specific mechanism and role of IR energy have yet to be defined for the process of EZ development. To further develop an understanding of the role of IR energy in such phenomena, a feasible study may be seen through the lens of the relationships between external forces and microfluidic flow. In the phenomena, the increase of SIF velocity under a rise of IR radiation resonant characteristics is shown in the participation of the external electric field near the microchannel walls under electro-osmotic viscoelastic fluid flow systems. The buildup of negative charges at the hydrophilic surfaces in EZ is analogous to the mechanism of electrical double layer formation. Indeed, research has initiated the exploration of the core mechanisms for EZ formation through the lens of the electrokinetic phenomena. 

(107) Such a similarity of the role of IR energy and the transport phenomena of SIF with electrokinetic phenomena paves the way for the definition of the unknown SIF phenomena and EZ formation. Furthermore, Li and Pollack 

(106) suggest whether CFL formation might contribute to a SIF of blood using solely IR radiation, a commonly available source of energy in nature, as an external driving force. The proposition may be proven feasible with the presence of the CFL region next to the negatively charged hydrophilic endothelial glycocalyx layer, coating the luminal side of blood vessels. 

(108) Further research can dive into the resonating characteristics between the formation of the CFL region next to the hydrophilic endothelial glycocalyx layer and that of the EZ formation close to hydrophilic microchannel walls. Indeed, an increase in IR energy is known to rapidly accelerate EZ formation and SIF velocity, depicting similarity to the increase in the magnitude of electric field forces and greater shear rates at microchannel walls affecting CFL formation and EOF velocity. Such correlation depicts a future direction in whether SIF blood flow can be observed and characterized theoretically further through the lens of the relationship between blood flow and shear forces exhibited by external energy.

The intricate link between the CFL and external forces, more specifically the externally applied electric field, can receive further attention to provide a more complete framework for the mechanisms between IR radiation and EZ formation. Such characterization may also contribute to a greater comprehension of the role IR can play in CFL formation next to the endothelial glycocalyx layer as well as its role as a driving force to propel blood flow, similar to the SIF, but without the commonly assumed pressure force from heart contraction as a source of driving force.

5.3. Challenges

Although there have been significant improvements in blood flow modeling under LOC systems over the past decade, there are still notable constraints that may require special attention for numerical simulation applications to benefit the adaptability of the designs and functionalities of LOC devices. Several points that require special attention are mentioned below:

1.The majority of CFD models operate under the relationship between the viscoelasticity of blood and the shear rate conditions of flow. The relative effect exhibited by the presence of highly populated RBCs in whole blood and their forces amongst the cells themselves under complex flows often remains unclearly defined. Furthermore, the full range of cell populations in whole blood requires a much more computational load for numerical modeling. Therefore, a vital goal for future research is to evaluate a reduced modeling method where the impact of cell–cell interaction on the viscoelastic property of blood is considered.
2.Current computational methods on hemodynamics rely on continuum models based upon non-Newtonian rheology at the macroscale rather than at molecular and cellular levels. Careful considerations should be made for the development of a constructive framework for the physical and temporal scales of micro/nanoscale systems to evaluate the intricate relationship between fluid driving forces, dynamic viscosity, and elasticity.
3.Viscoelastic fluids under the impact of externally applied electric forces often deviate from the assumptions of no-slip boundary conditions due to the unique flow conditions induced by externally applied forces. Furthermore, the mechanism of vortex formation and viscoelastic flow instability at laminar flow conditions should be better defined through the lens of the microfluidic flow phenomenon to optimize the prediction of viscoelastic flow across different geometrical layouts. Mathematical models and numerical methods are needed to better predict such disturbance caused by external forces and the viscoelasticity of fluids at such a small scale.
4.Under practical situations, zeta potential distribution at channel walls frequently deviates from the common assumption of a constant distribution because of manufacturing faults or inherent surface charges prior to the introduction of electrokinetic influence. These discrepancies frequently lead to inconsistent surface potential distribution, such as excess positive ions at relatively more negatively charged walls. Accordingly, unpredicted vortex formation and flow instability may occur. Therefore, careful consideration should be given to these discrepancies and how they could trigger the transport process and unexpected results of a microdevice.

Author Information

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  • Corresponding Authors
    • Zhe Chen – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Email: zaccooky@sjtu.edu.cn
    • Bo Ouyang – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Email: bouy93@sjtu.edu.cn
    • Zheng-Hong Luo – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Orcidhttps://orcid.org/0000-0001-9011-6020; Email: luozh@sjtu.edu.cn
  • Authors
    • Bin-Jie Lai – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Orcidhttps://orcid.org/0009-0002-8133-5381
    • Li-Tao Zhu – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Orcidhttps://orcid.org/0000-0001-6514-8864
  • NotesThe authors declare no competing financial interest.

Acknowledgments

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This work was supported by the National Natural Science Foundation of China (No. 22238005) and the Postdoctoral Research Foundation of China (No. GZC20231576).

Vocabulary

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Microfluidicsthe field of technological and scientific study that investigates fluid flow in channels with dimensions between 1 and 1000 μm
Lab-on-a-Chip Technologythe field of research and technological development aimed at integrating the micro/nanofluidic characteristics to conduct laboratory processes on handheld devices
Computational Fluid Dynamics (CFD)the method utilizing computational abilities to predict physical fluid flow behaviors mathematically through solving the governing equations of corresponding fluid flows
Shear Ratethe rate of change in velocity where one layer of fluid moves past the adjacent layer
Viscoelasticitythe property holding both elasticity and viscosity characteristics relying on the magnitude of applied shear stress and time-dependent strain
Electro-osmosisthe flow of fluid under an applied electric field when charged solid surface is in contact with the bulk fluid
Vortexthe rotating motion of a fluid revolving an axis line

References

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This article references 108 other publications.

  1. 1Neethirajan, S.; Kobayashi, I.; Nakajima, M.; Wu, D.; Nandagopal, S.; Lin, F. Microfluidics for food, agriculture and biosystems industries. Lab Chip 201111 (9), 1574– 1586,  DOI: 10.1039/c0lc00230eViewGoogle Scholar
  2. 2Whitesides, G. M. The origins and the future of microfluidics. Nature 2006442 (7101), 368– 373,  DOI: 10.1038/nature05058ViewGoogle Scholar
  3. 3Burklund, A.; Tadimety, A.; Nie, Y.; Hao, N.; Zhang, J. X. J. Chapter One – Advances in diagnostic microfluidics; Elsevier, 2020; DOI:  DOI: 10.1016/bs.acc.2019.08.001 .ViewGoogle Scholar
  4. 4Abdulbari, H. A. Chapter 12 – Lab-on-a-chip for analysis of blood. In Nanotechnology for Hematology, Blood Transfusion, and Artificial Blood; Denizli, A., Nguyen, T. A., Rajan, M., Alam, M. F., Rahman, K., Eds.; Elsevier, 2022; pp 265– 283.ViewGoogle Scholar
  5. 5Vladisavljević, G. T.; Khalid, N.; Neves, M. A.; Kuroiwa, T.; Nakajima, M.; Uemura, K.; Ichikawa, S.; Kobayashi, I. Industrial lab-on-a-chip: Design, applications and scale-up for drug discovery and delivery. Advanced Drug Delivery Reviews 201365 (11), 1626– 1663,  DOI: 10.1016/j.addr.2013.07.017ViewGoogle Scholar
  6. 6Kersaudy-Kerhoas, M.; Dhariwal, R.; Desmulliez, M. P. Y.; Jouvet, L. Hydrodynamic blood plasma separation in microfluidic channels. Microfluid. Nanofluid. 20108 (1), 105– 114,  DOI: 10.1007/s10404-009-0450-5ViewGoogle Scholar
  7. 7Popel, A. S.; Johnson, P. C. Microcirculation and Hemorheology. Annu. Rev. Fluid Mech. 200537 (1), 43– 69,  DOI: 10.1146/annurev.fluid.37.042604.133933ViewGoogle Scholar
  8. 8Fedosov, D. A.; Peltomäki, M.; Gompper, G. Deformation and dynamics of red blood cells in flow through cylindrical microchannels. Soft Matter 201410 (24), 4258– 4267,  DOI: 10.1039/C4SM00248BViewGoogle Scholar
  9. 9Chakraborty, S. Dynamics of capillary flow of blood into a microfluidic channel. Lab Chip 20055 (4), 421– 430,  DOI: 10.1039/b414566fViewGoogle Scholar
  10. 10Tomaiuolo, G.; Guido, S. Start-up shape dynamics of red blood cells in microcapillary flow. Microvascular Research 201182 (1), 35– 41,  DOI: 10.1016/j.mvr.2011.03.004ViewGoogle Scholar
  11. 11Sherwood, J. M.; Dusting, J.; Kaliviotis, E.; Balabani, S. The effect of red blood cell aggregation on velocity and cell-depleted layer characteristics of blood in a bifurcating microchannel. Biomicrofluidics 20126 (2), 24119,  DOI: 10.1063/1.4717755ViewGoogle Scholar
  12. 12Nader, E.; Skinner, S.; Romana, M.; Fort, R.; Lemonne, N.; Guillot, N.; Gauthier, A.; Antoine-Jonville, S.; Renoux, C.; Hardy-Dessources, M.-D. Blood Rheology: Key Parameters, Impact on Blood Flow, Role in Sickle Cell Disease and Effects of Exercise. Frontiers in Physiology 201910, 01329,  DOI: 10.3389/fphys.2019.01329ViewGoogle Scholar
  13. 13Trejo-Soto, C.; Lázaro, G. R.; Pagonabarraga, I.; Hernández-Machado, A. Microfluidics Approach to the Mechanical Properties of Red Blood Cell Membrane and Their Effect on Blood Rheology. Membranes 202212 (2), 217,  DOI: 10.3390/membranes12020217ViewGoogle Scholar
  14. 14Wagner, C.; Steffen, P.; Svetina, S. Aggregation of red blood cells: From rouleaux to clot formation. Comptes Rendus Physique 201314 (6), 459– 469,  DOI: 10.1016/j.crhy.2013.04.004ViewGoogle Scholar
  15. 15Kim, H.; Zhbanov, A.; Yang, S. Microfluidic Systems for Blood and Blood Cell Characterization. Biosensors 202313 (1), 13,  DOI: 10.3390/bios13010013ViewGoogle Scholar
  16. 16Fåhræus, R.; Lindqvist, T. THE VISCOSITY OF THE BLOOD IN NARROW CAPILLARY TUBES. American Journal of Physiology-Legacy Content 193196 (3), 562– 568,  DOI: 10.1152/ajplegacy.1931.96.3.562ViewGoogle Scholar
  17. 17Ascolese, M.; Farina, A.; Fasano, A. The Fåhræus-Lindqvist effect in small blood vessels: how does it help the heart?. J. Biol. Phys. 201945 (4), 379– 394,  DOI: 10.1007/s10867-019-09534-4ViewGoogle Scholar
  18. 18Bento, D.; Fernandes, C. S.; Miranda, J. M.; Lima, R. In vitro blood flow visualizations and cell-free layer (CFL) measurements in a microchannel network. Experimental Thermal and Fluid Science 2019109, 109847,  DOI: 10.1016/j.expthermflusci.2019.109847ViewGoogle Scholar
  19. 19Namgung, B.; Ong, P. K.; Wong, Y. H.; Lim, D.; Chun, K. J.; Kim, S. A comparative study of histogram-based thresholding methods for the determination of cell-free layer width in small blood vessels. Physiological Measurement 201031 (9), N61,  DOI: 10.1088/0967-3334/31/9/N01ViewGoogle Scholar
  20. 20Hymel, S. J.; Lan, H.; Fujioka, H.; Khismatullin, D. B. Cell trapping in Y-junction microchannels: A numerical study of the bifurcation angle effect in inertial microfluidics. Phys. Fluids (1994) 201931 (8), 082003,  DOI: 10.1063/1.5113516ViewGoogle Scholar
  21. 21Li, X.; Popel, A. S.; Karniadakis, G. E. Blood-plasma separation in Y-shaped bifurcating microfluidic channels: a dissipative particle dynamics simulation study. Phys. Biol. 20129 (2), 026010,  DOI: 10.1088/1478-3975/9/2/026010ViewGoogle Scholar
  22. 22Yin, X.; Thomas, T.; Zhang, J. Multiple red blood cell flows through microvascular bifurcations: Cell free layer, cell trajectory, and hematocrit separation. Microvascular Research 201389, 47– 56,  DOI: 10.1016/j.mvr.2013.05.002ViewGoogle Scholar
  23. 23Shibeshi, S. S.; Collins, W. E. The Rheology of Blood Flow in a Branched Arterial System. Appl. Rheol 200515 (6), 398– 405,  DOI: 10.1515/arh-2005-0020ViewGoogle Scholar
  24. 24Sequeira, A.; Janela, J. An Overview of Some Mathematical Models of Blood Rheology. In A Portrait of State-of-the-Art Research at the Technical University of Lisbon; Pereira, M. S., Ed.; Springer Netherlands: Dordrecht, 2007; pp 65– 87.ViewGoogle Scholar
  25. 25Walburn, F. J.; Schneck, D. J. A constitutive equation for whole human blood. Biorheology 197613, 201– 210,  DOI: 10.3233/BIR-1976-13307ViewGoogle Scholar
  26. 26Quemada, D. A rheological model for studying the hematocrit dependence of red cell-red cell and red cell-protein interactions in blood. Biorheology 198118, 501– 516,  DOI: 10.3233/BIR-1981-183-615ViewGoogle Scholar
  27. 27Varchanis, S.; Dimakopoulos, Y.; Wagner, C.; Tsamopoulos, J. How viscoelastic is human blood plasma?. Soft Matter 201814 (21), 4238– 4251,  DOI: 10.1039/C8SM00061AViewGoogle Scholar
  28. 28Apostolidis, A. J.; Moyer, A. P.; Beris, A. N. Non-Newtonian effects in simulations of coronary arterial blood flow. J. Non-Newtonian Fluid Mech. 2016233, 155– 165,  DOI: 10.1016/j.jnnfm.2016.03.008ViewGoogle Scholar
  29. 29Luo, X. Y.; Kuang, Z. B. A study on the constitutive equation of blood. J. Biomech. 199225 (8), 929– 934,  DOI: 10.1016/0021-9290(92)90233-QViewGoogle Scholar
  30. 30Oldroyd, J. G.; Wilson, A. H. On the formulation of rheological equations of state. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1950200 (1063), 523– 541,  DOI: 10.1098/rspa.1950.0035ViewGoogle Scholar
  31. 31Prado, G.; Farutin, A.; Misbah, C.; Bureau, L. Viscoelastic transient of confined red blood cells. Biophys J. 2015108 (9), 2126– 2136,  DOI: 10.1016/j.bpj.2015.03.046ViewGoogle Scholar
  32. 32Huang, C. R.; Pan, W. D.; Chen, H. Q.; Copley, A. L. Thixotropic properties of whole blood from healthy human subjects. Biorheology 198724 (6), 795– 801,  DOI: 10.3233/BIR-1987-24630ViewGoogle Scholar
  33. 33Anand, M.; Kwack, J.; Masud, A. A new generalized Oldroyd-B model for blood flow in complex geometries. International Journal of Engineering Science 201372, 78– 88,  DOI: 10.1016/j.ijengsci.2013.06.009ViewGoogle Scholar
  34. 34Horner, J. S.; Armstrong, M. J.; Wagner, N. J.; Beris, A. N. Investigation of blood rheology under steady and unidirectional large amplitude oscillatory shear. J. Rheol. 201862 (2), 577– 591,  DOI: 10.1122/1.5017623ViewGoogle Scholar
  35. 35Horner, J. S.; Armstrong, M. J.; Wagner, N. J.; Beris, A. N. Measurements of human blood viscoelasticity and thixotropy under steady and transient shear and constitutive modeling thereof. J. Rheol. 201963 (5), 799– 813,  DOI: 10.1122/1.5108737ViewGoogle Scholar
  36. 36Armstrong, M.; Tussing, J. A methodology for adding thixotropy to Oldroyd-8 family of viscoelastic models for characterization of human blood. Phys. Fluids 202032 (9), 094111,  DOI: 10.1063/5.0022501ViewGoogle Scholar
  37. 37Crank, J.; Nicolson, P. A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type. Mathematical Proceedings of the Cambridge Philosophical Society 194743 (1), 50– 67,  DOI: 10.1017/S0305004100023197ViewGoogle Scholar
  38. 38Clough, R. W. Original formulation of the finite element method. Finite Elements in Analysis and Design 19907 (2), 89– 101,  DOI: 10.1016/0168-874X(90)90001-UViewGoogle Scholar
  39. 39Liu, W. K.; Liu, Y.; Farrell, D.; Zhang, L.; Wang, X. S.; Fukui, Y.; Patankar, N.; Zhang, Y.; Bajaj, C.; Lee, J.Immersed finite element method and its applications to biological systems. Computer Methods in Applied Mechanics and Engineering 2006195 (13), 1722– 1749,  DOI: 10.1016/j.cma.2005.05.049ViewGoogle Scholar
  40. 40Lopes, D.; Agujetas, R.; Puga, H.; Teixeira, J.; Lima, R.; Alejo, J. P.; Ferrera, C. Analysis of finite element and finite volume methods for fluid-structure interaction simulation of blood flow in a real stenosed artery. International Journal of Mechanical Sciences 2021207, 106650,  DOI: 10.1016/j.ijmecsci.2021.106650ViewGoogle Scholar
  41. 41Favero, J. L.; Secchi, A. R.; Cardozo, N. S. M.; Jasak, H. Viscoelastic flow analysis using the software OpenFOAM and differential constitutive equations. J. Non-Newtonian Fluid Mech. 2010165 (23), 1625– 1636,  DOI: 10.1016/j.jnnfm.2010.08.010ViewGoogle Scholar
  42. 42Pimenta, F.; Alves, M. A. Stabilization of an open-source finite-volume solver for viscoelastic fluid flows. J. Non-Newtonian Fluid Mech. 2017239, 85– 104,  DOI: 10.1016/j.jnnfm.2016.12.002ViewGoogle Scholar
  43. 43Chee, C. Y.; Lee, H. P.; Lu, C. Using 3D fluid-structure interaction model to analyse the biomechanical properties of erythrocyte. Phys. Lett. A 2008372 (9), 1357– 1362,  DOI: 10.1016/j.physleta.2007.09.067ViewGoogle Scholar
  44. 44Xu, D.; Kaliviotis, E.; Munjiza, A.; Avital, E.; Ji, C.; Williams, J. Large scale simulation of red blood cell aggregation in shear flows. J. Biomech. 201346 (11), 1810– 1817,  DOI: 10.1016/j.jbiomech.2013.05.010ViewGoogle Scholar
  45. 45Johnson, K. L.; Kendall, K.; Roberts, A. Surface energy and the contact of elastic solids. Proceedings of the royal society of London. A. mathematical and physical sciences 1971324 (1558), 301– 313,  DOI: 10.1098/rspa.1971.0141ViewGoogle Scholar
  46. 46Shi, L.; Pan, T.-W.; Glowinski, R. Deformation of a single red blood cell in bounded Poiseuille flows. Phys. Rev. E 201285 (1), 016307,  DOI: 10.1103/PhysRevE.85.016307ViewGoogle Scholar
  47. 47Yoon, D.; You, D. Continuum modeling of deformation and aggregation of red blood cells. J. Biomech. 201649 (11), 2267– 2279,  DOI: 10.1016/j.jbiomech.2015.11.027ViewGoogle Scholar
  48. 48Mainardi, F.; Spada, G. Creep, relaxation and viscosity properties for basic fractional models in rheology. European Physical Journal Special Topics 2011193 (1), 133– 160,  DOI: 10.1140/epjst/e2011-01387-1ViewGoogle Scholar
  49. 49Gracka, M.; Lima, R.; Miranda, J. M.; Student, S.; Melka, B.; Ostrowski, Z. Red blood cells tracking and cell-free layer formation in a microchannel with hyperbolic contraction: A CFD model validation. Computer Methods and Programs in Biomedicine 2022226, 107117,  DOI: 10.1016/j.cmpb.2022.107117ViewGoogle Scholar
  50. 50Aryan, H.; Beigzadeh, B.; Siavashi, M. Euler-Lagrange numerical simulation of improved magnetic drug delivery in a three-dimensional CT-based carotid artery bifurcation. Computer Methods and Programs in Biomedicine 2022219, 106778,  DOI: 10.1016/j.cmpb.2022.106778ViewGoogle Scholar
  51. 51Czaja, B.; Závodszky, G.; Azizi Tarksalooyeh, V.; Hoekstra, A. G. Cell-resolved blood flow simulations of saccular aneurysms: effects of pulsatility and aspect ratio. J. R Soc. Interface 201815 (146), 20180485,  DOI: 10.1098/rsif.2018.0485ViewGoogle Scholar
  52. 52Rydquist, G.; Esmaily, M. A cell-resolved, Lagrangian solver for modeling red blood cell dynamics in macroscale flows. J. Comput. Phys. 2022461, 111204,  DOI: 10.1016/j.jcp.2022.111204ViewGoogle Scholar
  53. 53Dadvand, A.; Baghalnezhad, M.; Mirzaee, I.; Khoo, B. C.; Ghoreishi, S. An immersed boundary-lattice Boltzmann approach to study the dynamics of elastic membranes in viscous shear flows. Journal of Computational Science 20145 (5), 709– 718,  DOI: 10.1016/j.jocs.2014.06.006ViewGoogle Scholar
  54. 54Krüger, T.; Holmes, D.; Coveney, P. V. Deformability-based red blood cell separation in deterministic lateral displacement devices─A simulation study. Biomicrofluidics 20148 (5), 054114,  DOI: 10.1063/1.4897913ViewGoogle Scholar
  55. 55Takeishi, N.; Ito, H.; Kaneko, M.; Wada, S. Deformation of a Red Blood Cell in a Narrow Rectangular Microchannel. Micromachines 201910 (3), 199,  DOI: 10.3390/mi10030199ViewGoogle Scholar
  56. 56Krüger, T.; Varnik, F.; Raabe, D. Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method. Computers & Mathematics with Applications 201161 (12), 3485– 3505,  DOI: 10.1016/j.camwa.2010.03.057ViewGoogle Scholar
  57. 57Balachandran Nair, A. N.; Pirker, S.; Umundum, T.; Saeedipour, M. A reduced-order model for deformable particles with application in bio-microfluidics. Computational Particle Mechanics 20207 (3), 593– 601,  DOI: 10.1007/s40571-019-00283-8ViewGoogle Scholar
  58. 58Balachandran Nair, A. N.; Pirker, S.; Saeedipour, M. Resolved CFD-DEM simulation of blood flow with a reduced-order RBC model. Computational Particle Mechanics 20229 (4), 759– 774,  DOI: 10.1007/s40571-021-00441-xViewGoogle Scholar
  59. 59Mittal, R.; Iaccarino, G. IMMERSED BOUNDARY METHODS. Annu. Rev. Fluid Mech. 200537 (1), 239– 261,  DOI: 10.1146/annurev.fluid.37.061903.175743ViewGoogle Scholar
  60. 60Piquet, A.; Roussel, O.; Hadjadj, A. A comparative study of Brinkman penalization and direct-forcing immersed boundary methods for compressible viscous flows. Computers & Fluids 2016136, 272– 284,  DOI: 10.1016/j.compfluid.2016.06.001ViewGoogle Scholar
  61. 61Akerkouch, L.; Le, T. B. A Hybrid Continuum-Particle Approach for Fluid-Structure Interaction Simulation of Red Blood Cells in Fluid Flows. Fluids 20216 (4), 139,  DOI: 10.3390/fluids6040139ViewGoogle Scholar
  62. 62Barker, A. T.; Cai, X.-C. Scalable parallel methods for monolithic coupling in fluid-structure interaction with application to blood flow modeling. J. Comput. Phys. 2010229 (3), 642– 659,  DOI: 10.1016/j.jcp.2009.10.001ViewGoogle Scholar
  63. 63Cetin, A.; Sahin, M. A monolithic fluid-structure interaction framework applied to red blood cells. International Journal for Numerical Methods in Biomedical Engineering 201935 (2), e3171  DOI: 10.1002/cnm.3171ViewGoogle Scholar
  64. 64Freund, J. B. Numerical Simulation of Flowing Blood Cells. Annu. Rev. Fluid Mech. 201446 (1), 67– 95,  DOI: 10.1146/annurev-fluid-010313-141349ViewGoogle Scholar
  65. 65Ye, T.; Phan-Thien, N.; Lim, C. T. Particle-based simulations of red blood cells─A review. J. Biomech. 201649 (11), 2255– 2266,  DOI: 10.1016/j.jbiomech.2015.11.050ViewGoogle Scholar
  66. 66Arabghahestani, M.; Poozesh, S.; Akafuah, N. K. Advances in Computational Fluid Mechanics in Cellular Flow Manipulation: A Review. Applied Sciences 20199 (19), 4041,  DOI: 10.3390/app9194041ViewGoogle Scholar
  67. 67Rathnayaka, C. M.; From, C. S.; Geekiyanage, N. M.; Gu, Y. T.; Nguyen, N. T.; Sauret, E. Particle-Based Numerical Modelling of Liquid Marbles: Recent Advances and Future Perspectives. Archives of Computational Methods in Engineering 202229 (5), 3021– 3039,  DOI: 10.1007/s11831-021-09683-7ViewGoogle Scholar
  68. 68Li, X.; Vlahovska, P. M.; Karniadakis, G. E. Continuum- and particle-based modeling of shapes and dynamics of red blood cells in health and disease. Soft Matter 20139 (1), 28– 37,  DOI: 10.1039/C2SM26891DViewGoogle Scholar
  69. 69Beris, A. N.; Horner, J. S.; Jariwala, S.; Armstrong, M. J.; Wagner, N. J. Recent advances in blood rheology: a review. Soft Matter 202117 (47), 10591– 10613,  DOI: 10.1039/D1SM01212FViewGoogle Scholar
  70. 70Arciero, J.; Causin, P.; Malgaroli, F. Mathematical methods for modeling the microcirculation. AIMS Biophysics 20174 (3), 362– 399,  DOI: 10.3934/biophy.2017.3.362ViewGoogle Scholar
  71. 71Maria, M. S.; Chandra, T. S.; Sen, A. K. Capillary flow-driven blood plasma separation and on-chip analyte detection in microfluidic devices. Microfluid. Nanofluid. 201721 (4), 72,  DOI: 10.1007/s10404-017-1907-6ViewGoogle Scholar
  72. 72Huhtamäki, T.; Tian, X.; Korhonen, J. T.; Ras, R. H. A. Surface-wetting characterization using contact-angle measurements. Nat. Protoc. 201813 (7), 1521– 1538,  DOI: 10.1038/s41596-018-0003-zViewGoogle Scholar
  73. 73Young, T., III. An essay on the cohesion of fluids. Philosophical Transactions of the Royal Society of London 180595, 65– 87,  DOI: 10.1098/rstl.1805.0005ViewGoogle Scholar
  74. 74Kim, Y. C.; Kim, S.-H.; Kim, D.; Park, S.-J.; Park, J.-K. Plasma extraction in a capillary-driven microfluidic device using surfactant-added poly(dimethylsiloxane). Sens. Actuators, B 2010145 (2), 861– 868,  DOI: 10.1016/j.snb.2010.01.017ViewGoogle Scholar
  75. 75Washburn, E. W. The Dynamics of Capillary Flow. Physical Review 192117 (3), 273– 283,  DOI: 10.1103/PhysRev.17.273ViewGoogle Scholar
  76. 76Cito, S.; Ahn, Y. C.; Pallares, J.; Duarte, R. M.; Chen, Z.; Madou, M.; Katakis, I. Visualization and measurement of capillary-driven blood flow using spectral domain optical coherence tomography. Microfluid Nanofluidics 201213 (2), 227– 237,  DOI: 10.1007/s10404-012-0950-6ViewGoogle Scholar
  77. 77Berthier, E.; Dostie, A. M.; Lee, U. N.; Berthier, J.; Theberge, A. B. Open Microfluidic Capillary Systems. Anal Chem. 201991 (14), 8739– 8750,  DOI: 10.1021/acs.analchem.9b01429ViewGoogle Scholar
  78. 78Berthier, J.; Brakke, K. A.; Furlani, E. P.; Karampelas, I. H.; Poher, V.; Gosselin, D.; Cubizolles, M.; Pouteau, P. Whole blood spontaneous capillary flow in narrow V-groove microchannels. Sens. Actuators, B 2015206, 258– 267,  DOI: 10.1016/j.snb.2014.09.040ViewGoogle Scholar
  79. 79Hirt, C. W.; Nichols, B. D. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 198139 (1), 201– 225,  DOI: 10.1016/0021-9991(81)90145-5ViewGoogle Scholar
  80. 80Chen, J.-L.; Shih, W.-H.; Hsieh, W.-H. AC electro-osmotic micromixer using a face-to-face, asymmetric pair of planar electrodes. Sens. Actuators, B 2013188, 11– 21,  DOI: 10.1016/j.snb.2013.07.012ViewGoogle Scholar
  81. 81Zhao, C.; Yang, C. Electrokinetics of non-Newtonian fluids: A review. Advances in Colloid and Interface Science 2013201-202, 94– 108,  DOI: 10.1016/j.cis.2013.09.001ViewGoogle Scholar
  82. 82Oh, K. W. 6 – Lab-on-chip (LOC) devices and microfluidics for biomedical applications. In MEMS for Biomedical Applications; Bhansali, S., Vasudev, A., Eds.; Woodhead Publishing, 2012; pp 150– 171.ViewGoogle Scholar
  83. 83Bello, M. S.; De Besi, P.; Rezzonico, R.; Righetti, P. G.; Casiraghi, E. Electroosmosis of polymer solutions in fused silica capillaries. ELECTROPHORESIS 199415 (1), 623– 626,  DOI: 10.1002/elps.1150150186ViewGoogle Scholar
  84. 84Park, H. M.; Lee, W. M. Effect of viscoelasticity on the flow pattern and the volumetric flow rate in electroosmotic flows through a microchannel. Lab Chip 20088 (7), 1163– 1170,  DOI: 10.1039/b800185eViewGoogle Scholar
  85. 85Afonso, A. M.; Alves, M. A.; Pinho, F. T. Analytical solution of mixed electro-osmotic/pressure driven flows of viscoelastic fluids in microchannels. J. Non-Newtonian Fluid Mech. 2009159 (1), 50– 63,  DOI: 10.1016/j.jnnfm.2009.01.006ViewGoogle Scholar
  86. 86Sousa, J. J.; Afonso, A. M.; Pinho, F. T.; Alves, M. A. Effect of the skimming layer on electro-osmotic─Poiseuille flows of viscoelastic fluids. Microfluid. Nanofluid. 201110 (1), 107– 122,  DOI: 10.1007/s10404-010-0651-yViewGoogle Scholar
  87. 87Zhao, C.; Yang, C. Electro-osmotic mobility of non-Newtonian fluids. Biomicrofluidics 20115 (1), 014110,  DOI: 10.1063/1.3571278ViewGoogle Scholar
  88. 88Pimenta, F.; Alves, M. A. Electro-elastic instabilities in cross-shaped microchannels. J. Non-Newtonian Fluid Mech. 2018259, 61– 77,  DOI: 10.1016/j.jnnfm.2018.04.004ViewGoogle Scholar
  89. 89Bezerra, W. S.; Castelo, A.; Afonso, A. M. Numerical Study of Electro-Osmotic Fluid Flow and Vortex Formation. Micromachines (Basel) 201910 (12), 796,  DOI: 10.3390/mi10120796ViewGoogle Scholar
  90. 90Ji, J.; Qian, S.; Liu, Z. Electroosmotic Flow of Viscoelastic Fluid through a Constriction Microchannel. Micromachines (Basel) 202112 (4), 417,  DOI: 10.3390/mi12040417ViewGoogle Scholar
  91. 91Zhao, C.; Yang, C. Exact solutions for electro-osmotic flow of viscoelastic fluids in rectangular micro-channels. Applied Mathematics and Computation 2009211 (2), 502– 509,  DOI: 10.1016/j.amc.2009.01.068ViewGoogle Scholar
  92. 92Gerum, R.; Mirzahossein, E.; Eroles, M.; Elsterer, J.; Mainka, A.; Bauer, A.; Sonntag, S.; Winterl, A.; Bartl, J.; Fischer, L. Viscoelastic properties of suspended cells measured with shear flow deformation cytometry. Elife 202211, e78823,  DOI: 10.7554/eLife.78823ViewGoogle Scholar
  93. 93Sadek, S. H.; Pinho, F. T.; Alves, M. A. Electro-elastic flow instabilities of viscoelastic fluids in contraction/expansion micro-geometries. J. Non-Newtonian Fluid Mech. 2020283, 104293,  DOI: 10.1016/j.jnnfm.2020.104293ViewGoogle Scholar
  94. 94Spanjaards, M.; Peters, G.; Hulsen, M.; Anderson, P. Numerical Study of the Effect of Thixotropy on Extrudate Swell. Polymers 202113 (24), 4383,  DOI: 10.3390/polym13244383ViewGoogle Scholar
  95. 95Rashidi, S.; Bafekr, H.; Valipour, M. S.; Esfahani, J. A. A review on the application, simulation, and experiment of the electrokinetic mixers. Chemical Engineering and Processing – Process Intensification 2018126, 108– 122,  DOI: 10.1016/j.cep.2018.02.021ViewGoogle Scholar
  96. 96Matsubara, K.; Narumi, T. Microfluidic mixing using unsteady electroosmotic vortices produced by a staggered array of electrodes. Chemical Engineering Journal 2016288, 638– 647,  DOI: 10.1016/j.cej.2015.12.013ViewGoogle Scholar
  97. 97Qaderi, A.; Jamaati, J.; Bahiraei, M. CFD simulation of combined electroosmotic-pressure driven micro-mixing in a microchannel equipped with triangular hurdle and zeta-potential heterogeneity. Chemical Engineering Science 2019199, 463– 477,  DOI: 10.1016/j.ces.2019.01.034ViewGoogle Scholar
  98. 98Cho, C.-C.; Chen, C.-L.; Chen, C. o.-K. Mixing enhancement in crisscross micromixer using aperiodic electrokinetic perturbing flows. International Journal of Heat and Mass Transfer 201255 (11), 2926– 2933,  DOI: 10.1016/j.ijheatmasstransfer.2012.02.006ViewGoogle Scholar
  99. 99Zhao, W.; Yang, F.; Wang, K.; Bai, J.; Wang, G. Rapid mixing by turbulent-like electrokinetic microflow. Chemical Engineering Science 2017165, 113– 121,  DOI: 10.1016/j.ces.2017.02.027ViewGoogle Scholar
  100. 100Tran, T.; Chakraborty, P.; Guttenberg, N.; Prescott, A.; Kellay, H.; Goldburg, W.; Goldenfeld, N.; Gioia, G. Macroscopic effects of the spectral structure in turbulent flows. Nat. Phys. 20106 (6), 438– 441,  DOI: 10.1038/nphys1674ViewGoogle Scholar
  101. 101Toner, M.; Irimia, D. Blood-on-a-chip. Annu. Rev. Biomed Eng. 20057, 77– 103,  DOI: 10.1146/annurev.bioeng.7.011205.135108ViewGoogle Scholar
  102. 102Maria, M. S.; Rakesh, P. E.; Chandra, T. S.; Sen, A. K. Capillary flow of blood in a microchannel with differential wetting for blood plasma separation and on-chip glucose detection. Biomicrofluidics 201610 (5), 054108,  DOI: 10.1063/1.4962874ViewGoogle Scholar
  103. 103Tripathi, S.; Varun Kumar, Y. V. B.; Prabhakar, A.; Joshi, S. S.; Agrawal, A. Passive blood plasma separation at the microscale: a review of design principles and microdevices. Journal of Micromechanics and Microengineering 201525 (8), 083001,  DOI: 10.1088/0960-1317/25/8/083001ViewGoogle Scholar
  104. 104Mohammadi, M.; Madadi, H.; Casals-Terré, J. Microfluidic point-of-care blood panel based on a novel technique: Reversible electroosmotic flow. Biomicrofluidics 20159 (5), 054106,  DOI: 10.1063/1.4930865ViewGoogle Scholar
  105. 105Kang, D. H.; Kim, K.; Kim, Y. J. An anti-clogging method for improving the performance and lifespan of blood plasma separation devices in real-time and continuous microfluidic systems. Sci. Rep 20188 (1), 17015,  DOI: 10.1038/s41598-018-35235-4ViewGoogle Scholar
  106. 106Li, Z.; Pollack, G. H. Surface-induced flow: A natural microscopic engine using infrared energy as fuel. Science Advances 20206 (19), eaba0941  DOI: 10.1126/sciadv.aba0941ViewGoogle Scholar
  107. 107Mercado-Uribe, H.; Guevara-Pantoja, F. J.; García-Muñoz, W.; García-Maldonado, J. S.; Méndez-Alcaraz, J. M.; Ruiz-Suárez, J. C. On the evolution of the exclusion zone produced by hydrophilic surfaces: A contracted description. J. Chem. Phys. 2021154 (19), 194902,  DOI: 10.1063/5.0043084ViewGoogle Scholar
  108. 108Yalcin, O.; Jani, V. P.; Johnson, P. C.; Cabrales, P. Implications Enzymatic Degradation of the Endothelial Glycocalyx on the Microvascular Hemodynamics and the Arteriolar Red Cell Free Layer of the Rat Cremaster Muscle. Front Physiol 20189, 168,  DOI: 10.3389/fphys.2018.00168ViewGoogle Scholar
The Simulation of Droplet Impact on the Super-Hydrophobic Surface with Micro-Pillar Arrays Fabricated by Laser Irradiation and Silanization Processes

The simulation of droplet impact on the super-hydrophobic surface with micro-pillar arrays fabricated by laser irradiation and silanization processes

레이저 조사 및 silanization 공정으로 제작된 micro-pillar arrays를 사용하여 초 소수성 표면에 대한 액적 영향 시뮬레이션

ZhenyanXiaa YangZhaoa ZhenYangabc ChengjuanYangab LinanLia ShibinWanga MengWangab
aSchool of Mechanical Engineering, Tianjin University, Tianjin, 300054, China
bKey Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin, 300072, Chinac
School of Engineering, University of Warwick, Coventry, CV4 7AL, UK

Received 23 September 2020, Revised 17 November 2020, Accepted 26 November 2020, Available online 11 December 2020.

Abstract

Super-hydrophobicity is one of the significant natural phenomena, which has inspired researchers to fabricate artificial smart materials using advanced manufacturing techniques. In this study, a super-hydrophobic aluminum surface was prepared by nanosecond laser texturing and FAS modification in sequence. The surface wettability turned from original hydrophilicity to super-hydrophilicity immediately after laser treatment. Then it changed to super-hydrophobicity showing a WCA of 157.6 ± 1.2° with a SA of 1.7 ± 0.7° when the laser-induced rough surface being coated with a layer of FAS molecules. The transforming mechanism was further explored from physical and chemical aspects based on the analyses of surface morphology and surface chemistry. Besides, the motion process of droplet impacting super-hydrophobic surface was systematically analyzed via the optimization of simulation calculation grid and the simulation method of volume of fluid (VOF). Based on this simulation method, the morphological changes, the inside pressure distribution and velocity of the droplet were further investigated. And the motion mechanism of the droplet on super-hydrophobic surface was clearly revealed in this paper. The simulation results and the images captured by high-speed camera were highly consistent, which indicated that the computational fluid dynamics (CFD) is an effective method to predict the droplet motion on super- hydrophobic surfaces. This paper can provide an explicit guidance for the selection of suitable methods for functional surfaces with different requirements in the industry.

Korea Abstract

초 소수성은 연구원들이 첨단 제조 기술을 사용하여 인공 스마트 재료를 제작하도록 영감을 준 중요한 자연 현상 중 하나 입니다. 이 연구에서 초 소수성 알루미늄 표면은 나노초 레이저 텍스처링과 FAS 수정에 의해 순서대로 준비되었습니다.

레이저 처리 직후 표면 습윤성은 원래의 친수성에서 초 친수성으로 바뀌 었습니다. 그런 다음 레이저 유도 거친 표면을 FAS 분자 층으로 코팅했을 때 WCA가 157.6 ± 1.2 °이고 SA가 1.7 ± 0.7 ° 인 초 소수성으로 변경되었습니다.

변형 메커니즘은 표면 형태 및 표면 화학 분석을 기반으로 물리적 및 화학적 측면에서 추가로 탐구 되었습니다. 또한, 초 소수성 표면에 영향을 미치는 물방울의 운동 과정은 시뮬레이션 계산 그리드의 최적화와 유체 부피 (VOF) 시뮬레이션 방법을 통해 체계적으로 분석되었습니다.

이 시뮬레이션 방법을 바탕으로 형태학적 변화, 내부 압력 분포 및 액 적의 속도를 추가로 조사했습니다. 그리고 초 소수성 표면에 있는 물방울의 운동 메커니즘이 이 논문에서 분명하게 드러났습니다.

시뮬레이션 결과와 고속 카메라로 캡처한 이미지는 매우 일관적 이었습니다. 이는 전산 유체 역학 (CFD)이 초 소수성 표면에서 액적 움직임을 예측하는 효과적인 방법임을 나타냅니다.

이 백서는 업계의 다양한 요구 사항을 가진 기능 표면에 적합한 방법을 선택하기 위한 명시적인 지침을 제공 할 수 있습니다.

Keywords: Laser irradiation; Wettability; Droplet impact; Simulation; VOF

Introduction

서식지에 적응하기 위해 많은 자연 식물과 동물에서 특별한 습윤 표면이 진화되었습니다 [1-3]. 연잎은 먼지에 의한 오염으로부터 스스로를 보호하기 위해 우수한 자가 청소 특성을 나타냅니다 [4]. 사막 딱정벌레는 공기에서 물을 수확할 수 있는 기능적 표면 때문에 건조한 사막에서 생존 할 수 있습니다 [5].

자연 세계에서 영감을 받아 고체 기질의 표면 습윤성을 수정하는데 더 많은 관심이 집중되었습니다 [6-7]. 기능성 표면의 우수한 성능은 고유 한 표면 습윤성에 기인하며, 이는 고체 표면에서 액체의 확산 능력을 반영하는 중요한 특성 중 하나입니다 [8].

일반적으로 물 접촉각 (WCA) 값에 따라 90 °는 친수성과 소수성의 경계로 간주됩니다. WCA가 90 ° 이상인 소수성 표면, WCA가 90 ° 미만인 친수성 표면 [9 ]. 특히 고체 표면은 WCA가 10 ° 미만의 슬라이딩 각도 (SA)에서 150 °를 초과 할 때 특별한 초 소수성을 나타냅니다 [10-11].

<내용 중략> ……

 The Simulation of Droplet Impact on the Super-Hydrophobic Surface with Micro-Pillar Arrays Fabricated by Laser Irradiation and Silanization Processes
The Simulation of Droplet Impact on the Super-Hydrophobic Surface with Micro-Pillar Arrays Fabricated by Laser Irradiation and Silanization Processes

References

[1] H.W. Chen, P.F. Zhang, L.W. Zhang, Y. Jiang, H.L. Liu, D.Y. Zhang, Z.W. Han, L.
Jiang, Continuous directional water transport on the peristome surface of Nepenthes
alata, Nature 532 (2016) 85-89.
[2] Y. Liu, K.T. Zhang, W.G. Yao, J.A. Liu, Z.W. Han, L.Q. Ren, Bioinspired
structured superhydrophobic and superoleophilic stainless steel mesh for efficient oilwater separation, Colloids Surf., A 500 (2016) 54-63.
[3] Y.X. Liu, W.L. Liu, G.L. Wang, J.C. Hou, H. Kong, W.L. Wang, A facile one-step
approach to superhydrophilic silica film with hierarchical structure using
fluoroalkylsilane, Colloids Surf., A 539 (2018) 109-115.
[4] F.P. Wang, S. Li, L. Wang, Fabrication of artificial super-hydrophobic lotus-leaflike bamboo surfaces through soft lithography, Colloids Surf., A 513 (2017) 389-395.
[5] W. Huang, X.Y. Tang, Z. Qiu, W.X. Zhu, Y.G. Wang, Y.L. Zhu, Z.F. Xiao, H.G.
Wang, D.X. Liang, Jian, L. Y.J Xie, Cellulose-based Superhydrophobic Surface
Decorated with Functional Groups Showing Distinct Wetting Abilities to Manipulate
Water Harvesting, ACS Appl. Mater. Interfaces DOI: 10.1021/acsami.0c12504.
[6] M.Y. Zhang, L.J. Ma, Q. Wang, P. Hao, X. Zheng, Wettability behavior of
nanodroplets on copper surfaces with hierarchical nanostructures, Colloids Surf., A
604 (2020) 125291.
[7] A.F. Pan, W.J. Wang, X.S. Mei, K.D. Wang, X.B. Yang, Rutile TiO2 flocculent
ripples with high antireflectivity and superhydrophobicity on the surface of titanium
under 10 ns laser irradiation without focusing, Langmuir 33 (2017) 9530-9538.
[8] M. Li, X.H. Liu, N. Liu, Z.H. Guo, P.K. Singh, S.Y. Fu, Effect of surface
wettability on the antibacterial activity of nanocellulose-based material with
quaternary ammonium groups, Colloids Surf., A 554 (2018) 122-128.
[9] T.C. Chen, H.T. Liu, H.F. Yang, W. Yan, W. Zhu, H. Liu, Biomimetic fabrication
of robust self-assembly superhydrophobic surfaces with corrosion resistance
properties on stainless steel substrate, RSC Adv. 6 (2016) 43937-43949.
[10] P. Zhang, F.Y. Lv, A review of the recent advances in superhydrophobic surfaces
and the emerging energy-related applications, Energy 82 (2015) 1068-1087.
[11] Z. Yang, X.P. Liu, Y.L. Tian, Novel metal-organic super-hydrophobic surface
fabricated by nanosecond laser irradiation in solution, Colloids Surf., A 587 (2020)
124343.
[12] J.Y. Peng, X.J. Zhao, W.F. Wang, X. Gong, Durable Self-Cleaning Surfaces with
Superhydrophobic and Highly Oleophobic Properties, Langmuir, 35 (2019) 8404-
8412.
[13] Z. Yang, X.P. Liu, Y.L. Tian, A contrastive investigation on anticorrosive
performance of laser-induced super-hydrophobic and oil-infused slippery coatings,
Prog. Org. Coat. 138 (2020) 105313.
[14] J.L. Yong, F. Chen, Q. Yang, J.L. Huo, X. Hou, Superoleophobic Surfaces,
Chem. Soc. Rev. 46 (2017) 4168-4217.
[15] D.W. Li, H.Y. Wang, Y. Liu, D.S. Wei, Z.X. Zhao, Large-Scale Fabrication of
Durable and Robust Super-Hydrophobic Spray Coatings with Excellent Repairable
and Anti-Corrosion Performance, Chem. Eng. J. 367 (2019) 169-179.
[16] R.J. Liao, Z.P. Zuo, C. Guo, Y. Yuan, A.Y. Zhuang, Fabrication of
superhydrophobic surface on aluminum by continuous chemical etching and its antiicing property, Appl. Surf. Sci. 317 (2014) 701-709.
[17] Z. Yang. X.P. Liu, Y.L. Tian, Hybrid laser ablation and chemical modification for
fast fabrication of bio-inspired super-hydrophobic surface with excellent selfcleaning, stability and corrosion resistance, J Bionic Eng 16 (2019) 13-26.
[18] Z. Yang, Y.L. Tian, Y.C. Zhao, C.J. Yang, Study on the fabrication of superhydrophobic surface on Inconel alloy via nanosecond laser ablation, Materials 12
(2019) 278.
[19] Y. Wang, X. Gong, Superhydrophobic Coatings with Periodic Ring Structured
Patterns for Self-Cleaning and Oil-Water Separation, Adv. Mater. Interfaces 4 (2017)
1700190.
[20] N. Chik, W.S.W.M. Zain, A.J. Mohamad, M.Z. Sidek, W.H.W. Ibrahim, A. Reif,
J.H. Rakebrandt, W. Pfleging, X. Liu, Bacterial adhesion on the titanium and
stainless-steel surfaces undergone two different treatment methods: Polishing and ultrafast laser treatment, IOP Conf. Ser.: Mater. Sci. Eng.358 (2018) 012034.
[21] N.K.K. Win, P. Jitareerat, S. Kanlayanarat, S. Sangchote, Effects of cinnamon
extract, chitosan coating, hot water treatment and their combinations on crown rot
disease and quality of banana fruit, Postharvest Biol. Technol. 45 (2007) 333–340.
[22] A. Yarin, Drop impact dynamics: splashing, spreading, receding, bouncing, Annu.
Rev. Fluid Mech. 38 (2006) 159–192.
[23] N. Wang, L.L. Tang, Y.F. Cai, W. Tong, D.S. Xiong, Scalable superhydrophobic
coating with controllable wettability and investigations of its drag reduction, Colloids
Surf. A 555 (2018) 290–295.
[24] R. Fürstner, W. Barthlott, C. Neinhuis, P. Walzel, Wetting and self-cleaning
properties of artificial superhydrophobic surfaces, Langmuir 21 (2005) 956–61.
[25] U. Trdan, M. Hočevar, P. Gregorčič, Transition from superhydrophilic to
superhydrophobic state of laser textured stainless steel surface and its effect on
corrosion resistance, Corros. Sci. 123 (2017) 21–44.
[26] A.L. Biance, C. Clanet, D. Quere, First steps in the spreading of a liquid droplet,
Phys. Rev. E 69 (2004) 016301.
[27] S. Kulju, L. Riegger, P. Koltay et al, Fluid flow simulations meet high-speed
video: computer vision comparison of droplet dynamics, J. Colloid Interface Sci. 522
(2018) 48.
[28] C.J. Yong, B. Bhushan, Dynamic effects of bouncing water droplets on
superhydrophobic surfaces, Langmuir 24.12 (2008) 6262–6269.
[29] G. Karapetsas, N.T. Chamakos, A.G. Papathanasiou, Efficient modelling of
droplet dynamics on complex surfaces, J. Phys.: Condens. Matter 28.8 (2016) 085101.
[30] D. Khojasteh, N.M. Kazerooni, S. Salarian et al, Droplet impact on
superhydrophobic surfaces: a review of recent developments, J. Ind. Eng. Chem. 42
(2016) 1–14.
[31] S.H. Kim, Y. Jiang, H. Kim, Droplet impact and LFP on wettability and
nanostructured surface, Exp. Therm. Fluid Sci. 99 (2018) 85–93.
[32] M. Rudman, Volume‐Tracking Methods for Interfacial Flow Calculations, Int.
J. Numer. Methods Fluids 24.7 (1997) 671-691.

Figure 2.6 ESI apparatus for offline analysis with microscope imaging.

MODELING AND CHARACTERIZATION OF MICROFABRICATED EMITTERS: IN PURSUIT OF IMPROVED ESI-MS PERFORMANCE

미세 가공 방사체의 모델링 및 특성화 : 개선된 ESI-MS 성능 추구

by XINYUN WU

A thesis submitted to the Department of Chemistry in conformity with the requirements for the degree of Master of Science Queen’s University Kingston, Ontario, Canada December, 2011 Copyright © Xinyun Wu, 2011

Abstract

ESI (Electrospray ionization)는 특히 탁월한 감도, 견고성 및 단순성으로 대형 생체 분자를 분석하는 데있어 질량 분석 (MS)에 매우 귀중한 기술이었습니다. ESI 기술 개발에 많은 노력을 기울였습니다. 그 형태와 기하학적 구조가 전기 분무 성능과 추가 MS 감지에 중추적 인 것으로 입증 되었기 때문입니다.

막힘 및 낮은 처리량을 포함하여 전통적인 단일 홀 이미터의 본질적인 문제는 기술의 적용 가능성을 제한합니다. 이 문제를 해결하기 위해 현재 프로젝트는 향상된 ESI-MS 분석을위한 다중 전자 분무(MES) 방출기를 개발하는데 초점을 맞추고 있습니다.

이 논문에서는 스프레이 전류 측정을 위한 전기 분무와 오프라인 전기 분무 실험을 위한 전산 유체 역학 (CFD) 시뮬레이션의 공동 작업이 수행되었습니다. 전기 분무 성능에 대한 다양한 이미터 설계의 영향을 테스트하기 위해 수치 시뮬레이션이 사용되었으며 실험실 결과는 가이드 및 검증으로 사용되었습니다.

CFD 코드는 Taylor-Melcher 누설 유전체 모델(LDM)을 기반으로 하며 과도 전기 분무 공정이 성공적으로 시뮬레이션되었습니다.

이 방법은 750 μm 내경 (i.d.) 이미 터를 통해 먼저 검증되었으며 20 μm i.d.에 추가로 적용되었습니다. 모델. 전기 분무 공정의 여러 단계가 시각적으로 시연되었으며 다양한 적용 전기장 및 유속에서 분무 전류의 변화에 ​​대한 정량적 조사는 이전 시뮬레이션 및 측정과 잘 일치합니다.

단일 조리개 프로토 타입을 기반으로 2 홀 및 3 홀 이미터로 MES 시뮬레이션을 수행했습니다. 시뮬레이션 예측은 실험 결과와 유사하게 비교되었습니다. 이 작업의 증거는 CFD 시뮬레이션이 MES의 이미 터 설계를 테스트하는 효과적인 수치 도구로 사용될 수 있음을 입증했습니다.

이 작업에서 달성 된 마이크로 스케일 에미 터 전기 분무의 성공적인 시뮬레이션에 대한 벤치마킹 결과는 현재까지 발표 된 전기 분무에 대한 동적 시뮬레이션의 가장 작은 규모로 여겨집니다.

Co-Authorship

공동 저자: 이 논문에 대한 모든 연구는 Natalie M. Cann 박사와 Richard D. Oleschuk 박사의 지도하에 완료되었습니다. 다중 전자 분무에 관한 4 장에서 제시된 연구 작업의 일부는 Ramin Wright가 공동 저술했으며, 이 작업은 press에서 다음 논문에서 인용되었습니다.

ibson,G.T.T.; Wright, R.D.; Oleschuk, R.D. Multiple electrosprays generated from a single poly carbonate microstructured fibre. Journal of Mass Spectrometry, 2011, in press.

Chapter 1 Introduction

소프트 이온화 방법으로 ESI (electrospray ionization)의 도입은 질량 분석법 (MS)의 적용 가능성에 혁명을 일으켰습니다. 이 기술의 부드러운 특징은 상대적으로 높은 전하를 가진 이온을 생성하는 고유한 이점으로 인해 액상에서 직접 펩티드 및 단백질과 같은 큰 생체 분자를 분석 할 수 있게했습니다 [1].

지난 10 년 동안 ESI-MS는 놀라운 성장을 보였으며 현재는 단백질 체학, 대사 체학, 글리코 믹스, 합성 화학자를 위한 식별 도구 등 다양한 생화학 분야에서 광범위하게 채택되고 있습니다 [2-3].

ESI-MS는 겔 전기 영동과 같은 생물학적 분자에 대한 기존의 질량 측정 기술보다 훨씬 빠르고 민감하며 정확합니다. 또한, 액체상에서 직접 분석 할 수 있는 큰 비 휘발성 분자의 능력은 고성능 액체 크로마토 그래피 (HPLC) 및 모세관 전기 영동 (CE)과 같은 업스트림 분리 기술과의 결합을 가능하게합니다 [4].

일반적인 ESI 공정은 일반적으로 액적 형성, 액적 수축 및 기상 이온의 최종 형성을 포함합니다. 일렉트로 스프레이의 성능에 영향을 미치는 많은 요소 중에서 스프레이를 위한 이미터의 구조 (즉, 기하학, 모양 등)가 중요한 요소입니다.

전통적인 전기 분무 이미터는 일반적으로 풀링 또는 에칭 기술로 제작 된 단일 채널 테이퍼 형 또는 비 테이퍼 형입니다. 그러나 이러한 이미터는 종종 막힘, 부적절한 처리량 등과 같은 문제로 어려움을 겪습니다. [5]

향상된 감도 및 샘플 활용을 위해 다중 스프레이를 생성하는 새로운 이미터 설계 개발로 분명한 발전이 있었습니다. 새로운 ESI 이미터 설계에 대한 연구는 실험적으로나 이론적으로 큰 관심을 불러 일으켰습니다 [3]. 그러나 ESI의 복잡한 물리적 과정은 팁 형상 외에도 많은 다른 변수에 의존하기 때문에 연구간 직접 비교의 어려움은 장애물이 됩니다.

또한 새로운 나노 이미터 제조 및 테스트 비용이 상당히 높을 수 있습니다. 이 논문은 CFD 시뮬레이션 도구를 활용하여 가상 랩을 설정함으로써 이러한 문제를 해결합니다. 다른 매개 변수로 인해 상호 연결된 변경 없이 다양한 이미터 설계를 비교할 수 있도록 이상적으로 균일한 물리적 조건을 제공합니다.

맞춤 제작된 프로토 타입의 실험 측정 값도 수집되어 더 나은 계산 체계를 형성하는 데 도움이 되는 지침과 검증을 모두 제공합니다. 특히 이 분야의 주요 미래 플랫폼으로 여겨지는 다중 노즐 이미 터 설계에 중점을 둘 것입니다.

전기 분무 거동에 영향을 미치는 요인에 대한 추가 기본 연구는 다양한 기하학적 및 작동 매개 변수와 관련하여 수행됩니다. 이는 보다 효율적이고 견고한 이미터의 개발을 가능하게 할 뿐만 아니라 더 넓은 영역에서 ESI의 적용을 향상시킬 수 있습니다.

Figure 1.1Schematic setup for ESI-MS technique
Figure 1.1Schematic setup for ESI-MS technique
Figure 1.2 Schematic of major processes occurring in electrospray [5].
Figure 1.2 Schematic of major processes occurring in electrospray [5].
Figure 1.3 Illustration of detailed geometric parameters of a spraying Taylor cone wherera is the radius of curvature of the best fitting circle at the tip of the cone; re is the radius of the emission region for droplets at the tip of a Taylor cone;is the liquid cone angle.
Figure 1.3 Illustration of detailed geometric parameters of a spraying Taylor cone wherera is the radius of curvature of the best fitting circle at the tip of the cone; re is the radius of the emission region for droplets at the tip of a Taylor cone;is the liquid cone angle.
Figure 1.4 (A)Externally tapered emitter  (B) Optical image of a clogged tapered emitter with normal use [46].
Figure 1.4 (A)Externally tapered emitter (B) Optical image of a clogged tapered emitter with normal use [46].
Figure 1.5 (A)Three by three configuration of an emitter array made with polycarbonate using laser ablation; (B) Photomicrograph of nine stable electrosprays generated from the nine-emitter array [52]
Figure 1.5 (A)Three by three configuration of an emitter array made with polycarbonate using laser ablation; (B) Photomicrograph of nine stable electrosprays generated from the nine-emitter array [52]
Figure 1.6 SEM images of the distal ends of four multichannel nanoelectrospray emitters and a tapered emitter: (A) 30 orifice emitter; (B) 54 orifice emitter; (C) 84 orifice emitter; (D) 168 orifice emitter; Scale bars in A, B, and C represent 50 μm, and 100 μm in D[54]
Figure 1.6 SEM images of the distal ends of four multichannel nanoelectrospray emitters and a tapered emitter: (A) 30 orifice emitter; (B) 54 orifice emitter; (C) 84 orifice emitter; (D) 168 orifice emitter; Scale bars in A, B, and C represent 50 μm, and 100 μm in D[54]
Figure 1.7 Photomicrographs of electrospray from of a 168-hole MCN emitter at different flow rates. (A) A traditional integrated Taylor cone observed from offline electrospray of water with 0.1% formic acid at 300 nL/min; (B) A mist of coalesced Taylor cones observed from offline electrospray at 25 nL/min[54]
Figure 1.7 Photomicrographs of electrospray from of a 168-hole MCN emitter at different flow rates. (A) A traditional integrated Taylor cone observed from offline electrospray of water with 0.1% formic acid at 300 nL/min; (B) A mist of coalesced Taylor cones observed from offline electrospray at 25 nL/min[54]
Figure 1.8 Circular arrays of etched emitters for better electric field homogeneity [53].
Figure 1.8 Circular arrays of etched emitters for better electric field homogeneity [53].
Figure 2.6 ESI apparatus for offline analysis with microscope imaging.
Figure 2.6 ESI apparatus for offline analysis with microscope imaging.
Figure 3.9 Typical panel for displaying instant simulation result during simulation process.
Figure 3.9 Typical panel for displaying instant simulation result during simulation process.
Figure 5.3 Generation of a Taylor cone-jet mode (simulation) plotted with iso-potential lines at times    (Top to bottom panels correspond to 0.002 s, 0.012 s, 0.018 s, 0.08 s respectively).
Figure 5.3 Generation of a Taylor cone-jet mode (simulation) plotted with iso-potential lines at times (Top to bottom panels correspond to 0.002 s, 0.012 s, 0.018 s, 0.08 s respectively).
Figure 5.8 (A) Taylor cone-jet profiles with different contact angle of 30 degrees and 20 degrees (B) under the same physical conditions of 6 kV and 0.04 m/s. (C) Cone-jet profile generated from a tapered tip with a 20 degree contact angle at 6 kV and 0.04 m/s (as a comparison with (B)).
Figure 5.8 (A) Taylor cone-jet profiles with different contact angle of 30 degrees and 20 degrees (B) under the same physical conditions of 6 kV and 0.04 m/s. (C) Cone-jet profile generated from a tapered tip with a 20 degree contact angle at 6 kV and 0.04 m/s (as a comparison with (B)).

Omit below: Please refer to the original text for the full content.

Bibliography

1. Mclafferty, F.W., Tandem Fourier-Transform Mass-Spectrometry of Large Molecules.Abstracts of Papers of the American Chemical Society, 1986. 192: p. 21-Anyl. 2. Griffiths, W.J. and Y.Q. Wang, Mass spectrometry: from proteomics to metabolomics and lipidomics. Chemical Society Reviews, 2009. 38(7): p. 1882-1896. 3. Gibson, G.T.T., S.M. Mugo, and R.D. Oleschuk, Nanoelectrospray Emitters: Trends and Perspective. Mass Spectrometry Reviews, 2009. 28(6): p. 918-936. 4. Cech, N.B. and C.G. Enke, Practical implications of some recent studies in electrospray ionization fundamentals. Mass Spectrometry Reviews, 2001. 20(6): p. 362-387. 5. Su, S., Development and Application of Non-tapered Electrospray Emitters for Nano-ESI Mass Spectrometry, in Chemistry. 2008, Queen’s University: Kingston. p. 185. 6. Zeleny, J., The electrical discharge from liquid points, and a hydrostatic method of measuring the electric intensity at their surfaces. Physical Review, 1914. 3(2): p. 69-91. 7. Dole, M., L.L. Mack, and R.L. Hines, Molecular Beams of Macroions. Journal of Chemical Physics, 1968. 49(5): p. 2240-&. 8. Yamashita, M. and J.B. Fenn, Negative-Ion Production with the Electrospray Ion-Source.Journal of Physical Chemistry, 1984. 88(20): p. 4671-4675. 9. Kebarle, P. and U.H. Verkerk, Electrospray: From Ions in Solution to Ions in the Gas Phase, What We Know Now. Mass Spectrometry Reviews, 2009. 28(6): p. 898-917. 10. Taylor, G., Disintegration of Water Drops in Electric Field. Proceedings of the Royal Society of London Series a-Mathematical and Physical Sciences, 1964. 280(138): p. 383. 11. Cole, R.B., Some tenets pertaining to electrospray ionization mass spectrometry. Journal of Mass Spectrometry, 2000. 35(7): p. 763-772. 12. Rayleigh, L., On the equilibrium of liquid conducting masses charged with electricity.Philos. Mag., 1882. 14: p. 184-186. 13. Mack, L.L., et al., Molecular Beams of Macroions .2. Journal of Chemical Physics, 1970. 52(10): p. 4977-&. 14. Gamero-Castano, M. and J.F. de la Mora, Kinetics of small ion evaporation from the charge and mass distribution of multiply charged clusters in electrosprays. Journal of Mass Spectrometry, 2000. 35(7): p. 790-803. 15. Gamero-Castano, M. and J.F. de la Mora, Modulations in the abundance of salt clusters in electrosprays. Analytical Chemistry, 2000. 72(7): p. 1426-1429. 16. Loscertales, I.G. and J.F. Delamora, Experiments on the Kinetics of Field Evaporation of Small Ions from Droplets. Journal of Chemical Physics, 1995. 103(12): p. 5041-5060. 17. Rohner, T.C., N. Lion, and H.H. Girault, Electrochemical and theoretical aspects of electrospray ionisation. Physical Chemistry Chemical Physics, 2004. 6(12): p. 3056-3068.

18. Iribarne, J.V. and B.A. Thomson, Evaporation of Small Ions from Charged Droplets.Journal of Chemical Physics, 1976. 64(6): p. 2287-2294. 19. Meng, C.K. and J.B. Fenn, Formation of Charged Clusters during Electrospray Ionization of Organic Solute Species. Organic Mass Spectrometry, 1991. 26(6): p. 542-549. 20. Nohmi, T. and J.B. Fenn, Electrospray Mass-Spectrometry of Poly(Ethylene Glycols) with Molecular-Weights up to 5 Million. Journal of the American Chemical Society, 1992. 114(9): p. 3241-3246. 21. de la Mora, J.F., Electrospray ionization of large multiply charged species proceeds via Dole’s charged residue mechanism. Analytica Chimica Acta, 2000. 406(1): p. 93-104. 22. Iavarone, A.T., J.C. Jurchen, and E.R. Williams, Supercharged protein and peptide lone formed by electrospray ionization. Analytical Chemistry, 2001. 73(7): p. 1455-1460. 23. Hogan, C.J., et al., Charge carrier field emission determines the number of charges on native state proteins in electrospray ionization. Journal of the American Chemical Society, 2008. 130(22): p. 6926-+. 24. Nguyen, S. and J.B. Fenn, Gas-phase ions of solute species from charged droplets of solutions. Proceedings of the National Academy of Sciences of the United States of America, 2007. 104(4): p. 1111-1117. 25. Luedtke, W.D., et al., Nanojets, electrospray, and ion field evaporation: Molecular dynamics simulations and laboratory experiments. Journal of Physical Chemistry A, 2008. 112(40): p. 9628-9649. 26. Enke, C.G., A predictive model for matrix and analyte effects in electrospray ionization of singly-charged ionic analytes. Analytical Chemistry, 1997. 69(23): p. 4885-4893. 27. Maze, J.T., T.C. Jones, and M.F. Jarrold, Negative droplets from positive electrospray.Journal of Physical Chemistry A, 2006. 110(46): p. 12607-12612. 28. Kebarle, P. and M. Peschke, On the mechanisms by which the charged droplets produced by electrospray lead to gas phase ions. Analytica Chimica Acta, 2000. 406(1): p. 11-35. 29. Loeb, L.B., A.F. Kip, and G.G. Hudson, Pulses in negative point-to-plane corona.Physical Review, 1941. 60(10): p. 714-722. 30. Cole, R.B., Electrospray ionization mass spectrometry : fundamentals, instrumentation, and applications. 1997, New York: Wiley. xix, 577 p. 31. Smith, D.P.H., The Electrohydrodynamic Atomization of Liquids. Ieee Transactions on Industry Applications, 1986. 22(3): p. 527-535. 32. Taylor, G.I. and A.D. Mcewan, Stability of a Horizontal Fluid Interface in a Vertical Electric Field. Journal of Fluid Mechanics, 1965. 22: p. 1-&. 33. Ikonomou, M.G., A.T. Blades, and P. Kebarle, Electrospray Mass-Spectrometry of Methanol and Water Solutions Suppression of Electric-Discharge with Sf6 Gas. Journal of the American Society for Mass Spectrometry, 1991. 2(6): p. 497-505.

34. Wampler, F.M., A.T. Blades, and P. Kebarle, Negative-Ion Electrospray Mass-Spectrometry of Nucleotides – Ionization from Water Solution with Sf6 Discharge Suppression. Journal of the American Society for Mass Spectrometry, 1993. 4(4): p. 289-295. 35. Marginean, I., P. Nemes, and A. Vertes, Order-chaos-order transitions in electrosprays: The electrified dripping faucet. Physical Review Letters, 2006. 97(6): p. -. 36. Marginean, I., P. Nemes, and A. Vertes, Astable regime in electrosprays. Physical Review E, 2007. 76(2): p. -. 37. Nemes, P., I. Marginean, and A. Vertes, Spraying mode effect on droplet formation and ion chemistry in electrosprays. Analytical Chemistry, 2007. 79(8): p. 3105-3116. 38. Marginean, I., et al., Electrospray characteristic curves: In pursuit of improved performance in the nanoflow regime. Analytical Chemistry, 2007. 79(21): p. 8030-8036. 39. Page, J.S., et al., Subambient pressure ionization with nanoelectrospray source and interface for improved sensitivity in mass spectrometry. Analytical Chemistry, 2008. 80(5): p. 1800-1805. 40. Delamora, J.F. and I.G. Loscertales, The Current Emitted by Highly Conducting Taylor Cones. Journal of Fluid Mechanics, 1994. 260: p. 155-184. 41. Ganan-Calvo, A.M., On the general scaling theory for electrospraying. Journal of Fluid Mechanics, 2004. 507: p. 203-212. 42. Smith, D.R., G. Sagerman, and T.D. Wood, Design and development of an interchangeable nanomicroelectrospray source for a quadrupole mass spectrometer.Review of Scientific Instruments, 2003. 74(10): p. 4474-4477. 43. Barnidge, D.R., S. Nilsson, and K.E. Markides, A design for low-flow sheathless electrospray emitters. Analytical Chemistry, 1999. 71(19): p. 4115-4118. 44. Guzzetta, A.W., R.A. Thakur, and I.C. Mylchreest, A robust micro-electrospray ionization technique for high-throughput liquid chromatography/mass spectrometry proteomics using a sanded metal needle as an emitter. Rapid Communications in Mass Spectrometry, 2002. 16(21): p. 2067-2072. 45. Wilm, M. and M. Mann, Analytical properties of the nanoelectrospray ion source.Analytical Chemistry, 1996. 68(1): p. 1-8. 46. Covey, T.R. and D. Pinto, Practical Spectroscopy. Vol. 32. 2002. 47. Kelly, R.T., et al., Nanoelectrospray emitter arrays providing interemitter electric field uniformity. Analytical Chemistry, 2008. 80(14): p. 5660-5665. 48. Choi, Y.S. and T.D. Wood, Polyaniline-coated nanoelectrospray emitters treated with hydrophobic polymers at the tip. Rapid Communications in Mass Spectrometry, 2007. 21(13): p. 2101-2108. 49. Tojo, H., Properties of an electrospray emitter coated with material of low surface energy. Journal of Chromatography A, 2004. 1056(1-2): p. 223-228.

50. Liu, J., et al., Electrospray ionization with a pointed carbon fiber emitter. Analytical Chemistry, 2004. 76(13): p. 3599-3606. 51. Sen, A.K., et al., Modeling and characterization of a carbon fiber emitter for electrospray ionization. Journal of Micromechanics and Microengineering, 2006. 16(3): p. 620-630. 52. Tang, K.Q., et al., Generation of multiple electrosprays using microfabricated emitter arrays for improved mass spectrometric sensitivity. Analytical Chemistry, 2001. 73(8): p. 1658-1663. 53. Deng, W. and A. Gomez, Influence of space charge on the scale-up of multiplexed electrosprays. Journal of Aerosol Science, 2007. 38(10): p. 1062-1078. 54. Su, S.Q., et al., Microstructured Photonic Fibers as Multichannel Electrospray Emitters.Analytical Chemistry, 2009. 81(17): p. 7281-7287. 55. Sen, A.K., J. Darabi, and D.R. Knapp, Simulation and parametric study of a novel multi-spray emitter for ESI-MS applications. Microfluidics and Nanofluidics, 2007. 3(3): p. 283-298. 56. Hayati, I., A. Bailey, and T.F. Tadros, Investigations into the Mechanism of Electrohydrodynamic Spraying of Liquids .2. Mechanism of Stable Jet Formation and Electrical Forces Acting on a Liquid Cone. Journal of Colloid and Interface Science, 1987. 117(1): p. 222-230. 57. Glonti, G.A., On the Theory of the Stability of Liquid Jets in an Electric Field. Soviet Physics Jetp-Ussr, 1958. 7(5): p. 917-918. 58. Nayyar, N.K. and G.S. Murty, The Stability of a Dielectric Liquid Jet in the Presence of a Longitudinal Electric Field. Proceedings of the Physical Society of London, 1960. 75(483): p. 369-373. 59. Allan, R.S. and S.G. Mason, Particle Behaviour in Shear and Electric Fields .1. Deformation and Burst of Fluid Drops. Proceedings of the Royal Society of London Series a-Mathematical and Physical Sciences, 1962. 267(1328): p. 45-&. 60. Melcher, J.R. and G.I. Taylor, Electrohydrodynamics – a Review of Role of Interfacial Shear Stresses. Annual Review of Fluid Mechanics, 1969. 1: p. 111-&. 61. Saville, D.A., Electrohydrodynamics: The Taylor-Melcher leaky dielectric model. Annual Review of Fluid Mechanics, 1997. 29: p. 27-64. 62. Carretero Benignos, J.A. and Massachusetts Institute of Technology. Dept. of Mechanical Engineering., Numerical simulation of a single emitter colloid thruster in pure droplet cone-jet mode. 2005. p. 117 leaves. 63. Hartman, R.P.A., et al., The evolution of electrohydrodynamic sprays produced in the cone-jet mode, a physical model. Journal of Electrostatics, 1999. 47(3): p. 143-170. 64. Hartman, R.P.A., et al., Electrohydrodynamic atomization in the cone-jet mode physical modeling of the liquid cone and jet. Journal of Aerosol Science, 1999. 30(7): p. 823-849.

65. Yoon, S.S., et al., Modeling multi-jet mode electrostatic atomization using boundary element methods. Journal of Electrostatics, 2001. 50(2): p. 91-108. 66. Zeng, J., D. Sobek, and T. Korsmeyer, Electro-hydrodynamic modeling of electrospray ionization: Cad for a mu fluidic device – Mass spectrometer interface. Boston Transducers’03: Digest of Technical Papers, Vols 1 and 2, 2003: p. 1275-1278, 1938. 67. Lastow, O. and W. Balachandran, Numerical simulation of electrohydrodynamic (EHD) atomization. Journal of Electrostatics, 2006. 64(12): p. 850-859. 68. http://www.flow3d.com. 69. Valaskovic, G.A., et al., Attomole-Sensitivity Electrospray Source for Large-Molecule Mass-Spectrometry. Analytical Chemistry, 1995. 67(20): p. 3802-3805. 70. Kriger, M.S., K.D. Cook, and R.S. Ramsey, Durable Gold-Coated Fused-Silica Capillaries for Use in Electrospray Mass-Spectrometry. Analytical Chemistry, 1995. 67(2): p. 385-389. 71. Fang, L.L., et al., Online Time-of-Flight Mass-Spectrometric Analysis of Peptides Separated by Capillary Electrophoresis. Analytical Chemistry, 1994. 66(21): p. 3696-3701. 72. Cao, P. and M. Moini, A novel sheathless interface for capillary electrophoresis/electrospray ionization mass spectrometry using an in-capillary electrode. Journal of the American Society for Mass Spectrometry, 1997. 8(5): p. 561-564. 73. Fong, K.W.Y. and T.W.D. Chan, A novel nonmetallized tip for electrospray mass spectrometry at nanoliter flow rate. Journal of the American Society for Mass Spectrometry, 1999. 10(1): p. 72-75. 74. Emmett, M.R. and R.M. Caprioli, Micro-Electrospray Mass-Spectrometry – Ultra-High-Sensitivity Analysis of Peptides and Proteins. Journal of the American Society for Mass Spectrometry, 1994. 5(7): p. 605-613. 75. Gatlin, C.L., et al., Protein identification at the low femtomole level from silver-stained gels using a new fritless electrospray interface for liquid chromatography microspray and nanospray mass spectrometry. Analytical Biochemistry, 1998. 263(1): p. 93-101. 76. Aturki, Z., et al., On-line CE-MS using pressurized liquid junction nanoflow electrospray interface and surface-coated capillaries. Electrophoresis, 2006. 27(23): p. 4666-4673. 77. Edwards, J.L., et al., Negative mode sheathless capillary electrophoresis electrospray ionization-mass spectrometry for metabolite analysis of prokaryotes. Journal of Chromatography A, 2006. 1106(1-2): p. 80-88. 78. http://www.kiriama.com/kiriama%20single-mode%20polymer%20fibers_009.htm. 79. Wilm, M.S. and M. Mann, Electrospray and Taylor-Cone Theory, Doles Beam of Macromolecules at Last. International Journal of Mass Spectrometry, 1994. 136(2-3): p. 167-180.

80. Hirt, C.W. and B.D. Nichols, Volume of Fluid (Vof) Method for the Dynamics of Free Boundaries. Journal of Computational Physics, 1981. 39(1): p. 201-225. 81. Melcher, J.R., Continuum electromechanics. 1981, Cambridge, Mass.: MIT Press. 1 v. (various pagings). 82. http://www.flow3d.com/cfd-101/cfd-101-FAVOR.html. 83. http://www.flow3d.com/cfd-101/cfd-101-FAVOR-no-loss.html. 84. Savage, B.M. and M.C. Johnson, Flow over ogee spillway: Physical and numerical model case study. Journal of Hydraulic Engineering-Asce, 2001. 127(8): p. 640-649. 85. http://www.flow3d.com/cfd-101/cfd-101-free-surface-fluid-flow.html. 86. Graham T. T. Gibson, R.D.W.a.R.D.O., Multiple electrosprays generated from a single poly carbonate microstructured fibre. Mass Spectrometry, 2011. 87. Smith, R.D., et al., Analytical characterization of the electrospray ion source in the nanoflow regime. Analytical Chemistry, 2008. 80(17): p. 6573-6579. 88. Hirt, C.W., Electro-hydrodynamics of semi-conductive fluids: with application to electro-spraying. Flow Science Technical Note, 2004. 70(FSI–04–TN70): p. 1-7. 89. de la Mora, J.F., The fluid dynamics of Taylor cones. Annual Review of Fluid Mechanics, 2007. 39: p. 217-243. 90. Cloupeau, M. and B. Prunetfoch, Electrostatic Spraying of Liquids in Cone-Jet Mode.Journal of Electrostatics, 1989. 22(2): p. 135-159. 91. Hayati, I., A.I. Bailey, and T.F. Tadros, Investigations into the Mechanisms of Electrohydrodynamic Spraying of Liquids .1. Effect of Electric-Field and the Environment on Pendant Drops and Factors Affecting the Formation of Stable Jets and Atomization. Journal of Colloid and Interface Science, 1987. 117(1): p. 205-221. 92. FLOW-3D User Manual, Ver. 9.4. 93. Sen, A.K., J. Darabi, and D.R. Knapp, Analysis of Droplet Generation in Electrospray Using a Carbon Fiber Based Microfluidic Emitter. Journal of Fluids Engineering-Transactions of the Asme, 2011. 133(7).

Figure 1.1: A water droplet with a radius of 1 mm resting on a glass substrate. The surface of the droplet takes on a spherical cap shape. The contact angle θ is defined by the balance of the interfacial forces.

Effect of substrate cooling and droplet shape and composition on the droplet evaporation and the deposition of particles

기판 냉각 및 액적 모양 및 조성이 액적 증발 및 입자 증착에 미치는 영향

by Vahid Bazargan
M.A.Sc., Mechanical Engineering, The University of British Columbia, 2008
B.Sc., Mechanical Engineering, Sharif University of Technology, 2006
B.Sc., Chemical & Petroleum Engineering, Sharif University of Technology, 2006

고착 방울은 평평한 기판에 놓인 액체 방울입니다. 작은 고정 액적이 증발하는 동안 액적의 접촉선은 고정된 접촉 영역이 있는 고정된 단계와 고정된 접촉각이 있는 고정 해제된 단계의 두 가지 단계를 거칩니다. 고정된 접촉 라인이 있는 증발은 액적 내부에서 접촉 라인을 향한 흐름을 생성합니다.

이 흐름은 입자를 운반하고 접촉 선 근처에 침전시킵니다. 이로 인해 일반적으로 관찰되는 “커피 링”현상이 발생합니다. 이 논문은 증발 과정과 고착성 액적의 증발 유도 흐름에 대한 연구를 제공하고 콜로이드 현탁액에서 입자의 침착에 대한 통찰력을 제공합니다. 여기서 우리는 먼저 작은 고착 방울의 증발을 연구하고 증발 과정에서 기판의 열전도도의 중요성에 대해 논의합니다.

현재 증발 모델이 500µm 미만의 액적 크기에 대해 심각한 오류를 생성하는 방법을 보여줍니다. 우리의 모델에는 열 효과가 포함되어 있으며, 특히 증발 잠열의 균형을 맞추기 위해 액적에 열을 제공하는 기판의 열전도도를 포함합니다. 실험 결과를 바탕으로 접촉각의 진화와 관련된 접촉 선의 가상 움직임을 정의하여 고정 및 고정 해제 단계의 전체 증발 시간을 고려합니다.

우리의 모델은 2 % 미만의 오차로 500 µm보다 작은 물방울에 대한 실험 결과와 일치합니다. 또한 유한한 크기의 라인 액적의 증발을 연구하고 증발 중 접촉 라인의 복잡한 동작에 대해 논의합니다. 에너지 공식을 적용하고 접촉 선이 구형 방울의 후퇴 접촉각보다 높은 접촉각을 가진 선 방울의 두 끝에서 후퇴하기 시작 함을 보여줍니다. 그리고 라인 방울 내부의 증발 유도 흐름을 보여줍니다.

마지막으로, 계면 활성제 존재 하에서 접촉 라인의 거동을 논의하고 입자 증착에 대한 Marangoni 흐름 효과에 대해 논의합니다. 열 Marangoni 효과는 접촉 선 근처에 증착 된 입자의 양에 영향을 미치며, 기판 온도가 낮을수록 접촉 선 근처에 증착되는 입자의 양이 많다는 것을 알 수 있습니다.

Figure 1.1: A water droplet with a radius of 1 mm resting on a glass substrate. The surface of the droplet takes on a spherical cap shape. The contact angle θ is defined by the balance of the interfacial forces.
Figure 1.1: A water droplet with a radius of 1 mm resting on a glass substrate. The surface of the droplet takes on a spherical cap shape. The contact angle θ is defined by the balance of the interfacial forces.
Figure 2.1: Evaporation modes of sessile droplets on a substrate: (a) evaporation at constant contact angle (de-pinned stage) and (b) evaporation at constant contact area (pinned stage)
Figure 2.1: Evaporation modes of sessile droplets on a substrate: (a) evaporation at constant contact angle (de-pinned stage) and (b) evaporation at constant contact area (pinned stage)
Figure 2.2: A sessil droplet with its image can be profiled as the equiconvex lens formed by two intersecting spheres with radius of a.
Figure 2.2: A sessil droplet with its image can be profiled as the equiconvex lens formed by two intersecting spheres with radius of a.
Figure 2.3: The droplet life time for both evaporation modes derived from Equation 2.2.
Figure 2.3: The droplet life time for both evaporation modes derived from Equation 2.2.
Figure 2.4: A probability of escape for vapor molecules at two different sites of the surface of the droplet for diffusion controlled evaporation. The random walk path initiated from a vapor molecule is more likely to result in a return to the surface if the starting point is further away from the edge of the droplet.
Figure 2.4: A probability of escape for vapor molecules at two different sites of the surface of the droplet for diffusion controlled evaporation. The random walk path initiated from a vapor molecule is more likely to result in a return to the surface if the starting point is further away from the edge of the droplet.
Figure 2.5: Schematic of the sessile droplet on a substrate
Figure 2.5: Schematic of the sessile droplet on a substrate. The evaporation rate at the surface of the droplet is enhanced toward the edge of the droplet.
Figure 2.6: The domain mesh (a) and the solution of the Laplace equation for diffusion of the water vapor molecule with the concentration of Cv = 1.9×10−8 g/mm3 at the surface of the droplet into the ambient air with the relative humidity of 55%, i.e. φ = 0.55 (b).
Figure 2.6: The domain mesh (a) and the solution of the Laplace equation for diffusion of the water vapor molecule with the concentration of Cv = 1.9×10−8 g/mm3 at the surface of the droplet into the ambient air with the relative humidity of 55%, i.e. φ = 0.55 (b).
Figure 3.1: The portable micro printing setup. A motorized linear stage from Zaber Technologies Inc. was used to control the place and speed of the micro nozzle.
Figure 3.1: The portable micro printing setup. A motorized linear stage from Zaber Technologies Inc. was used to control the place and speed of the micro nozzle.
Figure 4.6: Temperature contours inside the substrate adjacent to the droplet
Figure 4.6: Temperature contours inside the substrate adjacent to the droplet
Figure 4.7: The effect of substrate cooling on the evaporation rate, the basic model shows the same value for all substrates.
Figure 4.7: The effect of substrate cooling on the evaporation rate, the basic model shows the same value for all substrates.

Bibliography

[1] R. G. Picknett and R. Bexon, “The evaporation of sessile or pendant drops in still air,” Journal of Colloid and Interface Science, vol. 61, pp. 336–350, Sept. 1977. → pages viii, 8, 9, 18, 42
[2] H. Y. Erbil, “Evaporation of pure liquid sessile and spherical suspended drops: A review,” Advances in Colloid and Interface Science, vol. 170, pp. 67–86, Jan. 2012. → pages 1
[3] R. Sharma, C. Y. Lee, J. H. Choi, K. Chen, and M. S. Strano, “Nanometer positioning, parallel alignment, and placement of single anisotropic nanoparticles using hydrodynamic forces in cylindrical droplets,” Nano Lett., vol. 7, no. 9, pp. 2693–2700, 2007. → pages 1, 54, 71
[4] S. Tokonami, H. Shiigi, and T. Nagaoka, “Review: Micro- and nanosized molecularly imprinted polymers for high-throughput analytical applications,” Analytica Chimica Acta, vol. 641, pp. 7–13, May 2009. →pages 71
[5] A. A. Sagade and R. Sharma, “Copper sulphide (CuxS) as an ammonia gas sensor working at room temperature,” Sensors and Actuators B: Chemical, vol. 133, pp. 135–143, July 2008. → pages
[6] W. R. Small, C. D. Walton, J. Loos, and M. in het Panhuis, “Carbon nanotube network formation from evaporating sessile drops,” The Journal of Physical Chemistry B, vol. 110, pp. 13029–13036, July 2006. → pages 71
[7] S. H. Ko, H. Lee, and K. H. Kang, “Hydrodynamic flows in electrowetting,” Langmuir, vol. 24, pp. 1094–1101, Feb. 2008. → pages 42
[8] T. T. Nellimoottil, P. N. Rao, S. S. Ghosh, and A. Chattopadhyay, “Evaporation-induced patterns from droplets containing motile and nonmotile bacteria,” Langmuir, vol. 23, pp. 8655–8658, Aug. 2007. → pages 1
[9] R. Sharma and M. S. Strano, “Centerline placement and alignment of anisotropic nanotubes in high aspect ratio cylindrical droplets of nanometer diameter,” Advanced Materials, vol. 21, no. 1, p. 6065, 2009. → pages 1, 54, 71
[10] V. Dugas, J. Broutin, and E. Souteyrand, “Droplet evaporation study applied to DNA chip manufacturing,” Langmuir, vol. 21, pp. 9130–9136, Sept. → pages 2, 71
[11] Y.-C. Hu, Q. Zhou, Y.-F. Wang, Y.-Y. Song, and L.-S. Cui, “Formation mechanism of micro-flows in aqueous poly(ethylene oxide) droplets on a substrate at different temperatures,” Petroleum Science, vol. 10, pp. 262–268, June 2013. → pages 2, 34, 54
[12] T.-S. Wong, T.-H. Chen, X. Shen, and C.-M. Ho, “Nanochromatography driven by the coffee ring effect,” Analytical Chemistry, vol. 83, pp. 1871–1873, Mar. 2011. → pages 71
[13] J.-H. Kim, S.-B. Park, J. H. Kim, and W.-C. Zin, “Polymer transports inside evaporating water droplets at various substrate temperatures,” The Journal of Physical Chemistry C, vol. 115, pp. 15375–15383, Aug. 2011. → pages 54
[14] S. Choi, S. Stassi, A. P. Pisano, and T. I. Zohdi, “Coffee-ring effect-based three dimensional patterning of Micro/Nanoparticle assembly with a single droplet,” Langmuir, vol. 26, pp. 11690–11698, July 2010. → pages
[15] D. Wang, S. Liu, B. J. Trummer, C. Deng, and A. Wang, “Carbohydrate microarrays for the recognition of cross-reactive molecular markers of microbes and host cells,” Nature biotechnology, vol. 20, pp. 275–281, Mar. PMID: 11875429. → pages 2, 54, 71
[16] H. K. Cammenga, “Evaporation mechanisms of liquids,” Current topics in materials science, vol. 5, pp. 335–446, 1980. → pages 3
[17] C. Snow, “Potential problems and capacitance for a conductor bounded by two intersecting spheres,” Journal of Research of the National Bureau of Standards, vol. 43, p. 337, 1949. → pages 9
[18] R. D. Deegan, O. Bakajin, T. F. Dupont, G. Huber, S. R. Nagel, and T. A. Witten, “Contact line deposits in an evaporating drop,” Physical Review E, vol. 62, p. 756, July 2000. → pages 10, 14, 18, 27, 53, 54, 71, 84
[19] H. Hu and R. G. Larson, “Evaporation of a sessile droplet on a substrate,” The Journal of Physical Chemistry B, vol. 106, pp. 1334–1344, Feb. 2002. → pages 12, 18, 29, 43, 44, 48, 49, 53, 61, 71, 84
[20] Y. O. Popov, “Evaporative deposition patterns: Spatial dimensions of the deposit,” Physical Review E, vol. 71, p. 036313, Mar. 2005. → pages 14, 27, 43, 44, 45, 54
[21] H. Gelderblom, A. G. Marin, H. Nair, A. van Houselt, L. Lefferts, J. H. Snoeijer, and D. Lohse, “How water droplets evaporate on a superhydrophobic substrate,” Physical Review E, vol. 83, no. 2, p. 026306,→ pages
[22] F. Girard, M. Antoni, S. Faure, and A. Steinchen, “Influence of heating temperature and relative humidity in the evaporation of pinned droplets,” Colloids and Surfaces A: Physicochemical and Engineering Aspects, vol. 323, pp. 36–49, June 2008. → pages 18
[23] Y. Y. Tarasevich, “Simple analytical model of capillary flow in an evaporating sessile drop,” Physical Review E, vol. 71, p. 027301, Feb. 2005. → pages 19, 54, 62, 72
[24] A. J. Petsi and V. N. Burganos, “Potential flow inside an evaporating cylindrical line,” Physical Review E, vol. 72, p. 047301, Oct. 2005. → pages 22, 55, 62, 68, 71
[25] A. J. Petsi and V. N. Burganos, “Evaporation-induced flow in an inviscid liquid line at any contact angle,” Physical Review E, vol. 73, p. 041201, Apr.→ pages 23, 53, 55, 72
[26] H. Masoud and J. D. Felske, “Analytical solution for stokes flow inside an evaporating sessile drop: Spherical and cylindrical cap shapes,” Physics of Fluids, vol. 21, pp. 042102–042102–11, Apr. 2009. → pages 23, 55, 62, 71, 72
[27] H. Hu and R. G. Larson, “Analysis of the effects of marangoni stresses on the microflow in an evaporating sessile droplet,” Langmuir, vol. 21, pp. 3972–3980, Apr. 2005. → pages 24, 28, 53, 54, 56, 62, 68, 71, 72, 74, 84
[28] R. Bhardwaj, X. Fang, and D. Attinger, “Pattern formation during the evaporation of a colloidal nanoliter drop: a numerical and experimental study,” New Journal of Physics, vol. 11, p. 075020, July 2009. → pages 28
[29] A. Petsi, A. Kalarakis, and V. Burganos, “Deposition of brownian particles during evaporation of two-dimensional sessile droplets,” Chemical Engineering Science, vol. 65, pp. 2978–2989, May 2010. → pages 28
[30] J. Park and J. Moon, “Control of colloidal particle deposit patterns within picoliter droplets ejected by ink-jet printing,” Langmuir, vol. 22, pp. 3506–3513, Apr. 2006. → pages 28
[31] H. Hu and R. G. Larson, “Marangoni effect reverses coffee-ring depositions,” The Journal of Physical Chemistry B, vol. 110, pp. 7090–7094, Apr. 2006. → pages 29, 74
[32] K. H. Kang, S. J. Lee, C. M. Lee, and I. S. Kang, “Quantitative visualization of flow inside an evaporating droplet using the ray tracing method,” Measurement Science and Technology, vol. 15, pp. 1104–1112, June 2004. → pages 34
[33] S. T. Beyer and K. Walus, “Controlled orientation and alignment in films of single-walled carbon nanotubes using inkjet printing,” Langmuir, vol. 28, pp. 8753–8759, June 2012. → pages 42, 71
[34] G. McHale, “Surface free energy and microarray deposition technology,” Analyst, vol. 132, pp. 192–195, Feb. 2007. → pages 42
[35] R. Bhardwaj, X. Fang, P. Somasundaran, and D. Attinger, “Self-assembly of colloidal particles from evaporating droplets: Role of DLVO interactions and proposition of a phase diagram,” Langmuir, vol. 26, pp. 7833–7842, June→ pages 42
[36] G. J. Dunn, S. K. Wilson, B. R. Duffy, S. David, and K. Sefiane, “The strong influence of substrate conductivity on droplet evaporation,” Journal of Fluid Mechanics, vol. 623, no. 1, p. 329351, 2009. → pages 44
[37] M. S. Plesset and A. Prosperetti, “Flow of vapour in a liquid enclosure,” Journal of Fluid Mechanics, vol. 78, pp. 433–444, 1976. → pages 44
[38] S. Das, P. R. Waghmare, M. Fan, N. S. K. Gunda, S. S. Roy, and S. K. Mitra, “Dynamics of liquid droplets in an evaporating drop: liquid droplet coffee stain? effect,” RSC Advances, vol. 2, pp. 8390–8401, Aug. 2012. → pages 53
[39] B. J. Fischer, “Particle convection in an evaporating colloidal droplet,” Langmuir, vol. 18, pp. 60–67, Jan. 2002. → pages 54
[40] J. L. Wilbur, A. Kumar, H. A. Biebuyck, E. Kim, and G. M. Whitesides, “Microcontact printing of self-assembled monolayers: applications in microfabrication,” Nanotechnology, vol. 7, p. 452, Dec. 1996. → pages 54
[41] T. Kawase, H. Sirringhaus, R. H. Friend, and T. Shimoda, “Inkjet printed via-hole interconnections and resistors for all-polymer transistor circuits,” Advanced Materials, vol. 13, no. 21, p. 16011605, 2001. → pages 71
[42] B.-J. de Gans, P. C. Duineveld, and U. S. Schubert, “Inkjet printing of polymers: State of the art and future developments,” Advanced Materials, vol. 16, no. 3, p. 203213, 2004. → pages 71
[43] H. Sirringhaus, T. Kawase, R. H. Friend, T. Shimoda, M. Inbasekaran, W. Wu, and E. P. Woo, “High-resolution inkjet printing of all-polymer transistor circuits,” Science, vol. 290, pp. 2123–2126, Dec. 2000. PMID:→ pages
[44] D. Soltman and V. Subramanian, “Inkjet-printed line morphologies and temperature control of the coffee ring effect,” Langmuir, vol. 24, pp. 2224–2231, Mar. 2008. → pages 54
[45] R. Tadmor and P. S. Yadav, “As-placed contact angles for sessile drops,” Journal of Colloid and Interface Science, vol. 317, pp. 241–246, Jan. 2008. → pages 56
[46] J. Drelich, “The significance and magnitude of the line tension in three-phase (solid-liquid-fluid) systems,” Colloids and Surfaces A: Physicochemical and Engineering Aspects, vol. 116, pp. 43–54, Sept. 1996. → pages 56
[47] R. Tadmor, “Line energy, line tension and drop size,” Surface Science, vol. 602, pp. L108–L111, July 2008. → pages 69
[48] C.-H. Choi and C.-J. C. Kim, “Droplet evaporation of pure water and protein solution on nanostructured superhydrophobic surfaces of varying heights,” Langmuir, vol. 25, pp. 7561–7567, July 2009. → pages 71
[49] K. F. Baughman, R. M. Maier, T. A. Norris, B. M. Beam, A. Mudalige, J. E. Pemberton, and J. E. Curry, “Evaporative deposition patterns of bacteria from a sessile drop: Effect of changes in surface wettability due to exposure to a laboratory atmosphere,” Langmuir, vol. 26, pp. 7293–7298, May 2010.
[50] D. Brutin, B. Sobac, and C. Nicloux, “Influence of substrate nature on the evaporation of a sessile drop of blood,” Journal of Heat Transfer, vol. 134, pp. 061101–061101, May 2012. → pages 71
[51] D. Pech, M. Brunet, P.-L. Taberna, P. Simon, N. Fabre, F. Mesnilgrente, V. Condra, and H. Durou, “Elaboration of a microstructured inkjet-printed carbon electrochemical capacitor,” Journal of Power Sources, vol. 195, pp. 1266–1269, Feb. 2010. → pages 71
[52] J. Bachmann, A. Ellies, and K. Hartge, “Development and application of a new sessile drop contact angle method to assess soil water repellency,” Journal of Hydrology, vol. 231232, pp. 66–75, May 2000. → pages 71
[53] H. Y. Erbil, G. McHale, and M. I. Newton, “Drop evaporation on solid surfaces: constant contact angle mode,” Langmuir, vol. 18, no. 7, pp. 2636–2641, 2002. → pages
[54] X. Fang, B. Li, J. C. Sokolov, M. H. Rafailovich, and D. Gewaily, “Hildebrand solubility parameters measurement via sessile drops evaporation,” Applied Physics Letters, vol. 87, pp. 094103–094103–3, Aug.→ pages
[55] Y. C. Jung and B. Bhushan, “Wetting behaviour during evaporation and condensation of water microdroplets on superhydrophobic patterned surfaces,” Journal of Microscopy, vol. 229, no. 1, p. 127140, 2008. → pages 71
[56] J. Drelich, J. D. Miller, and R. J. Good, “The effect of drop (bubble) size on advancing and receding contact angles for heterogeneous and rough solid surfaces as observed with sessile-drop and captive-bubble techniques,”
Journal of Colloid and Interface Science, vol. 179, pp. 37–50, Apr. 1996. →pages 72, 75
[57] D. Bargeman and F. Van Voorst Vader, “Effect of surfactants on contact angles at nonpolar solids,” Journal of Colloid and Interface Science, vol. 42, pp. 467–472, Mar. 1973. → pages 73
[58] J. Menezes, J. Yan, and M. Sharma, “The mechanism of alteration of macroscopic contact angles by the adsorption of surfactants,” Colloids and Surfaces, vol. 38, no. 2, pp. 365–390, 1989. → pages
[59] T. Okubo, “Surface tension of structured colloidal suspensions of polystyrene and silica spheres at the air-water interface,” Journal of Colloid and Interface Science, vol. 171, pp. 55–62, Apr. 1995. → pages 73, 76
[60] R. Pyter, G. Zografi, and P. Mukerjee, “Wetting of solids by surface-active agents: The effects of unequal adsorption to vapor-liquid and solid-liquid interfaces,” Journal of Colloid and Interface Science, vol. 89, pp. 144–153, Sept. 1982. → pages 73
[61] T. Mitsui, S. Nakamura, F. Harusawa, and Y. Machida, “Changes in the interfacial tension with temperature and their effects on the particle size and stability of emulsions,” Kolloid-Zeitschrift und Zeitschrift fr Polymere, vol. 250, pp. 227–230, Mar. 1972. → pages 73
[62] S. Phongikaroon, R. Hoffmaster, K. P. Judd, G. B. Smith, and R. A. Handler, “Effect of temperature on the surface tension of soluble and insoluble surfactants of hydrodynamical importance,” Journal of Chemical & Engineering Data, vol. 50, pp. 1602–1607, Sept. 2005. → pages 73, 80
[63] V. S. Vesselovsky and V. N. Pertzov, “Adhesion of air bubbles to the solid surface,” Zh. Fiz. Khim, vol. 8, pp. 245–259, 1936. → pages 75
[64] Hideo Nakae, Ryuichi Inui, Yosuke Hirata, and Hiroyuki Saito, “Effects of surface roughness on wettability,” Acta Materialia, vol. 46, pp. 2313–2318, Apr. 1998. → pages
[65] R. J. Good and M. Koo, “The effect of drop size on contact angle,” Journal of Colloid and Interface Science, vol. 71, pp. 283–292, Sept. 1979. → pages

Damascene templates

High-Rate Nanoscale Offset Printing Process Using Directed Assembly and Transfer of Nanomaterials

지난 10 년 동안 나노 크기의 재료와 공정을 제품에 통합하는 데 제한적인 성공을 거두면서 나노 기술에 상당한 투자와 발전이 있었습니다.

잉크젯, 그라비아, 스크린 프린팅과 같은 접근 방식은 나노 물질을 사용하여 구조와 장치를 만드는 데 사용됩니다. [1–7] 그러나 상당히 느리고 µm 스케일 분해능 만 제공 할 수 있습니다. 다양한 모양과 크기의 100nm 미만의 특징을 달성하기 위해 딥펜 리소그래피 (DPN) [8-11] 및 소프트 리소그래피 [12-16]와 같은 다양한 기술이 개발되고 광범위하게 연구되었습니다.

DPN은 직접 쓰기 기술로, atomic force microscopy 현미경 팁을 사용하여 다양한 기판에 여러 패턴을 생성합니다. DPN을 사용한 확장 성을 해결하기 위해 단일 AFM 팁 대신 2D 형식으로 배포 된 AFM (Atomic Force Microscopy) 팁 [17,18]이 사용되었습니다. 소프트 리소그래피에서는 나노 물질을 포함하는 잉크로 적셔진 원하는 릴리프 패턴을 가진 경화된 엘라스토머가 기판과 컨 포멀 접촉하게 되며, 여기서 패턴 화 된 나노 물질이 전달되어 기판에서 원하는 특징을 달성합니다.

이 논문에서는 작거나 큰 영역에서 몇 분 만에 나노, 마이크로 또는 거시적 구조를 인쇄 할 수 있는 다중 스케일 오프셋 인쇄 접근 방식을 제시합니다. 이 프로세스는 나노 입자 (NP), 탄소 나노 튜브 (CNT) 또는 용해 된 폴리머를 포함하는 서스펜션 (잉크)에서 나노 물질의 전기 영동 방향 조립을 사용하여 특별히 제작 된 재사용 가능한 Damascene 템플릿에 패턴을 “inking” 하는 것으로 시작됩니다. 이 잉크 프로세스는 실온과 압력에서 수행됩니다.

두 번째 단계는 템플릿에 조립된 나노 물질이 다른 기판으로 전송되는 “printing”로 구성됩니다. 전송 프로세스가 끝나면 템플릿은 다음 조립 및 전송주기에서 즉시 재사용 할 수 있습니다. 이 오프셋 인쇄 프로세스를 통해 NP (폴리스티렌 라텍스 (PSL), 실리카,은) 및 CNT (다중 벽 및 단일 벽)를 100μm에서 500nm까지의 크기 범위를 가진 패턴에 조립하고 유동성 기판에 성공적으로 옮깁니다.

다양한 나노 물질을 다양한 아키텍처로 조립하기 위해 템플릿 유도 유동, 대류, 유전 영동 (DEP) 및 전기 영동 조립과 같은 몇 가지 직접 조립 프로세스가 조사되었습니다. 모세관력이 지배적인 조립 메커니즘인 유체 조립 공정은 다양한 나노 물질에 적용 할 수 있습니다.

대류 조립 공정은 현탁 메니 스커 스와 증발을 활용하여 단일 나노 입자 분해능으로 정밀 조립을 가능하게 합니다. 이러한 조립 공정 중 많은 부분이 트렌치와 같은 마이크로 및 나노 스케일 기능으로 고해상도의 직접 조립을 보여 주었지만, 확장성 부족, 느린 공정 속도 및 반복성과 같은 많은 단점이 있습니다.

DEP 어셈블리는 NP와 전극 사이에 고배향 탄소 나노 튜브 어셈블리를 사용하여 나노 와이어 및 구조를 만드는 데 사용되었습니다. 조립 효율은 전기장과 전기장 구배에 상당한 영향을 미치는 전극의 기하학적 구조와 간격에 크게 좌우됩니다. 전기 영동 기반 조립 공정은 유체 조립에 비해 훨씬 짧은 시간에 전도성 표면에 표면 전하를 가진 나노 물질을 조립하는 것을 포함합니다. [34–37]

그러나 전기 영동 조립은 조립이 전도성 표면에 발생해야 하므로 다양한 장치를 만드는 데 실용적이지 않습니다. 한 가지 해결책은 원하는 나노 스케일 구조를 기반으로 전도성 패턴이 있는 템플릿을 만들고, 전기 영동 공정을 사용하여 패턴 위에 나노 물질을 조립 한 다음 조립 된 구조를 수용 기판에 옮기는 것입니다.

그림 1a와 같이 절연 필름에 전도성 와이어와 같은 패턴 구조가있는 기존 템플릿을 사용하면 나노 스케일 와이어의 잠재적 인 큰 강하로 인해 어셈블리가 불균일 해지며 대부분의 입자는 그림 1에 표시된 마이크로 와이어 b. 또한 NP는 3D 와이어의 측벽에도 조립되므로 바람직하지 않습니다. 또한 나노 스케일 와이어와 템플릿 사이의 작은 접촉 면적으로 인해 나노 스케일 와이어는 이송 과정에서 쉽게 벗겨집니다.

Damascene templates
Figure 1. Damascene templates: a) A schematic of a conventional wire template used for electrophoretic assembly. In these templates nanowire are connected to a micrometer scale electrodes, which are in turn connected, to a large metal pad through which the potential is applied. b) SEM images of a typical nanoparticle assembly result obtained for confi guration shown in (a). c) A schematic of a Damascene template where all of the wires (nano- or micrometer scale) and the metal pad are connected to a conductive fi lm underneath the insulating fi lm. d) A schematic of Damascene template fabrication. Inset is artifi cially colored cross-sectional SEM image showing the metal nanowires to be at the same height as that of the SiO 2 and showing the conductive fi lm underneath the insulator. e) An optical image of a 3 inch Damascene template.
Offset printing
Figure 2. Offset printing: a) A schematic of the nanoscale offset printing approach. The insulating (SiO 2 ) surface of the Damascene template is selectively coated with a hydrophobic SAM (OTS). Using electrophoresis, nanomaterials are assembled on the conductive patterns of the Damascene template (“inking”), which are then transferred to a recipient substrate (“printing”). After the transfer, the template is ready for the next assembly and transfer cycle. b) SEM image of 50 nm PSL particles assembly with high density on 1 µm wide electrodes. c) Silica particles (20 nm) assembly on crossbar 2D patterns demonstrating the versatility of the Damascene template. Inset fi gure is a high-resolution image of assembled silica particles. d) SEM image of assembled SWNTs on micrometer scale patterns. e) MWNTs assembled on 100 µm features. f) Cellulose assembled on 2 µm electrodes. g) SWNTs assembled in cross bar architecture patterns. h) Flexible devices with array of transferred SWNTs and metal electrodes (printed on PEN). Inset is the microscopy image of two electropads and transferred SWNTs on PEN fi lm.
Analysis of nanomaterial assembly on electrodes
Figure 3. Analysis of nanomaterial assembly on electrodes

이것은 또한 그림 3b에 표시된대로 유한 체적 모델링 (Flow 3D)을 사용하는 전기장 윤곽 시뮬레이션 결과에 의해 확인됩니다. 전기장 강도의 윤곽은 전도성 패턴의 가장자리에있는 전기장이 중앙에있는 것보다 더 강하다는 것을 나타냅니다. 그러나 적용된 전위가 2.5V로 증가하면 그림 3c에 표시된대로 100nm 실리카 입자가 Damascene 템플릿을 가로 질러 전도성 패턴의 표면에 완전히 조립되어 조립을위한 임계 전기장 강도에 도달했음을 나타냅니다. 정렬 된 SWNT는 여과 전달 경로를 피하고 나노 튜브 사이의 접합 저항을 최소화하여 소자 성능의 최소 변화를 가져 오기 때문에 많은 응용 분야에서 고도로 조직화 된 SWNT가 필요합니다.

References

[1] M.Abulikemu, E.H.Da’as, H.Haverinen, D.Cha, M.A.Malik, G.E.Jabbour, Angew.Chem.Int.Ed.2014, 53, 599.
[2] a) Z.Lu, M.Layani, X.Zhao, L.P.Tan, T.Sun, S.Fan, Q.Yan, S.Magdassi, H.H.Hng, Small 2014, 10, 3551; b) H.Ko, J.Lee, Y.Kim, B.Lee, C.H.Jung, J.H.Choi, O.S.Kwon, K.Shin, Adv.Mater.2014, 26, 2286.
[3] C.J.Hansen, R.Saksena, D.B.Kolesky, J.J.Vericella, S.J.Kranz, G.P.Muldowney, K.T.Christensen, J.A.Lewis, Adv.Mater.2013, 25, 2.
[4] F.C.Krebs, N.Espinosa, M.Hösel, R.R.Søndergaard, M.Jørgensen, Adv.Mater.2014, 26, 29.
[5] W.Honda, S.Harada, T.Arie, S.Akita, K.Takei, Adv.Funct.Mater. 2014, 24, 3298.
[6] R.Guo, Y.Yu, Z.Xie, X.Liu, X.Zhou, Y.Gao, Z.Liu, F.Zhou, Y.Yang, Z.Zheng, Adv.Mater.2013, 25, 3343.
[7] A.Dzwilewski, T.Wågberg, L.Edman, J.Am.Chem.Soc.2009, 131, 4006.
[8] R.D.Piner, J.Zhu, F.Xu, S.Hong, C.A.Mirkin, Science 1999, 283, 661.
[9] J.-H.Lim, C.A.Mirkin, Adv.Mater.2002, 14, 1474.
[10] X.Liu, L.Fu, S.Hong, V.P.Dravid, C.A.Mirkin, Adv.Mater.2002,14, 231.
[11] D.A.Weinberger, S.Hong, C.A.Mirkin, B.W.Wessels, T.B.Higgins, Adv.Mater.2000, 12, 1600.
[12] J.P.Rolland, E.C.Hagberg, G.M.Denison, K.R.Carter, J.M.DeSimone, Angew.Chem.2004, 116, 5920.
[13] T.Granlund, T.Nyberg, L.S.Roman, M.Svensson, O.Inganäs, Adv.Mater.2000, 12, 269.
[14] Y.Xia, G.M.Whitesides, Annu.Rev.Mater.Sci.1998, 28, 153.
[15] W.S.Beh, I.T.Kim, D.Qin, Y.Xia, G.M.Whitesides.Adv.Mater. 1999, 11, 1038.
[16] Y.Yin, B.Gates, Y.Xia.Adv.Mater.2000, 12, 1426.
[17] K.Salaita, Y.Wang, J.Fragala, R.A.Vega, C.Liu, C.A.Mirkin,Angew.Chem.2006, 118, 7378.
[18] D.Bullen, S.-W.Chung, X.Wang, J.Zou, C.A.Mirkin, C.Liu, Appl.Phys.Lett.2004, 84, 789.
[19] Y.L.Kim, H.Y.Jung, S.Park, B.Li, F.Liu, J.Hao, Y.-K.Kwon, Y.J.Jung, S.Kar, Nat.Photonics 2014, 8, 239.
[20] X.Xiong, L.Jaberansari, M.G.Hahm, A.Busnaina, Y.J.Jung, Small 2007, 3, 2006.
[21] A.B.Marciel, M.Tanyeri, B.D.Wall, J.D.Tovar, C.M.Schroeder, W.L.Wilson, Adv.Mater.2013, 25, 6398.
[22] J.T.Wang, J.Wang, J.J.Han, Small 2011, 7, 1728.
[23] S.Y.Lee, S.H.Kim, H.Hwang, J.Y.Sim, S.M.Yang, Adv.Mater. 2014, 26, 2391.
[24] J.Y.Oh, J.T.Park, H.J.Jang, W.J.Cho, M.S.Islam, Adv.Mater. 2014, 26, 1929.
[25] K.W.Song, R.Costi, V.Bulovi, Adv.Mater.2013, 25, 1420.
[26] P.Maury, M.Escalante, D.N.Reinhoudt, J.Huskens, Adv.Mater. 2005, 17, 2718.
[27] Y.Xia, Y.Yin, Y.Lu, J.McLellan, Adv.Funct.Mater.2003, 13, 907.
[28] L.Jaber-Ansari, M.G.Hahm, S.Somu, Y.E.Sanz, A.Busnaina, Y.J.Jung, J.Am.Chem.Soc.2008, 131, 804.
[29] T.Kraus, L.Malaquin, H.Schmid, W.Riess, N.D.Spencer, H.Wolf,Nat.Nanotechnol.2007, 2, 570.
[30] K.D.Hermanson, S.O.Lumsdon, J.P.Williams, E.W.Kaler, O.D.Velev, Science 2001, 294, 1082.
[31] H.-W.Seo, C.-S.Han, D.-G.Choi, K.-S.Kim, Y.-H.Lee, Microelectron.Eng.2005, 81, 83.
[32] E.M.Freer, O.Grachev, X.Duan, S.Martin, D.P.Stumbo, Nat.Nanotechnol.2010, 5, 525.
[33] D.Xu, A.Subramanian, L.Dong, B.J.Nelson, IEEE Trans.Nanotechnol.2009, 8, 449.
[34] X.Xiong, P.Makaram, A.Busnaina, K.Bakhtari, S.Somu, N.McGruer, J.Park, Appl.Phys.Lett.2006, 89, 193108.
[35] R.C.Bailey, K.J.Stevenson, J.T.Hupp, Adv.Mater.2000, 12, 1930.
[36] Q.Zhang, T.Xu, D.Butterfi eld, M.J.Misner, D.Y.Ryu, T.Emrick, T.P.Russell, Nano Lett.2005, 5, 357.
[37] E.Kumacheva, R.K.Golding, M.Allard, E.H.Sargent, Adv.Mater. 2002, 14, 221.
[38] M.Wei, Z.Tao, X.Xiong, M.Kim, J.Lee, S.Somu, S.Sengupta, A.Busnaina, C.Barry, J.Mead, Macromol.Rapid Commun.2006, 27, 1826.
[39] a) D.Schwartz, S.Steinberg, J.Israelachvili, J.Zasadzinski, Phys.Rev.Lett.1992, 69, 3354; b) W.Yang, P.Thordarson, J.J.Gooding, S.P.Ringer, F.Braet, Nanotechnology 2007, 18, 412001.
[40] S.Siavoshi, C.Yilmaz, S.Somu, T.Musacchio, J.R.Upponi, V.P.Torchilin, A.Busnaina, Langmuir 2011, 27, 7301.
[41] E.Artukovic, M.Kaempgen, D.Hecht, S.Roth, G.Grüner, NanoLett.2005, 5, 757.
[42] L.Hu, D.Hecht, G.Grüner, Nano Lett.2004, 4, 2513.
[43] M.Fuhrer, J.Nygård, L.Shih, M.Forero, Y.G.Yoon, H.J.Choi, J.Ihm, S.G.Louie, A.Zettl, P.L.McEuen, Science 2000, 288,
494.
[44] J.J.Gooding, A.Chou, J.Liu, D.Losic, J.G.Shapter, D.B.Hibbert,Electrochem.Commun.2007, 9, 1677.
[45] A.Chou, T.Böcking, N.K.Singh, J.J.Gooding, Chem.Commun. 2005, 7, 842.
[46] D.Hines, V.Ballarotto, E.Williams, Y.Shao, S.Solin, J.Appl.Phys. 2007, 101, 024503.
[47] H.Park, A.Afzali, S.-J.Han, G.S.Tulevski, A.D.Franklin, J.Tersoff, J.B.Hannon, W.Haensch, Nat.Nanotechnol.2012, 7, 787.
[48] S.Somu, H.Wang, Y.Kim, L.Jaberansari, M.G.Hahm, B.Li, T.Kim, X.Xiong, Y.J.Jung, M.Upmanyu, A.Busnaina, ACS Nano 2010, 4, 4142.
[49] L.Jaber-Ansari, M.G.Hahm, T.H.Kim, S.Somu, A.Busnaina, Y.J.Jung, Appl.Phys.A 2009, 96, 373.
[50] B.Li, M.G.Hahm, Y.L.Kim, H.Y.Jung, S.Kar, Y.J.Jung, ACS Nano 2011, 5, 4826.
[51] B.Li, H.Y.Jung, H.Wang, Y.L.Kim, T.Kim, M.G.Hahm, A.Busnaina, M.Upmanyu, Y.J.Jung, Adv.Funct.Mater.2011, 21, 1810.
[52] M.A.Meitl, Z.T.Zhu, V.Kumar, K.J.Lee, X.Feng, Y.Y.Huang, I.Adesida, R.G.Nuzzo, J.A.Rogers, Nat.Mater.2005, 5, 33.
[53] F.N.Ishikawa, H.Chang, K.Ryu, P.Chen, A.Badmaev, L.GomezDe Arco, G.Shen, C.Zhou, ACS Nano 2008, 3, 73.
[54] N.Inagaki, Plasma Surface Modifi cation and Plasma Polymerization, CRC, Boca Raton, FL, USA 1996.
[55] E.Liston, L.Martinu, M.Wertheimer, J.Adhes.Sci.Technol.1993, 7, 1091.
[56] T.Tsai, C.Lee, N.Tai, W.Tuan, Appl.Phys.Lett.2009, 95, 013107.
[57] J.G.Bai, Z.Z.Zhang, J.N.Calata, G.-Q.Lu, IEEE Trans.Compon.Packag.Technol.2006, 29, 589.
[58] J.G.Toffaletti, Crit.Rev.Clin.Lab.Sci.1991, 28, 253.
[59] J.-L.Vincent, P.Dufaye, J.Berré, M.Leeman, J.-P.Degaute, R.J.Kahn, Crit.Care Med.1983, 11, 449.
[60] R.Henning, M.Weil, F.Weiner, Circ.Shock 1982, 9, 307.

Agitational Stresses

Agitational Stresses / 동요 스트레스

This article was contributed by Ge Bai, Scientist, MedImmune LLC.

Agitation instruments and glass vial

Agitation 연구는 생물 요법 발달에 있어 흔하고 중요한 부분이지만, 관련된 스트레스의 근본적인 특성과 단백질 안정성에 대한 영향은 완전히 이해되지 않았습니다. 동요된 스트레스 방법의 특성화는 단백질 분해 메커니즘이나 특정 민감도를 식별하는데 매우 중요합니다. 전단, 경계면, 캐비 테이션 또는 기타 유체 및 계면 장력에 의한 응력은 실험적 방법으로 측정하기 어렵거나 불가능합니다. 최근에는 다양한 주파수에서 회전 장치(Rotator), 궤도 셰이커, 자석 교반기, 와류 혼합기(그림 1참조)를 포함한 다양한 계측기를 사용하여 3-4S 유리 바이알에서 동요하는 액체의 유체 역학을 모델링하여 단백질 안정성에 잠재적으로 중요한 응력을 확인하고 정량화하였습니다. 25°C에서 물의 유동성 특성이 이러한 시뮬레이션에 사용되었습니다.

Gaining better understanding on agitational stresses applied to proteins for biopharmaceutical development

표준 FLOW3D코드는 최대 시스템 전단율, 볼륨 평균 전단률, 공기-액체 및 고체-액체 인터페이스 근처의 볼륨 평균 전단률, 총 전단, 고체-액체 인터페이스의 면적, 그리고 공기음 재생 인터페이스와 같은 단백질에 대한 잠재적으로 유해한 응력을 수치적으로 계산할 수 있도록 맞춤화하였다. 표준 소프트웨어 패키지의 추가 출력으로 표시됩니다. 시뮬레이션과 실험 사이에 바이알에 있는 유체의 자유 표면 형태를 비교하여 CFD모델을 검증하였습니다(그림 2).

Orbital schaker simulation
그림 2. CFD시뮬레이션과 300rpm정상 상태에서의(A)궤도 쉐이커와(B)35rpm, 55°위치에서의 회전 장치(Rotator)회전 장치(Rotator)에 대한 실험 사이의 유체 없는 표면 형태 비교.
Instantaneous shear rates
그림 3. 최대 진동 주파수(A)궤도 쉐이커,(B)자기 교반기,(C)와류 혼합기 및(D)회전 장치(Rotator)에서의 경계면 부근에서의 순간 전단율.

응력(전단 속도 및 인터페이스 생성 속도)의 예와 공기 액상 및 고체 액체 인터페이스에서의 비교는 그림 3과 그림 4에 나와 있다. 전체적으로, 와류 혼합기는 가장 강한 응력을 제공하는 반면, 자석 교반기는 소수성 절 표면에 국소적으로 강한 전단을 제시하였다. 회전 장치(Rotator)는 부드러운 유체 응력을 제공하지만 낮은 회전 주파수를 고려할 때 공기-물 내부 영역 및 표면 응력은 상대적으로 높습니다. 궤도 셰이커는 중간 수준의 스트레스를 제공하지만 일관된 생체-생체 동질성을 위한 크고 안정적인 플랫폼의 이점을 제공합니다.

Air-liquid interface generation rates
그림 4. 최대 진동 주파수(A)궤도 쉐이커,(B)자기 교반기,(C)와류 혼합기 및(D)회전 장치(Rotator)에서의 공기 액상 인터페이스 생성 속도.

우리는 설명한 각각의 동요된 방법에서 유리 용기 안의 액체에 복수의 응력이 동시에 작용한다는 것을 발견했다. 이러한 스트레스는 다양한 방법에 따라 다양했으며 종종 교란 주파수의 강력한 기능으로 밝혀졌다. 또한 알려진 유형과 강도의 스트레스를 가진 적절한 촉진 방법을 선택하면 단백질 저하 메커니즘에 대한 영향을 더 잘 이해하는 데 도움이 될 수 있다는 것도 알아냈다. 우리는 CFD가 실험 시스템에서 유체 응력의 특성을 파악하고 실제 조건에 대한 관련성을 검증하는 데 중요한 역할을 할 수 있다고 결론지었습니다.

생명 공학 응용 분야

표준 FLOW-3D 코드는 시스템 전단 속도, 부피 평균 전단 속도, 공기-액체 및 고체-액체 계면 근처의 부피 평균 전단 속도, 총 전단, 고체 면적과 같은 단백질에 잠재적으로 유해한 응력이 발생하도록 맞춤화되었습니다. 액체 인터페이스 및 공기-액체 인터페이스 재생률을 수치적으로 계산하고, 표준 소프트웨어 패키지의 추가 출력과 비교할 수 있습니다. 시뮬레이션과 실험 사이에 VIAL에있는 유체의 자유 표면 모양을 비교하여 CFD 모델을 검증했습니다 (그림 2).

Orbital schaker simulation
Figure 2. Comparison of the shape of fluid free surface between CFD simulation and experiment for (A) orbital shaker at 300 rpm at steady state and (B) rotator at 35 rpm, 55° position.
Instantaneous shear rates
Figure 3. Instantaneous shear rates near interfaces at maximum agitation frequencies (A) orbital shaker, (B) magnetic stirrer, (C) vortex mixer and (D) rotator.

응력(전단 속도 및 인터페이스 생성 속도)의 예와 공기 액상 및 고체 액체 인터페이스에서의 비교는 그림 3과 그림 4에 나와 있습니다. 전체적으로, 와류 혼합기는 가장 강한 응력을 제공하는 반면, 자석 교반기는 hydrophobic stir bar 표면에 국소적으로 강한 전단을 제시합니다. 회전 장치(Rotator)는 부드러운 유체 응력을 제공하지만 낮은 회전 주파수를 고려할 때 공기-물 내부 영역 및 표면 응력은 상대적으로 높습니다. 궤도 셰이커는 중간 수준의 스트레스를 제공하지만 일관된 생체-생체 동질성을 위한 크고 안정적인 플랫폼의 이점을 제공합니다.

Air-liquid interface generation rates
Figure 4. Air-liquid interface generation rates at maximum agitation frequencies (A) orbital shaker, (B) magnetic stirrer, (C) vortex mixer and (D) rotator.

우리는 설명한 각각의 교반 방법에서 유리 용기 안의 액체에 여러가지 응력이 동시에 작용한다는 것을 발견했다. 이러한 스트레스는 다양한 방법에 따라 다양했으며 종종 교란 주파수의 강력한 기능으로 밝혀졌다. 또한 알려진 유형과 강도의 스트레스를 가진 적절한 촉진 방법을 선택하면 단백질 분해 메커니즘에 대한 영향을 더 잘 이해하는 데 도움이 될 수 있다는 것도 알아냈습니다. 우리는 CFD가 실험 시스템에서 유체 응력의 특성을 파악하고 실제 조건에 대한 관련성을 검증하는 데 중요한 역할을 할 수 있다고 결론지었습니다.

Lab-on-a-chip – Thermocapillary actuation (열 모세관 작동)

Thermocapillary actuation (열 모세관 작동)

  • 열 효과를 사용한 랩온어칩의 미세 액체의 길
    – 온도에 의존하는 표면 장력
    – 외부의 기계적인 힘이 필요하지 않음
    – 프로그래밍이 가능한 마이크로 히터 어레이를 통해 열 효과 추가
  • 유체의 고유한 습윤성으로 인해 유체 손실이 발생
    – 열 모세관 작동 외에도 패턴화 된 (친수성 또는 소수성) 표면을 배치하여 손실을 최소화 할 수 있음

공간의 다양한 표면 장력

  • 차가운 유체에서 표면 장력이 높기 때문에 공간의 변화가 발생함
    – 높은 표면 장력으로 유체를 함께 유지
    – 유체가 따뜻한 곳에서 차가운 곳으로 당겨짐
    – 유체의 움직임은 다음의 식을 통해 알 수 있음

FLOW-3D에서의 시뮬레이션

  • 미세 액체는 인접 구역의 온도에 따라 움직임 (소수성과 친수성)

Computational Analysis of Drop Formation and Detachment

Computational Analysis of Drop Formation and Detachment

Introduction and Problem Statement

신속, 반복, 작은 물방울의 생성 및 증착, 작은 형상의 프린팅 또는 패터닝 (예 : l = 10-3-1 mm), 스프레이로  균일한 두께의 박막 형성은 다양한 산업에 매우 중요합니다(1-5). 액체 이동과 액적 형성 / 증착 공정은 복잡한 자유 표면 흐름, 자연적인 모세관운동 형성, thinning, pinch-off를 수반한다 (1-5). 단순한 뉴턴 및 비탄성 유체에 대해 액적 생성 및 액적 이동을 분석하기위한 실험적, 이론적 및 1 차원 시뮬레이션 연구가 진행되었지만 프린팅 또는 패터닝에 대한 기계론적인 이해는 여전히 과제로 남아 있습니다. 현재의 계산에 대한 주된 목표는 뉴턴 유체의 pinch-off에 대한 기계론적 이해를 얻기 위해 FLOW-3D에 내장된 VOF(volume-of-fluid) 접근법으로 시험하는 것입니다. 전산해석은 모세관, 관성, 점성 응력의 복잡한 상호 작용을 포착하여 자기유사 모세관의 thinning and pinch-off를 결정합니다. 뉴턴 유체의 물방울 형성 ​​및 분리현상은  전산해석으로부터 얻어진 자기유사 모세관현상 이론, 보편적인 축소화 기법인 1D 시뮬레이션 (1-7)과 실험 (1, 2, 8-12)을 이용하여 설명될 수 있음을 보여준다. 이러한 우리가 진행한 원형흐름 시뮬레이션은 유한한 시간의 비선형 역학, 위성 낙하현상, 복잡한 형상의 프린팅과 같이 어려운 전산해석의 기반이 될 것 입니다.

방울 형성의 전산 분석
그림 1 : FLOW-3D를 사용하여 시뮬레이션 한 저점도 유체의 드롭 형성 및 분리에 대한 전산해석 : (a) 5개의 저점도 유체에 대한 물방울의 necking에 대한 반경이 시간변화에 따라 표시됩니다. 물방울 necking의 반지름이 오른쪽에서 왼쪽으로 시간에 따른 전개를 보여줍니다. 마찬가지로 스냅 샷은 necking의 반경이 오른쪽에서 왼쪽으로 줄어듭니다. 속도의 크기 (단위 : cm/s) 와 화살표의 방향에 대한 컬러 맵을 사용하면 변형장을 결정할 수 있으며 Fluid 5 (표 1 참조)의 경우에는 순식간에 신장이됩니다. 이미지 II에 캡처 된 pinch-off 하기 전에 형성된 원추형 necking은 실험을 통해 얻은 necking 모양과 유사합니다.

Modeling Approach and Parameter Space

표면 장력 및 중력 모델을 적용한 FLOW-3D 에서 균일한 메쉬 크기를 사용하여 노즐에서 드롭 형성 및 분리에 대한 시뮬레이션을 수행하였습니다. 유한 체적의 유체를 떨어뜨리거나 분리하는 일은 물방울의 성장과 드롭, 노즐에 연결되는 모세관 현상, 관성, 점도 및 중력에 대한 상호 작용을 수반합니다. 시뮬레이션에서 스테인레스 강 노즐 ( {{D} _ {0}} = 2 {{R} _ {0}} = 1.7 \, \ text {mm}) 에서 유한 체적의 뉴턴 유체가 발생합니다. 표면 장력이 중력을 겪으면 새로 형성된 액적 분리가 발생합니다 (mg> 2 \ pi \ sigma {{R} _ {0}}). 시뮬레이션은 유체점도의 영향을 설명하기 위해 두 그룹으로 나누어져 있습니다: 저점도 유체 (글리세롤 함량이 40 % 미만인 물과 글리세롤/물 혼합물) 및 점도가 높은 유체 (예 : 글리세롤과 글리세롤/물 혼합물 점도 > 100x 물 점도). 두 그룹의 유체 특성은 각각 표 1과 2에 나와 있습니다.

계산 분석 드롭 형성 저점도

그림 2 : FLOW-3D를 사용하여 시뮬레이션 한 저점도 유체의 드롭형성 및 분리에 대한 전산 해석 : 반경 플롯에서 4개의 고점도 뉴톤유체에 대해 necking 반경을 시간변화에 따라 표시합니다. 낙하 분리 중 모세관 현상이 스냅 샷으로 표시됩니다. 컬러 맵은 Fluid 8의 속도 크기 (단위 : cm/s)의 변화를 포착합니다 (표2 참조). 화살표는 성장하는 물방울과 얇아지는 물방울내에서 흐름방향을 나타냅니다. FLOW-3D 시뮬레이션으로 얻은 necking 모양은 고점도의 뉴턴유체에 대한 특징인 원통형 유체요소로 이어집니다.

 

<표 1 : FLOW-3D를 사용하여 시뮬레이션 된 저점도 유체의 특성>
Fluid PropertyFluid 1Fluid 2Fluid 3Fluid 4Fluid 5
Viscosity [Pa · s]0.050.020.010.00750.005
Surface Tension  [mN / m]6868686868
Density [g / cm 3 ]11111
Ohnesorge Number0.210.080.040.030.021
 저점도 유체 (표 1의 유체 2) 가 노즐에서 떨어지는 것을 시뮬레이션 합니다. 색상변수는 속도크기 (단위 : cm / s)이며 속도벡터가 표시됩니다.

 

<표 2 : FLOW-3D를 사용하여 시뮬레이션 된 고점도 유체의 특성>
Fluid PropertyFluid 6Fluid 7Fluid 8Fluid 9
Viscosity [Pa · s]1.50.80.50.25
Surface Tension  [mN / m ]68686868
Density [g / cm 3 ]1111
Ohnesorge Number6.243.332.081.04

고점도 유체 (표 2의 유체 8) 가 노즐에서 떨어지는 것을 시뮬레이션 합니다. 색상변수는 속도크기 (단위 : cm / s) 이며 속도 벡터가 표시됩니다.

Discussion of the Simulation Results

드롭 형성 및 분리는 표1과 표2에 열거 된 유체에 대해 FLOW-3D 를 사용하여 시뮬레이션 하였고, 시간 경과에 따른 necking 모양, 반경을 분석하였습니다. 물방울의 necking 모양과 저점도에서의 necking에 대한 역학(그림 1 참조)은 실험, 흐름 이론, 1D 시뮬레이션, 자기유사 관성에 대한 모세현상의 특성을 나타냅니다 (1, 2, 6, 7, 13) :

(1)  \ displaystyle \ frac {{R (t)}} {{{{R} _ {0}}}} \ approx 0.8 R {{{{왼쪽} {R} {0} 3}}} 오른쪽}) ^ {{{{frac {1} {3}}} {{왼쪽 {{{{왼쪽}}} {2} {3}}}}

여기서 R (t)가  necking의 순간 반경이고, R0는 노즐의 외부반경이며,  \ displaystyle \ sigma 는 표면 장력,  \ displaystyle \ rho 는 유체의 밀도 tC 는 pinch-off 시간이다. 마찬가지로, 이러한 더 높은 점도의 뉴턴유체에 대한 반경 변화데이터는 시간에 따른 반경의 감소를 나타내는 것이며,  Papageorgiou’s visco-capillary scaling (8, 9)은 아래의 식으로 표현된다.

(2)  \ {0 \} {} {} {} {} {} {} {} {} {} {} {} {} { } ({{t} _ {p}} - t)

모세관 속도(표면 장력과 점도의 비)의 측정 값은 McKinley와 Tripathi (8)에 의해 Capillary Break-Up Extensional Rheometer (CaBER)라고 불리는 상업적으로 이용 가능한 장비를 사용하여 얻은 값과 모세관 속도는 공칭 표면 장력과 점도를 사용하여 계산됩니다.

FLOW-3D 는 물방울의 necking부분을 속도 벡터로 시각화하여 유체의 흐름을 나타낼 수 있습니다. 또한, 이는 그림 1과 같이 전단, 확장을 겪은 후 얇아지는 물방울이 흐르는 과정의 순간을 결정할 수 있는 가능성을 줍니다. 추가로, 낮은 점도의 뉴턴유체는 높은 점도의 뉴턴 유체에 비해 질적으로 다른 거동을 보여준다(그림 2참조). 낮은 점도의 뉴턴 유체에 대한 necking 프로파일은 이론(6,13)에 따라 자기 유사성이 됩니다.

Conclusions, Outlook and Ongoing work

우리의 예비결과는 FLOW-3D 기반의 전산해석이 액적 형성과 탈착의 기초가 되는 프로토타입의 자유 표면흐름을 시뮬레이션하는데 사용될 수 있음을 보여줍니다 . 시뮬레이션된 반경변화 프로파일이 실험적으로 관찰된 높은 유체 및 이론적으로 예측된 유체인 스케일링 법칙 및 pinch-off dynamics과 일치하는 것을 발견하였습니다.

자주 사용되는 1D 또는 2D 모델과 달리 FLOW-3D 는 기본 응력 및 확장 유동장 (균일도 및 크기)의 강도와 얇은 액체 필라멘트 내 흐름에 대한 시각화를 나타낼 수 있습니다(그림1과 2 참조). 확장 유동장과 연관된 흐름 방향 속도 구배는 모세관현상이 나타나는 물방울의 얇은 부분 내에서 발생합니다. 유동학적으로 복잡한 유체에서 non Newtonian shear 및 신장, 점도뿐만 아니라 그외의 탄성 응력이 nonlinear pinch-off dynamics을 급격하게 변화시킵니다(2, 10-12). 우리는 현재 점탄성과 non-Newtonian 유동학을 사용하여 FLow-3D에 복합 유체의 처리 성능평가를 위한 강력한 연산 프로토콜을 개발하고 있습니다.

References

  1. J. Eggers, Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phys. 69, 865-929 (1997).
  2. G. H. McKinley, Visco-elasto-capillary thinning and break-up of complex fluids. Rheology Reviews, 1-48 (2005).
  3. B. Derby, Inkjet Printing of Functional and Structural Materials: Fluid Property Requirements, Feature Stability, and Resolution. Annual Review of Materials Research 40, 395-414 (2010).
  4. O. A. Basaran, H. Gao, P. P. Bhat, Nonstandard Inkjets. Annual Review of Fluid Mechanics 45, 85-113 (2013).
  5. S. Kumar, Liquid Transfer in Printing Processes: Liquid Bridges with Moving Contact Lines. Annual Review of Fluid Mechanics 47, 67-94 (2014).
  6. R. F. Day, E. J. Hinch, J. R. Lister, Self-similar capillary pinchoff of an inviscid fluid. Phys. Rev. Lett. 80, 704-707 (1998).
  7. J. Eggers, M. A. Fontelos, Singularities: Formation, Structure, and Propagation. (Cambridge University Press, Cambridge, UK, 2015), vol. 53.
  8. G. H. McKinley, A. Tripathi, How to extract the Newtonian viscosity from capillary breakup measurements in a filament rheometer. J. Rheol. 44, 653-670 (2000).
  9. D. T. Papageorgiou, On the breakup of viscous liquid threads. Phys. Fluids 7, 1529-1544 (1995).
  10. J. Dinic, L. N. Jimenez, V. Sharma, Pinch-off dynamics and dripping-onto-substrate (DoS) rheometry of complex fluids. Lab on a Chip 17, 460-473 (2017).
  11. J. Dinic, Y. Zhang, L. N. Jimenez, V. Sharma, Extensional Relaxation Times of Dilute, Aqueous Polymer Solutions. ACS Macro Letters 4, 804-808 (2015).
  12. V. Sharma et al., The rheology of aqueous solutions of Ethyl Hydroxy-Ethyl Cellulose (EHEC) and its hydrophobically modified Analogue (hmEHEC): Extensional flow response in capillary break-up, jetting (ROJER) and in a cross-slot extensional rheometer. Soft Matter 11, 3251-3270 (2015).
  13. J. R. Castrejón-Pita et al., Plethora of transitions during breakup of liquid filaments. Proc. Natl. Acad. Sci. U.S.A. 112, 4582-4587 (2015).