Figure 2. Simulation of droplet separation by EWOD

Non-Linear Electrohydrodynamics in Microfluidic Devices

미세 유체 장치의 비선형 전기 유체 역학

by Jun ZengHewlett-Packard Laboratories, Hewlett-Packard Company, 1501 Page Mill Road, Palo Alto, CA 94304, USAInt. J. Mol. Sci.201112(3), 1633-1649; 24 January 2011 / Revised: 10 February 2011 / Accepted: 24 February 2011 / Published: 3 March 2011


Since the inception of microfluidics, the electric force has been exploited as one of the leading mechanisms for driving and controlling the movement of the operating fluid and the charged suspensions. Electric force has an intrinsic advantage in miniaturized devices. Because the electrodes are placed over a small distance, from sub-millimeter to a few microns, a very high electric field is easy to obtain. The electric force can be highly localized as its strength rapidly decays away from the peak. This makes the electric force an ideal candidate for precise spatial control. The geometry and placement of the electrodes can be used to design electric fields of varying distributions, which can be readily realized by Micro-Electro-Mechanical Systems (MEMS) fabrication methods. In this paper, we examine several electrically driven liquid handling operations. The emphasis is given to non-linear electrohydrodynamic effects. We discuss the theoretical treatment and related numerical methods. Modeling and simulations are used to unveil the associated electrohydrodynamic phenomena. The modeling based investigation is interwoven with examples of microfluidic devices to illustrate the applications. 

Keywords: dielectrophoresiselectrohydrodynamicselectrowettinglab-on-a-chipmicrofluidicsmodelingnumerical simulationreflective display


미세 유체학이 시작된 이래로 전기력은 작동 유체와 충전 된 서스펜션의 움직임을 제어하고 제어하는 ​​주요 메커니즘 중 하나로 활용되어 왔습니다. 전기력은 소형 장치에서 본질적인 이점이 있습니다. 전극이 밀리미터 미만에서 수 미크론까지 작은 거리에 배치되기 때문에 매우 높은 전기장을 쉽게 얻을 수 있습니다. 

전기력은 강도가 피크에서 멀어지면서 빠르게 감소하기 때문에 고도로 국부화 될 수 있습니다. 이것은 전기력을 정밀한 공간 제어를 위한 이상적인 후보로 만듭니다.

전극의 기하학적 구조와 배치는 다양한 분포의 전기장을 설계하는 데 사용될 수 있으며, 이는 MEMS (Micro-Electro-Mechanical Systems) 제조 방법으로 쉽게 실현할 수 있습니다. 

이 논문에서 우리는 몇 가지 전기 구동 액체 처리 작업을 검토합니다. 비선형 전기 유체 역학적 효과에 중점을 둡니다. 이론적 처리 및 관련 수치 방법에 대해 논의합니다. 모델링과 시뮬레이션은 관련된 전기 유체 역학 현상을 밝히는 데 사용됩니다. 모델링 기반 조사는 응용 분야를 설명하기 위해 미세 유체 장치의 예와 결합됩니다. 

키워드 : 유전 영동 ; 전기 유체 역학 ; 전기 습윤 ; 랩 온어 칩 ; 미세 유체 ; 모델링 ; 수치 시뮬레이션 ; 반사 디스플레이

Droplet processing array Droplet based BioFlip
igure 1. Example of droplet-based digital microfluidics architecture. Above is an elevation view showing the layered structure of the chip. Below is a diagram illustrating the system (Adapted from [4]).
Figure 2. Simulation of droplet separation by EWOD
Figure 2. Simulation of droplet separation by EWOD. The top two figures illustrate the device configuration. Electric voltages are applied to all four electrodes embedded in the insulating material. The bottom left figure shows transient simulation solution. It illustrates the process of separating one droplet into two via EWOD. The bottom right figure shows the electric potential distribution inside the device. The color indicates the electric potential; the iso-potential surfaces are also drawn. The image shows the electric field is absent within the droplet body indicating the droplet is either conductive or highly polarizable.
Figure 4. Transient sequence of the Taylor cone formation
Figure 4. Transient sequence of the Taylor cone formation: simulation and experiment comparison. Experimental images are shown in the top row. Simulation results are shown in the bottom row. Their correspondence is indicated by the vertical alignment (Adapted from [4]).
Figure 6. Simulation of charge screening effect using a parallel-plate cell
Figure 6. Simulation of charge screening effect using a parallel-plate cell. Top-left image shows the electric current as function of time and driving voltage, top-right image shows the evolution of the species concentration as function of time and space, the bottom image shows the electric current readout after switching the applied voltage.
Figure 7. Transient simulation of electrohydrodynamic instability and the development of the cellular convective flow pattern.
Figure 7. Transient simulation of electrohydrodynamic instability and the development of the cellular convective flow pattern.
Figure 3. Simulation of dielectrophoresis driven axon migration
Figure 3. Simulation of dielectrophoresis driven axon migration. The set of small images on the left shows a transient simulation of single axon migration under an electric field generated by a pin electrode. The image on the right is a snapshot of a simulation where two axons are fused by dielectrophoresis using a pin electrode. Axons are outlined in white. Also shown are the iso-potential curves.


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[FLOW-3D 물리모델]Electro-mechanics / 기전역학

1. Electric Fields / 전기장

전기포텐셜은 계산영역 내에서 전하와 포텐셜 분포의 함수로 계산될 수 있다. 전기포텐셜은 Model Setup Physics Electro-mechanics 에서 활성화된다. Permittivity of vacuum 는 해석을 위해 시스템 단위에 맞게 지정되어야 한다. 해석하는 동안에 입자가 존재하면 입자전하가 정의되어야 한다. ; 영역 내 존재하는 모든 입자는 같은 전하를 갖는 것으로 가정한다. 게다가 Fluid electric charge field 모델은 또한 전기적으로 부하가 걸린 유체를 해석하도록 활성화 될 수가 있다.

유체#1 과 유체#2 의 전도도 및 유전체상수는 Fluids Properties Electrical Properties 에서 정의된다. Fluid electric charge field 가 사용되면 초기유체전하밀도는 Model Setup Meshing & Geometry Initial 에서 정의 된다. 그러나 전기포텐셜(전기장)은 계산영역 내에서 유체가 없이도 활성화 될 수 있다.

격자 경계에서의 조건들은 Model Setup Meshing & Geometry Mesh Boundaries 에서 정의된다. 전기 포텐셜의 경계조건은 전도 또는 절연일 수 있다. 한 경계는 Specified potential boundary 을 선택하고 그 경계에서의 전기 포텐셜의 특정 값을 지정함으로써 전도를 할 수가 있다. 또한 시간의 함수로 주어질 수도 있다. Fluid electric charge field 가 사용되면 밀도가 시간의 함수로 입구경계에서 정의될 수 있다.

계산영역 내에 고체구성요소가 존재하면 이들은 두 가지 형태를 갖는다: IOEPOTM 의 값에 따라 유전체거나 전도체. IOEPOTM 가 지정되지 않으면 그 구성요소는 고정 포텐셜을 갖는 것으로 간주된다. 이 속성들은 Meshing & Geometry Component Properties Electrical Properties 에서 정의된다. 구성요소의 초기부하밀도는 Meshing & Geometry Geometry Component Initial Electric Charge Density 에서 정의 된다.

포텐셜을 지배하는 Poisson 방정식의 해는 GMRES 반복법에 의해 구해진다. 수렴기준과 최대 반복수는 EPSELE 과 MAXPHIT에서 각기 정의된다. 두 매개변수 모두 적당한 디폴트 값을 가지며 일반적으로 이들을 변화시키지 않아야 한다. 이 모두 input (File Edit Simulation) 파일을 편집하여 변경된다.

See also:

  • Input Variable Summary and Units section Scalar Electrostatics, Electro-osmosis and Electromechanics Model Parameters
  • Model Reference -> Dielectrophoresis
  • Model Reference -> Electro-osmosis (Zeta Potential)
  • Model Reference -> Particles

2, Electro-osmosis (Zeta Potential) / 전기 삼투

많은 물질들(즉 실리카 또는 유리 같은)은 물(극성을 띠는)같은 매질(전해용액)과 접촉하게 될 때 표면전하를 가질 것이다. 이런 경우가 발생할 때에 EDL (Electric Double Layer)을 생성한다. EDL 이란 표면전하를 중립화하기 위해 양이온보다 많은 음이온이 존재하는 부하표면 가까이의 층을 말한다. 전기 포텐셜(zeta-potential) 이 실험적으로 측정될 수 있는 액체 고체쌍의 물성을 보여주는 EDL에 의해 생성된다. 전기삼투유동이 EDL 의 존재와 그 위에 부과된 외부 포텐셜로 인해 발생한다. 전기삼투를 모델링하기 위해 electric potential 모델이 Electric Fields 에서 기술된 바와 같이 Physics Electro-mechanics 에서 활성화되어야 한다. 전기삼투모델은 이때 같은 window 에서 활성화된다.


이 모델은 Physics Electro-mechanics 에서 정의되는 2개의 집중변수, F*C F/R*T 를 필요로 하는데 여기서 F 는 Faraday 상수, C 는 체적용액내의 이온농도, R 은 보편기체상수 그리고 T 는 Kelvin 단위의 주위 온도이다. 유체의 전기 물성치는 Fluids Properties Electrical Properties 에서 정의된다.

구성요소들의 전기적물성은 Meshing & Geometry Geometry Component Electrical Properties 에서 정의된다. 전기포텐셜 모델에서 필요한 물성에 추가하여 Zeta-potential 이 또한 정의되어야 한다. Zeta-potential 은 단지 개체(모든 격자 경계에서는 Zeta-potential 의 구배가 0으로 가정되어 있다.)와 관련되어 있고 디폴트 Zeta-potential 은 0이다.

See also:

3. Electro-thermal Effects / 전기열 효과

자유전하 및 Joule 발열은 물질의 전기전도에 따라 나타나는 두 결과이다. 전하의 형성, 이완 그리고 대류이송을 기술하는 전하밀도 방정식은 전기장 방정식과 함께 해석된다. 그 때에 전하층은 유체 경계면이나 유체와 전기와 유전체 힘을 유도하는 고체면사이의 경계에서 나타난다.

Joule 발열과 추가력이 전류에 의한 고체와 유체의 가열을 포함하도록 더해질 수 있다. 이런 모델들의 선택은 Physics Heat Transfer Fluid internal energy advectionPhysics Heat Transfer Full energy equation 에서 열에너지 전달의 활성화를 필요로 한다. 전기포텐셜모델 역시 Physics Electro-mechanics 에서 활성화되어야 한다.

electro-thermal forces 선택을 갖는 Joule 발열은 유전율과 온도에 따른 전도의 변화로 인해 발생하는 유체내의 힘들을 포함한다. 각 속성은 Permittivity temperature sensitivity, Conductivity temperature sensitivity 그리고 Electric field angular frequency 와 같이 Physics Electromechanics and Fluids에서 정의된다.

전기 전도도는 전기 열 효과가 작동하기 위해 유체에서 정의되어야 한다. 이는 Model Setup → Fluids → Fluid 1 or 2 → Electrical Properties 에서 정의된다.

4. Dielectrophoresis / 유전영동

유전력은 적용되는 전기장에서 유체분자 및 입자의 극성화에 의해 발생한다. 우선 전기 포텐셜 모델이 Physics → Electro-mechanics 에서 활성화되어야 한다. 그 후에 유전영동 모델은 같은 창에서 활성화된다. 유체에 대한 유전 속성은 Fluids → Properties → Electrical Properties 에서 정의된다.

형상 구성요소에서 관련물성은 Meshing & Geometry → Geometry → Component 에서 정의된다.

Electrical Properties:

유전영동 모델이 Physics → Electro-mechanics 에서 활성화되면 유전력은 1보다 큰 유전상수를 갖는 유체 안에서 작용한다. 유전력은 또한 모든 계산영역에 있는 질량입자에 적용된다. 이 경우 입자 유전율은 Physics → Electro-mechanics 에서 정의되어야 한다. 유전이동은 각 힘이 영향을 미치는 척도가 다르기 때문에 전기삼투모델과는 같이 사용될 수 없다. 유전이동모델은 전기삼투가 작동되면 자동적으로 비활성화된다. 전기삼투모델은 Physics → Electro-mechanics 에서 작동되는데 이 경우 추가 input 이 필요하고 같은 Electro-mechanics 창에서 주어질 수 있다. Meshing & Geometry → Geometry → Component Properties → Electrical Properties 에 있는 각 고체 구성요소에 대해 Zeta-potential 이 정의된다. Permittivity of vacuum (ELPERM)은 electrical units 에서 지정되는데 적정한 전기단위(즉, MKS 단위의 경우 볼트의 포텐셜, 쿨롱의 전하에 대해 ELPERM = 8.8542×10-12 C/(V m))를 반영하도록 정의되어야 한다. 모든 유전율들은 물질의 유전상수에 대한 진공의 유전상수 비율로 나타난다.

두 implicit solver, GMRES ADI 가 전기 포텐셜 방정식 풀이에 이용된다.
See also:
• Model Reference -> Electric Fields.
• Model Reference -> Electro-osmosis (Zeta Potential).
• Flow Science Technical Note 56 on modeling dielectric phenomena at

Electro-Hydrodynamics of Semi-Conductive Fluids With Application to Electro-Spraying

It has long been known that strong electric fields can disrupt liquid surfaces. One particularly useful application of this observation has been the development of electrospray-ionization (ESI) systems.

The basic concept is to eject liquid from a nozzle connected to a voltage source that has a relatively high electric potential compared to its surroundings. When adjusted for certain operating conditions, a thin jet of liquid is ejected from the nozzle that subsequently breaks up into charged droplets having a relatively uniform size. There are many useful industrial applications for a system that produces small droplets of specified size; particularly if the droplets don’t coalesce because of their electrical repulsion.

Having a charge also means that these drops can be electrically deflected toward a target. This technology, for example, has been advantageously applied to paint spraying, atomization of fuels, printing, mass spectroscopy and a variety of spray drying processes.

Addition of Dielectric Phenomena to FLOW-3D

There are situations where it would be helpful to account for the interaction of electric fields with liquid and solid materials. For example, electrostatic air cleaners rely on the ability to attract small particles in flowing air to a surface where they can be collected and removed from the air. In this case the primary attractive force arises from dielectric polarization of the particles.
Spraying liquid drops onto a surface, as in spray painting, is often improved by electrifying the drops so that they repel one another and produce a more uniform distribution. Also, electrified drops can be driven to overcome air resistance by suitable electric fields.
In many types of micro-electrical-mechanical-systems (MEMS) fluids are caused to move by the application of electric potentials. Usually this behavior is induced by electric forces acting on dielectric polarization charges generated at free fluid surfaces or at the interfaces between two fluids.

In some situations the effects of both dielectrically induced charges as well as free electric charges in a fluid must be considered. For these cases the fluid has some nonzero conductivity that must be accounted for by tracking charge densities and adding additional body forces to the fluid. The range of possibilities when conduction is present includes bound and free charges, recombination, ionization, currents without net charge densities, etc. As described next, we shall limit the present development to a useful subset of the many possibilities.

In this note we describe a set of program developments that give FLOW-3DÒ the capability to model fluid and particulate flows involving both free and induced charge densities. In the current released version of FLOW-3D® (Ver. 7.7) both particles and fluid can contain a fixed charge density, but there is no provision for dielectric materials.

Here we describe the addition of dielectric properties for particles, fluids, and solids. In addition, linear polarization forces acting on particles and fluids by electrostatic fields are added to the momentum equations for fluid and particles.

Self-Consistent Electric Fields and Electric Forces On Charged Particles

A recent addition to the computational fluid dynamics program FLOW-3D® is a capability for modeling discrete mass particles moving through a continuum. This model implicitly couples
the particles and continuum so that they may exchange momentum in a conservative way.
This report addresses how that model has been extended to account for mass particles having an electric charge and moving in an electric field. The extension is self-consistent in the sense that
the particle charges contribute to the electric field. For this reason the field is time dependent and must be recomputed for each time step of a numerical simulation.
In addition to the charged particles, solid objects (obstacles) located within the computational region may be assigned arbitrary, but constant in time, potentials. Each obstacle may have a
fixed potential value consistent with the obstacle being a conductor. A zero potential value is the default value if not otherwise specified. It should be noted that an electric potential can be
computed even when there are no charged particles, although this field will have no effect on flow processes unless the user adds some kind of additional interaction to the model.
Mesh boundaries that are rigid walls may be assigned non-zero potential values. All other boundaries are treated as symmetry boundaries with respect to the potential. Furthermore, no
insulated obstacles are allowed in this model. It is also assumed that if there are free fluid surfaces or fluid-fluid interfaces then the dielectric constants (i.e., ratios of material permittivities
to that of vacuum) of the different materials must be the same, otherwise additional development will be needed to solve for the electric potential. In general, this is not correct because the
dielectric constant does vary with material type; for example, water has a dielectric constant about 81 times that for air.