Modeling of Dielectrophoresis for Handling Bioparticles in Microdevices

G. F. Yao

Flow Science Inc.683 Harkle Rd, Suite A

Santa Fe, NM 87505, USAEmail: gyao@flow3d.com

ABSTRACT

Dielectrophoresis can be used to trap and positionbioparticles such as biological cells efficiently and suc-cessfully in BioMEMS devices. This paper presents acomputational model to simulate this process. In partic-ular, the model will solve for electric potential distribu-tion, bioparticle movement in a Lagrangian frame, Jouleheating, and medium flow due to electrothermal effects.As an illustration, the model was used to simulate a celltrapping process in a three-dimensional chamber.

Keywords: dielectrophoresis, Joule heating, cell traps,electrothermal effects

NOMENCLATURE

CD drag coefficientE electric field intensityf force due to electrothermal effectFDEP dielectrophoretic forceK medium thermal conductivitymp particle massP pressurerp particle radiusU velocity of suspending mediumV particle velocityX particle location

Greek Symbols

ε medium permittivityε∗ complex medium permittivityε∗p complex particle permittivityµ dynamic viscosity of mediumω angular frequency of electric fieldφ electric potentialρ medium densityσ electric conductivity

1 INTRODUCTION

Dielectrophoresis (DEP) means the creation of forceson polarizable particles and the resulting movement ofthem in a nonuniform electric field (usually AC electricfields)[1-2]. Dielectrophoretic forces can be used as a

mechanism in various BioMEMS devices for character-ization, handling, and manipulation of microscale andnanoscale bioparticles including sorting, trapping, andseparating of cells, viruses, bacteria, and DNA etc.[3-8].For example, compared to traditional laboratory experi-ments, manipulating an individual cell or a group of cellsin various BioMEMS devices based on dielectrophoreticforce allows scientists to obtain new kinds of biologi-cal information, leading to new insights into how cellswork. Therefore, dielectrophoresis, as well as MEMSdevices based on it for operation, plays more and moreimportant roles in the study of biology and medical sci-ences and it has a broad range of applications in drugdiscovery, diagnostics, and cell therapy. Developing acomputer model to simulate a dielectrophoresis processis not only important and useful for design of new DEPdevices for bioscience applications, but also for optimaloperation of them. Motivated by these facts, a modelfor particle dielectrophoresis is developed and presentedin this paper.

As mentioned above, the dielectrophoretic force isutilized in various BioMEMS devices for handling biopar-ticles. The magnitude and direction of DEP forces de-pend on the frequency of the AC electric field, conduc-tivity and permittivity of both particles and the mediumwhere particles are suspended, and the gradient of elec-tric field. The gradient of electric field is dependenton the geometry and numbers of microelectrodes used.In addition, the strong electric fields adopted in dielec-trophoresis generate a large power density (Joule orOhmic heating) in the suspending medium. Due tohigh nonuniformity of electric field thereby power den-sity, a temperature gradient yields, which results in gra-dients of conductivity and permittivity. The formerproduces a free volume charge and a Coulomb forcewhile the latter creates a dielectric force. These twoforces cause medium flow, called electrothermal ef-fect, and give rise to an effect of dielectrophoresis ofbioparticles[9]. In present work, a comprehensive modelis developed. In addition to the calculation of electricfield and dielectrophoretic force on bioparticles, Jouleheating and electrothermal effects are also included inthe model. In the following section, the related govern-ing equations and numerical methods are described. Todemonstrate the application of the developed model, a

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three-dimensional cell culture chamber is simulated andthe results are presented in a separate section. Finally,the paper is ended by a brief conclusion.

2 GOVERNING EQUATIONS AND

NUMERICAL METHODS

Flow of a suspending medium is described by thefollowing incompressible mass and momentum conser-vation equations (The vector variables are representedin bold face in this paper.)

∇ · U = 0 (1)

ρ

[∂U∂t

+ U(∇ · U)]

= −∇P + µ∇2U + f (2)

where the force created due to aforementioned electrother-mal effects can be calculated by

f = −0.5(∇σ

σ− ∇ε

ε

)·E εE

1 + (ωσ/ε)2−0.25E2∇ε (3)

with gradients of σ and ε determined in terms of tem-perature distribution[9]. Temperature distribution dueto Joule heating is solved from

K∇2T + σE2 = 0 (4)

while movement of bioparticles due to dielectrophoresisis given by

mpdVdt

= −12πr2

pρCD|V − U|(V − U) + FDEP (5)

dXdt

= V (6)

with the dielectrophoretic force imposed on a bioparticlecalculated by

FDEP = 2πεr3p�

[ε∗p(ω) − ε∗(ω)ε∗p(ω) + 2ε∗(ω)

]∇E2 (7)

where � represents the real part of a complex number[2].Electric potential is derived by solving

∇2φ = 0 (8)

followed by the calculation of the electric field distribu-tion using

E = −∇φ (9)

The model presented here is implemented in FLOW-

3D�—a general purpose commercial CFD code. Inparticular,equations (1-4) and (8-9) are discretized in aset of fixed Eulerian grids or control volumes. Handlingof a complicated computational domain is performed us-ing a fraction- area- volume- obstacle- representation(FAVOR

TM) method[10]. The movement of bioparti-

cles are tracked by solving Eqns.(5-6) in a Lagrangianframe. Detailed numerical methods adopted to solve forthese governing equations can be found in [11].

Figure 1: Cell culture chamber geometry

-2.40

-1.60

-0.80

0.00

0.80

1.60

2.40

0

15115

30231

45347

60463

75579

90695

Figure 2: Top: electric potential; Bottom: electric fieldstrength

300.00

300.15

300.31

300.46

300.61

300.76

300.92

Figure 3: Temperature distribution

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Figure 4: Particle distribution at two different times

L

H

Figure 5: Velocity distribution

3 NUMERICAL RESULTS

To demonstrate the application of the presented model,a cell culture process in a three-dimensional chamberis simulated. The chamber geometry is displayed inFig.1 with a chamber diameter equal to 800 µm anda depth equal to 100 µm. Also shown in the samefigure are four microscale electrodes deposited on thebottom of the chamber which provide the electric po-tential. Experimental studies of cell trapping in thiskind of device was performed by Heida et al.[6-8]. Theviscosity, density, permittivity, and electric conductiv-ity of suspending medium used in the simulation are8.55×10−4 N · s/m2, 1000 kg/m3, 6.95×10−6 C2/Jm,and 0.1 Sm−1, respectively. The value of � appearingin Eqn.(7) can be obtained from the related handbookbased on the angular frequency ω for a specific medium-particle pair. In the simulation presented here, a valueof -0.1 was used.

Cell culture operation involves particle movement(cell trapping) due to dielectrophoresis, Joule heatingcreated by a strong electric field and electrothermal ef-fects corresponding to Joule heating. The model pre-sented here captures all these physical processes. Thetop of Fig.2 shows electric potential distribution cre-ated by four microscale electrodes on a cross section5 µm above the chamber bottom. The magnitude ofthe rms (root mean square) value of electric potentialon the electrode surface is 3 volts. The electric fieldstrength distribution at the same cross section is plot-ted in the bottom of Fig.2. As expected, strong electricfield strength was observed near the edges of electrodes.In particular, a “potential energy well” in the center ofthe chamber, with minimum electric field strength at itscenter, is formed where some cells are trapped. To seethe trapping, particle distribution at beginning of theoperation (top) and at a later time (bottom) are dis-played in Fig.4. Even though it is not possible to makea qualitative comparison between numerical predictionsand corresponding experimental measurements due tothe lack of detailed information on experimental condi-tions, a quantitative comparison with the experimentsperformed by Heida et al.[6-8] indicates that particledistribution derived from the present model is consis-tent with the experimental observation. Due to the highelectric field and sensitivity of bioparticles on temper-ature, Joule heating may be significant. The temper-ature distribution due to Joule heating is provided inFig.3. About a 1K temperature increase was observed.Medium flow around the ”potential energy well” due toelectrothermal effects are illustrated in Fig.5 with thetop figure representing flow in a vertical cross sectionpassing through the middle of chamber and the bottomfigure representing flow on a horizontal cross section im-mediately above the chamber bottom. It can be seenthat medium flow could affect cell trapping depending

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on the operation conditions.Here, we provide some results to illustrate the ap-

plication of the presented model. For the design of aBioMEMS device, engineers need to know how to deter-mine the number of microelectrodes and their geometry.For the use of these devices, it will be useful to know howto control different physical processes involved and getoptimal operation. To this end, the present model willbe useful for both design and operation of the relatedBioMEMS devices.

4 CONCLUSION

A computational model was developed and imple-mented in FLOW-3D�—a general purpose commer-cial CFD code—to solve for electric potential distribu-tion, Joule heating, and medium flow created by elec-trothermal effects. Numerical results derived from thesimulation of cell trapping in a three-dimensional cham-ber demonstrated that the present model could be usefulfor the design and operation of the related BioMEMSdevices.

REFERENCES

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