Numerical Simulations ofDielectrophoresis

Yuan Lin Gustav Amberg Fredrik Aldaeus Johan Roeraadeyuan@mech.kth.se gustava@mech.kth.se aldaeus@analyt.kth.se jroe@analyt.kth.se

KTH Mekanik

Dielectrophoresis

Basic ConceptThe subject of separating microsize particles with differentproperties is always of great interest. Among those meth-ods, dielectrophoretic separation devices are most com-monly used as trap-and-release filters or particle sorters.Dielectrophoresis is the phenomenon that a polarizableparticle will move in a converging electrical field. If thefield is homogeneous, there will be no net force on theparticle. If the field is however heterogeneous, the parti-cle will have net force in the direction towards higher fieldstrength. If the particle is surrounded by a medium that ismore polarisable, the medium will have a larger motion inthe direction of higher field, hence pushing the particle inthe direction towards lower field strengthIf the motion is in the direction towards higher fieldstrength, it is referred to as positive dielectrophoresis(pDEP), while the case of motion towards lower fieldstrength is called negative dielectrophoresis (nDEP). Fol-lowing is the picture of pDEP.

Important Parameters and EquationsFor a spherical particle, the variation in the magnitude ofthe force with frequency is given by the real part of theClausius-Mossotti factor. The full expression for the time-averaged DEP force for a sphere particle is

� � � � � � � � � � � � � � �(1)

Here,�

is the radius of particle.�

is the real part of theClausius-Mossotti factor, which is defined as

� � � � � � ! �� # $ � � % (2)

� � ! '( * Here, + is the frequency of AC field. In microflows, the inertia effect could be neglected. If the inter-active forces and Brownian force are also neglected , wethen get the simplest and most commonly used model asfollow: � - / � ! � - 0 2 3

(3)

from which,together with the formular for sphree dragforce for a sphere,

� - 0 2 3 � 4 � 7 � 9(4)

we get how to compute the speed of particles

4 � 7 � 9 � � � � � � � � = � �(5)

Experimental FactBelow are experiment photo to show how the biologicalcells move under dielectrophoretic force.The cells showsthat the particles form the famous ’peal chains’, becausethey repulse each other in the direction perpendicular tothe electric, and attract each other in the direction parallelto the electric field.

Superpositioned DielectrophoresisSeveral strategies may be employed to increase the trap-ping efficiency. In our simulation [2], superpositionedelectrical fields have been used for trapping particles moreefficiently.That means, if an additional AC field with a dif-ferent frequency is applied on the system, it is possible tohave one field with nDEP, and another frequency intro-duce nDEP. We assumed the experiment setup is like fol-lowing

The dimensionless channel height is > , the width of

the electrodes and the distance between the electrodeswere ? @ ? C >

,the radii of the ellipsoid E.coli are E G �? @ ? C J L > N E � � E � � ? @ ? ? 4 O >

.While in the simulation, weregarded E G � E � � E � . Laminar flow is assumed to bringthe particles passing through the channel.

Simulation of Trapping EfficiencyBased on the parameters above, we compare three kind of geome-tries, A,B,C. A only have pDEP force in bottom, B has pDEPboth in the cell and bottom, and C has nDEP in the cell andbottom. We simulated E.coli, which is generally regarded to beconducting and the cell membrane is assumed to be insulating.We compute two kinds of solutions. One is, the particle trajec-tories in a medium conductivity solution:

From the figure above, we can see, that in this case, B typecan get highest trapping efficiency rate.(about 98 percents)Another solution is high conductivity solution.

From the figure above, we know type C is the most effi-cient geometry, the trapping efficiency is about 100 per-cents. The simulation was calculated by finite elementmethod in FemLego.[1] 3D meshes and unstructured tetra-hedrad elements were used.

Simulation of Trap-releaseDielectrophoresis trap-and-release devices utilize thenDEP and pDEP in different time, by changing the fre-quency of AC field [3]. We also simulated this situa-tion.Following figure is the trace of 20 particles in the mi-cro channel being trapped and released by the DEP forces.

0 2 4 6 8 10 12 14 16 18 200

0.5

1

Also, different geometries of electrodes distribution areimportant, and they has been simulated.

Simulation of inter-particle DEPIn order to simulate the ’peal chains’, interactive forces dueto dielectrophoretic dipole between particles must be in-cluded. Also a repulsive force between two particles whenthey collide need to be introduced. Below we simulated9 particles uniformly distributed in the uniform electricfield. Initially, the 9 particles are distributed as below:

After some time, the nine particles moved and formedthree short chains in the electric field direction and repulseeach other in the direction perpendicular to the electricfield.

This shows that the interactive dielectrophoretic force wecomputed make sense. Then we simulated 5 particles innonuniform electric field like dielectrophoresis sorter de-vices typically use. 5 particles are distributed in the mid-dle of channel, and they are attracted to the bottom whereelectrode edge gives the highest pDEP. We can still see thatthey form two ’peal chains’ ,which agrees with the experi-ment photo.

However, while the particles are elliptic, which is the gen-eral case in biology cells, the inter-particle DEP compu-tation would become much complicated. Moreover, thehydrodynamics forces between particle and fluid werealso neglected in our computation, which also needs to beadded to our model in future.

Work DistributionThe modeling and simulation work are done by the first

and second authors. Third and fourth authors contributedto the idea of simulation in trapping effiency.AcknowledgementFinancial support from the Swedish Research Council

(VR) is gratefully acknowledged. We also acknowledgeMinh Do-Quang, Walter Villanueva and Jerome Hoepffnerfor helpful discussions.

Reference[1] Amberg,G.,Tonhardt,R.,Winkler,C.

Math.Comp.Simulation,1999,49,257-274.

[2] Aldaeus,F.,Lin,Y.,Roeraade,J.,Amberg,G., Electrophore-sis,2005,accepted.

[3] Aldaeus,F.,Lin,Y.,Roeraade,J.,Amberg,G.,”Multi-stepped Dielectrophoretic Saparation”,to be submitted.