Numerical Simulations of Dielectrophoresis Yuan Lin Gustav Amberg Fredrik Aldaeus Johan Roeraade firstname.lastname@example.org email@example.com firstname.lastname@example.org email@example.com KTH Mekanik Dielectrophoresis Superpositioned Dielectrophoresis Simulation of Trap-release Several strategies may be employed to increase the trap- Dielectrophoresis trap-and-release devices utilize theBasic Concept ping efﬁciency. In our simulation , superpositioned nDEP and pDEP in different time, by changing the fre-The subject of separating microsize particles with different electrical ﬁelds have been used for trapping particles more quency of AC ﬁeld . We also simulated this situa-properties is always of great interest. Among those meth- efﬁciently.That means, if an additional AC ﬁeld with a dif- tion.Following ﬁgure is the trace of 20 particles in the mi-ods, dielectrophoretic separation devices are most com- ferent frequency is applied on the system, it is possible to cro channel being trapped and released by the DEP forces.monly used as trap-and-release ﬁlters or particle sorters. have one ﬁeld with nDEP, and another frequency intro-Dielectrophoresis is the phenomenon that a polarizable duce nDEP. We assumed the experiment setup is like fol- 1particle will move in a converging electrical ﬁeld. If the lowingﬁeld is homogeneous, there will be no net force on the 0.5particle. If the ﬁeld is however heterogeneous, the parti- 0cle will have net force in the direction towards higher ﬁeld 0 2 4 6 8 10 12 14 16 18 20strength. If the particle is surrounded by a medium that is Also, different geometries of electrodes distribution aremore polarisable, the medium will have a larger motion in important, and they has been simulated.the 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 The dimensionless channel height is , the width of b Simulation of inter-particle DEP(pDEP), while the case of motion towards lower ﬁeld the electrodes and the distance between the electrodes In order to simulate the ’peal chains’, interactive forces duestrength is called negative dielectrophoresis (nDEP). Fol- were ,the radii of the ellipsoid E.coli are to dielectrophoretic dipole between particles must be in- ¦ c d c f b i plowing is the picture of pDEP. .While in the simulation, we cluded. Also a repulsive force between two particles when w ¦ ¦ R y $ c d c f t u b i i c d c c b regarded . Laminar ﬂow is assumed to bring they collide need to be introduced. Below we simulated ¦ ¦ $ i i i p the particles passing through the channel. 9 particles uniformly distributed in the uniform electric ﬁeld. Initially, the 9 particles are distributed as below: Simulation of Trapping Efﬁciency Based on the parameters above, we compare three kind of geome- tries, A,B,C. A only have pDEP force in bottom, B has pDEP both in the cell and bottom, and C has nDEP in the cell and bottom. We simulated E.coli, which is generally regarded to be After some time, the nine particles moved and formedImportant Parameters and Equations conducting and the cell membrane is assumed to be insulating. three short chains in the electric ﬁeld direction and repulseFor a spherical particle, the variation in the magnitude of We compute two kinds of solutions. One is, the particle trajec- each other in the direction perpendicular to the electricthe force with frequency is given by the real part of the tories in a medium conductivity solution: ﬁeld.Clausius-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 the Clausius-Mossotti factor, which is deﬁned as This shows that the interactive dielectrophoretic force we ¨ 1 3 ¨ (2) ¦ ¢ ) ¨ ) 1 4 6 ¨ ) 7 computed make sense. Then we simulated 5 particles in nonuniform electric ﬁeld like dielectrophoresis sorter de- Here, is the frequency of AC ﬁeld. In micro vices typically use. 5 particles are distributed in the mid-¨ ¦ ¨ 3 9 @ A C )ﬂows, the inertia effect could be neglected. If the inter- dle of channel, and they are attracted to the bottom whereactive forces and Brownian force are also neglected , we electrode edge gives the highest pDEP. We can still see thatthen get the simplest and most commonly used model as they form two ’peal chains’ ,which agrees with the experi-follow: ment photo. (3) D F ¦ 3 D H I Q 1from which,together with the formular for sphree dragforce for a sphere, (4) D H I Q ¦ R § T W However, while the particles are elliptic, which is the gen-we get how to compute the speed of particles From the ﬁgure above, we can see, that in this case, B type eral case in biology cells, the inter-particle DEP compu- can get highest trapping efﬁciency rate.(about 98 percents) tation would become much complicated. Moreover, the (5) R § T W ¦ § ¨ ¨ ! ` ! $ Another solution is high conductivity solution. hydrodynamics forces between particle and ﬂuid were also neglected in our computation, which also needs to be added to our model in future. Experimental Fact Work DistributionBelow are experiment photo to show how the biological The modeling and simulation work are done by the ﬁrstcells move under dielectrophoretic force.The cells shows and second authors. Third and fourth authors contributedthat the particles form the famous ’peal chains’, because to the idea of simulation in trapping efﬁency.they repulse each other in the direction perpendicular to Acknowledgementthe electric, and attract each other in the direction parallel Financial support from the Swedish Research Councilto the electric ﬁeld. (VR) is gratefully acknowledged. We also acknowledge Minh Do-Quang, Walter Villanueva and Jerome Hoepffner for helpful discussions. Reference ¨  Amberg,G.,Tonhardt,R.,Winkler,C. Math.Comp.Simulation,1999,49,257-274.  Aldaeus,F.,Lin,Y.,Roeraade,J.,Amberg,G., Electrophore- sis,2005,accepted. From the ﬁgure above, we know type C is the most efﬁ-  Aldaeus,F.,Lin,Y.,Roeraade,J.,Amberg,G.,”Multi- cient geometry, the trapping efﬁciency is about 100 per- stepped Dielectrophoretic Saparation”,to be submitted. cents. The simulation was calculated by ﬁnite element method in FemLego. 3D meshes and unstructured tetra- hedrad elements were used.