1. Numerical Simulations of
Dielectrophoresis
Yuan Lin Gustav Amberg Fredrik Aldaeus Johan Roeraade
yuan@mech.kth.se gustava@mech.kth.se aldaeus@analyt.kth.se jroe@analyt.kth.se
KTH Mekanik
Dielectrophoresis Superpositioned Dielectrophoresis Simulation of Trap-release
Several strategies may be employed to increase the trap- Dielectrophoresis trap-and-release devices utilize the
Basic Concept
ping efficiency. In our simulation [2], 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 [3]. 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- 1
particle will move in a converging electrical field. If the
lowing
field is homogeneous, there will be no net force on the 0.5
particle. If the field is however heterogeneous, the parti- 0
cle will have net force in the direction towards higher field 0 2 4 6 8 10 12 14 16 18 20
strength. If the particle is surrounded by a medium that is Also, different geometries of electrodes distribution are
more polarisable, the medium will have a larger motion in important, and they has been simulated.
the direction of higher field, hence pushing the particle in
the direction towards lower field strength
If the motion is in the direction towards higher field
strength, 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 due
strength 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 p
lowing 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 formed
Important Parameters and Equations conducting and the cell membrane is assumed to be insulating. three short chains in the electric field direction and repulse
For 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 electric
the 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 where
active forces and Brownian force are also neglected , we electrode edge gives the highest pDEP. We can still see that
then 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
1
from which,together with the formular for sphree drag
force 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 Distribution
Below are experiment photo to show how the biological The modeling and simulation work are done by the first
cells move under dielectrophoretic force.The cells shows and second authors. Third and fourth authors contributed
that 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 Acknowledgement
the electric, and attract each other in the direction parallel Financial support from the Swedish Research Council
to the electric field. (VR) is gratefully acknowledged. We also acknowledge
Minh Do-Quang, Walter Villanueva and Jerome Hoepffner
for 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.
From the figure above, we know type C is the most effi- [3] 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.[1] 3D meshes and unstructured tetra-
hedrad elements were used.