Supplementary Information file
Polarization behavior of polystyrene particles under direct current and
low frequency (<1 kHz) electric fields in dielectrophoretic systems.
Mario A. Saucedo-Espinosa, Mallory M. Rauch, Alexandra LaLonde, and
Blanca H. Lapizco-Encinas*
Microscale Bioseparations Laboratory, Rochester Institute of Technology, Rochester NY, US.
*Correspondence should be addressed to Blanca H. Lapizco-Encinas (PhD), Email: bhlbme@rit.edu
Mathematical model
COMSOL Multiphysics version 4.4 (COMSOL, Inc., Newton, MA) with the AC/DC module was used to
estimate the distribution of the electric field, the gradient of the electric field squared (E2), and particle
velocities, considering EK and DEP forces. The model used a mesh of approximately 17,000 elements
considering a two-dimensional model. Previous studies have demonstrated that electric field gradients along
the channel depth are negligible [1].
A brief description of the mathematical model used to predict the distribution and the average values of E2 is
included below. First, Laplace equation was employed to describe the distribution of the electric potential in
the microchannel:
 2  0
(1)
where  is the applied electric potential. Considering the posts and channel walls as insulating surfaces, the
following boundary conditions were employed in the model:
 
n  J  0 at the boundaries (channels walls and posts surfaces)
(2)
  Vinlet at the inlet of the microchannel
(3)
  Voulet at the outlet of the microchannel
(4)
where

n

is the normal vector to the surface, J is the electrical current density and Vinlet and Voutlet
are the electrical potentials at the microchannel inlet and outlet reservoirs, respectively.
Electrokinetic and dielectrophoresis theory
Besides DEP, the other forces present in DC-iDEP and low frequency AC-iDEP systems are electrophoresis
(EP) and electroosmotic (EO) flow. The superposition of EP and EO is called electrokinetic (EK) force. The
individual expressions for the EP, EO and EK, velocities and mobilities, are as follows [2]:


v EP   EP E
(5)
 p m

(6)
 EP 


vEOF  EOF E
 EOF  
(7)
 wall m

(8)

 


vEK   EK E   EOF   EP E  m   wall   p E



(9)

where vEP , vEO , and vEK are the EP, EO and EK velocities, respectively; and EP, EO and EK are the EP, EOF
and EK mobilities, respectively;  is the viscosity of the suspending medium and wall and p are the zeta
potentials of the microchannel wall and the particle, respectively.

The expressions for the DEP velocity vDEP and DEP mobility DEP are:

 

v DEP   DEP E  E

(10)
rp  m Re f CM 
2
 DEP 
3
(11)
Modeling of particle velocities
Figure 2 in the article depicts the predictions for particle velocities for 100-nm and 1-m particles, where
100-nm particles exhibited positive dielectrophoretic behavior and the 1-m particles exhibited negative
dielectrophoretic behavior. The fCM values employed in these simulations were 0.4 and -0.2 for the 100nm and 1-m particles, respectively. These predicitons were performed assuming an applied AC voltage
of 2,800 Vpp for both particles. Apparent zeta potential values ( app=- wall+p) were assumed to be -0.65
mV and -13.3 mV for the 100-nm and 1-m particles, respectively.
References
[1] Baylon-Cardiel, J. L., Lapizco-Encinas, B. H., Reyes-Betanzo, C., Chávez-Santoscoy, A. V., Martínez
Chapa, S. O., Lab Chip 2009, 9, 2896-2901.
[2] Moncada-Hernandez, H., Baylon-Cardiel, J. L., Pérez-González, V. H., Lapizco-Encinas, B. H.,
Electrophoresis 2011, 32, 2502-2511.