Electrophoresis is the motion of a charged particle relative to the surrounding liquid due to an imposed external electric field1. Its applications include but are not limited to characterization and manipulation of organic and inorganic particles. In particular, electrophoresis has been applied to a variety of analytical separation problems involving nucleic acids, proteins and drugs. For electrophoresis on various Lab-on-a-chip platforms, the particles are of sizes comparable to the microchannel in which they flow. As such, particle-particle and particle-wall interactions are no longer negligible. Therefore, the electric field, the flow field and the particles motion are strongly coupled together. Numerical models based on a moving-grid method2 have been employed to investigate the related phenomena. Mesh regeneration as the particles move is an extra computational complication. To circumvent the complexity of mesh regeneration, a level-set based fixed-grid method3 is presented for electrophoretic motion of particles in this article. The particles are assumed to be a highly viscous liquid constraint to move with rigid body motion. A distance function is employed to represent the liquid-particle interfaces. The electric field, the flow field and the particles motion are governed respectively by the Poisson, the Navier-Stokes and the Euler-Newton equations. The effect of the electric field on the particle motion is accounted for by incorporating slip boundary conditions on the particles surfaces. The nonlinear governing equations are discretized and solved using a finite volume method4. The model is used to investigate electrophoretic motion of non-conducting circular and elliptical particles in a microsystem. Figure 1 shows the electrophoretic motion of a single circular particle in a microchannel. The induced electroosmotic flow is from the left to the right. The thick circles are the particle at t = 0. The direction of the particle movement is indicated by the arrows. The motions of the particle if neutral, positively or negatively charged are obviously different. Basically, a positively charged particle move faster than the main flow. However, a negatively charged particle flows slower. When the particle is highly charged negative, it can even flow against the streamwise direction toward upstream (+V) as in Fig. 1c. This suggests that there would be a situation where the particle can be kept static. Figure 2 shows the electrophoretic motion of multiple particles. The initial locations of the particles are shown in Fig. 2a. In the case of charged particles, particle 1, 2 and 3 are respectively negatively, neutral and positively charged. Particle 1 which is elliptical undergoes obvious rotational motion when charged (Fig. 2c). The case of the neutral particles (Fig. 2b) is included for comparison.

1.
Ghosal
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Electrokinetic flow and dispersion in capillary electrophoresis
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Ye
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3-D transient electrophoretic motion of a sphere particle in a T-shaped rectangular microchannel
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Y.F. Yap, J.C. Chai, T.N. Wong, N.T. Nguyen, K.C. Toh and H.Y. Zheng, Particle transport in microchannels, Numerical Heat Transfer (accepted).
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S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere Publisher, New York, 1980.
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