Nonlinear electrophoresis of ideally polarizable particles: a numerical approach
Bruno Figliuzzi (MIT), Cullen Buie (Massachusetts Institute of Technology), Wai Chan (Massachusetts Institute of Technology)
Electrohydrodynamics and electrokinetics of fluid systems
Mon 10:45 - 12:15
Barus-Holley 161
Despite continuous interest, nonlinear electrophoresis of ideally polarizable particles is not perfectly understood. When high voltages are applied, the conductivity of the electric double layer which forms around the particle increases, leading to significant ionic exchanges with the outer bulk solution. The velocity field, the electric potential and the ionic concentration in the immediate vicinity of the particle are then described by a complicated set of coupled nonlinear partial differential equations. Khair and Squires have recently shown that these equations can be linearized in the limit of a weak applied field, which enables further analytical progress (Phys. Fluids, 2010). Similarly, Schnitzer and Yariv found an analytical solution in strongly nonlinear regime, where ionic transport is dominated by advection in the bulk solution (J. Fluid Mech., 2012). However, in the general case, the equation governing the electrophoretic motion of the particle must be solved numerically. In this study, we rely on a numerical approach to determine the electric potential, ionic concentration and velocity field in the bulk solution surrounding the particle. The simulations are of particular interest in the strongly nonlinear regime, where advection cannot be neglected in the bulk solution. Advective transport introduces a coupling between the ionic concentration and the velocity field. In this situation, the calculation of the electrophoretic mobility of the particle can only be achieved through a complete determination of the velocity field. The numerical simulation uses a pseudo-spectral method based on Chebyshev polynomials which was used successfully by Chu and Bazant to determine the electric potential and the ionic concentration around an ideally polarizable metallic sphere (Physical Review E, 2006).