Technical Report MSC-2013-12

Title: Computational Electrokinetics
Authors: Roman Zeyde
Supervisors: Irad Yavneh
Abstract: In this work we study the electrokinetic migration of particles in an electrolyte solution due to the application of an external electric field, and propose a numerical framework for the iterative solution of such problems. The electrokinetic transport process can be used for transporting and manipulating microand nanoscale objects in many nanotechnology applications, nano-fluidic devices, packed-bed separation, desalination processes and various electrophoresis applications. Due to strong electrostatic forces, a thin boundary layer forms near the particle surface. This results in scale disparity of the boundary layer, which makes a full numerical solution challenging. We employ nonlinear macroscale effective boundary conditions that have been derived using the specific chemical properties of the particle (for an ion-exchanger particle by Yariv in [1] and for a surface charged inert particle by Schnitzer and Yariv in [2]). The resulting macroscale nonlinear partial differential system is discretized and an iterative Newton solver is constructed automatically from the discrete equations. Numerical results are obtained for an ion-exchanger and for a surface charged inert particle. An asymptotic analytical solution is used for the validation of the solver. The numerical results are compared to the asymptotic solutions, and good correspondence is achieved. Finally, the new solver is applied in the regime of moderately large values of the external field, where no analytical results are known. The numerical results uncover the strong-field scaling behavior, including a new boundary layer at the front of the particle that scales exponentially with respect to the external field, and also a well-defined dependence of the particle steady-state velocity on this field.
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