Numerical Modeling of Floating Potentials in Electrokinetic Problems Using an Asymptotic Method

Abstract

Floating potentials appear in electrokinetic problems when isolated high-conductive materials are included in a dielectric or weakly conductive ambient medium. The large contrast of conductivities generates numerical issues that make hard the computation of the electric potential. This article proposes a rigorous numerical method to tackle this kind of problem. Interestingly, a correction to the case of a perfect conductor is given in order to improve the accuracy of the computation. The method involves a cascade of two elementary problems set, respectively, in the ambient medium and in the high-conductive inclusions. An example is proposed with a 4-electrode system designed to both induce electroporation in a biological tissue sample and measure the resulting impedance. The approach is extended to a nonlinear problem by taking advantage of the iterative scheme that is necessarily applied in this case.