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. The paper proposes a rigorous numerical method to tackle such kind of problems. Interestingly, a correction to the case of 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.

Floating Potential Boundary Condition in Smooth Domains in an Electroporation Context

“…This paper also provides an efficient numerical method to compute accurately the floating potential problem in the case of N highly conductive inclusions, by replacing the PDE with nonlocal constraints on the total flux along the interfaces by the resolution of N + 1 Dirichlet problems uncoupled, the solution of the floating potential problem being obtained thanks to the inversion of a definite Gram matrix of size N . This efficient and rigorous approach has been used recently by the authors and colleagues in [12].…”

“…The computation of the electroquasistatic electric field in high contrasted domains is a research field which is active for several decades in both electrical engineering and applied mathematics research areas [3,1,9,4,12]. The interest has increased a lot for the last decade with the use of pulse electric field for clinical ablation [7,8,5].…”