Numerical modeling of floating potentials in electrokinetic problems

Floating potentials appear in electrokinetic problems when isolated domains with high conductivity are introduced. An asymptotic development is proposed in order to avoid the direct computation that leads to inaccurate numerical results when the contrast of conductivity is strong. We show that the problem where perfect conductors are assumed is the zero order solution of the initial problem; the solution can then be refined introducing a first order correction that implies two successive problems defined inside and outside the domains with high conductivity. The proposed example deals with a four electrodes system designed to both induce electroporation in a biological tissue sample and measure the resulting impedance. The proposed approach is extended to a nonlinear problem by taking advantage of the iterative solution that is necessary applied in this case