Upscaling of charge transport equations for strongly heterogeneous media

We consider the well-accepted Nernst-Planck-Poisson equations for describing charge transport and electrokinetic phenomena. Applications range from designing micro uidic devices, energy storage devices, and semiconductors, to emulating communication in biological cells by synthetic nanopores.ased on this well-accepted classical description, we derive a new set of e ective macroscopic equations which describe binary symmetric electrolytes in porous and strongly heterogeneous media. Heterogeneous materials require to correct transport parameters which we call material tensors". Our systematic upscaling by homogenization reliably shows how the micro-geometry inuences the transport on the macroscale. The new equations provide an essential computational advantage by a strong reduction of the degrees of freedom in comparison to the classical description which requires a full resolution of the pore geometry and hence a high-dimensional numerical problem. Finally, we can qualitatively and quantitatively characterize the suitability of the new upscaled equations for specific applications by error estimates which compare the exact microscopic solution with the solution of the new effective transport equations.

http://www.energy.hw.ac.uk/events2/icalrepeat.detail/2016/09/07/72/-/ups...