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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Marcus Schmuck
MIT
Title: A Porous Media Approximation of the Stokes-Poisson-Nernst-Planck Equations

Abstract: We first introduce a classical continuum model which allows to describe essential electrokinetic phenomena as electro-phoresis and -osmosis. Applications and corresponding theory range from design of micro uidic devices, energy storage devices, semiconductors over modeling communication in biological cells by nanopores.

Based on this classical formulation, we derive effective macroscopic equations which describe binary symmetric electrolytes in porous media. The inhomogeneous structure of porous materials naturally induces additional nonlinearities which are called material tensors. A better understanding of geometric effects in heterogeneous media on ionic transport is expected by the new formulation. The numerical advantage bases on a strong reduction of the degrees of freedom by upscaling the microstructure. The results are gained by the two-scale convergence method. In the remaining part of the talk, we motivate the derivation of first error bounds between the exact microscopic solution and its upscaled macroscopic approximation.

Date: Tuesday, November 9, 2010
Time: 1:30 pm
Location: Wean Hall 8220
Submitted by:  Noel Walkington