##### Department of Mathematics,

University of California San Diego

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### Informal Seminar on Mathematics and Biochemistry-Biophysics

## Markus Schmuck

#### Math and Chemical Engineering, Imperial College, London

## Upscaling Of Ionic Transport Equations In Porous and Heterogeneous Media

##### Abstract:

We consider a classical continuum model which allows to describe essential electrokinetichenomena such as electro-phoresis and -osmosis. Applications and correspondingheory range from design of micro fluidic devices, energy storage devices,emiconductors to emulating communication in biological cells by synthetic nanopores. Based on this classical formulation, we derive effective macroscopic equationshich describe binary symmetric electrolytes in porous media. Theeterogeneous materials naturally induce corrected transport parameters which weall "material tensors". A better understanding of the influence ofeterogeneous media on ionic transport is expected by the new formulation.he new equations provide also an essential computational advantage by reliablyeducing the degrees of freedom required to resolve the microstructure. The presented results are gained by asymptotic multi-scale expansions.his formal procedure is then made rigorous by the derivation of error boundsetween the exact microscopic solution and the new upscaled macroscopic approximation.

Organizers: Li-Tien Cheng and Bo Li

### November 20, 2012

### 1:00 PM

### AP&M 5829

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