UPSCALING OF IONIC TRANSPORT EQUATIONS IN POROUS AND
Departments of Chemical Engineering and Mathematics
Imperial College, London
E-mail address: firstname.lastname@example.org
We consider a classical continuum model which allows to describe essential electrokinetic
phenomena such as electro-phoresis and -osmosis. Applications and corresponding
theory range from design of micro fluidic devices, energy storage devices,
semiconductors to emulating communication in biological cells by synthetic nanopores.
Based on this classical formulation, we derive effective macroscopic equations
which describe binary symmetric electrolytes in porous media. The
heterogeneous materials naturally induce corrected transport parameters which we
call "material tensors". A better understanding of the influence of
heterogeneous media on ionic transport is expected by the new formulation.
The new equations provide also an essential computational advantage by reliably
reducing the degrees of freedom required to resolve the microstructure.
The presented results are gained by asymptotic multi-scale expansions.
This formal procedure is then made rigorous by the derivation of error bounds
between the exact microscopic solution and the new upscaled macroscopic approximation.