Driven particle flux through a membrane: Two-scale asymptotics of a diffusion equation with polynomial drift
arXiv: Analysis of PDEs(2018)
Abstract
Diffusion of particles through an heterogenous obstacle line is modeled as a two-dimensional diffusion problem with a one--directional nonlinear convective drift and is examined using two-scale asymptotic analysis. At the scale where the structure of heterogeneities is observable the obstacle line has an inherent thickness. Assuming the heterogeneity to be made of an array of periodically arranged microstructures (e.g. impenetrable solid rectangles), two scaling regimes are identified: the characteristic size of the microstructure is either significantly smaller than the thickness of the obstacle line or it is of the same order of magnitude. We scale up the convection-diffusion model and compute the effective diffusion and drift tensorial coefficients for both scaling regimes. The upscaling procedure combines ideas of two-scale asymptotics homogenization with dimension reduction arguments. Consequences of these results for the construction of more general transmission boundary conditions are discussed. We numerically illustrate the behavior of the upscaled membrane in the finite thickness regime and apply it to describe the transport of {rm CO}$_2$ through paperboard.
MoreTranslated text
AI Read Science
Must-Reading Tree
Example
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined