Journal
MATHEMATICS IN ENGINEERING
Volume 3, Issue 4, Pages -Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/mine.2021033
Keywords
heterogeneous porous media; asymptotic homogenization; locally unbounded source; ferrofluids; hierarchical materials
Categories
Funding
- EPSRC [EP/S030875/1]
Ask authors/readers for more resources
This study presents a new homogenized model for heterogeneous porous media by decoupling spatial variations and assuming periodicity at the fine scale to obtain a well-defined coarse scale Darcy-type model. The model can be used to predict the effects of externally applied magnetic (or electric) fields on ferrofluids (or electrolytes) flowing in porous media.
We derive a new homogenized model for heterogeneous porous media driven by inhomogeneous body forces. We assume that the fine scale, characterizing the heterogeneities in the medium, is larger than the pore scale, but nonetheless much smaller than the size of the material (the coarse scale). We decouple spatial variations and assume periodicity on the fine scale. Fine scale variations are formally reflected in a locally unbounded source for the arising system of partial differential equations. We apply the asymptotic homogenization technique to obtain a well-defined coarse scale Darcy-type model. The resulting problem is driven by an effective source which comprises both the coarse scale divergence of the average body force, and additional contributions which are to be computed solving a well-defined diffusion-type cell problem which is driven solely by fine scale variations of the given force. The present model can be used to predict the effect of externally applied magnetic (or electric) fields on ferrofluids (or electrolytes) flowing in porous media. This work can, in perspective, pave the way for investigations of the effect of applied forces on complex and heterogeneous hierarchical materials, such as systems of fractures or cancerous biological tissues.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available