Effective governing equations for heterogenous porous media subject to inhomogeneous body forces

Penta, R. , Ramirez Torres, A. , Merodio, J. and Rodríguez-Ramos, R. (2021) Effective governing equations for heterogenous porous media subject to inhomogeneous body forces. Mathematics in Engineering, 3(4), pp. 1-17. (doi: 10.3934/mine.2021033)

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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.

Item Type:Articles
Additional Information:ART acknowledges the Dipartimento di Scienze Matematiche (DISMA) “G.L. Lagrange” of the Politecnico di Torino, “Dipartimento di Eccellenza 2018-2022, project no. E11G18000350001”
Glasgow Author(s) Enlighten ID:Ramirez Torres, Dr Ariel and Penta, Dr Raimondo
Authors: Penta, R., Ramirez Torres, A., Merodio, J., and Rodríguez-Ramos, R.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Mathematics in Engineering
Publisher:AIMS Press
ISSN (Online):2640-3501
Published Online:21 August 2020
Copyright Holders:Copyright © 2021 the Author(s), licensee AIMS Press
First Published:First published in Mathematics in Engineering 3(4):1-17
Publisher Policy:Reproduced under a Creative Commons license

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
303232EPSRC Centre for Multiscale soft tissue mechanics with MIT and POLIMI (SofTMech-MP)Xiaoyu LuoEngineering and Physical Sciences Research Council (EPSRC)EP/S030875/1M&S - Mathematics