Effective equations governing an active poroelastic medium

Collis, Joe and Brown, D.L. and Hubbard, Matthew E. and O'Dea, Reuben D. (2017) Effective equations governing an active poroelastic medium. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473 (2198). pp. 1-27. ISSN 1471-2946

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Abstract

In this work we consider the spatial homogenization of a coupled transport and fluid-structure interaction model, to the end of deriving a system of effective equations describing the flow, elastic deformation, and transport in an active poroelastic medium. The `active' nature of the material results from a morphoelastic response to a chemical stimulant, in which the growth timescale is strongly separated from other elastic timescales. The resulting effective model is broadly relevant to the study of biological tissue growth, geophysical flows (e.g. swelling in coals and clays) and a wide range of industrial applications (e.g. absorbant hygiene products). The key contribution of this work is the derivation of a system of homogenized partial differential equations describing macroscale growth, coupled to transport of solute, that explicitly incorporates details of the structure and dynamics of the microscopic system, and, moreover, admits finite growth and deformation at the pore-scale. The resulting macroscale model comprises a Biot-type system, augmented with additional terms pertaining to growth, coupled to an advection-reaction-diffusion equation. The resultant system of effective equations is then compared to other recent models under a selection of appropriate simplifying asymptotic limits.

Item Type: Article
Keywords: Multiscale asymptotics, Fluid-structure interaction, Poroelasticity, Growing media
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1098/rspa.2016.0755
Depositing User: Eprints, Support
Date Deposited: 19 Jan 2017 13:43
Last Modified: 30 Mar 2017 21:29
URI: http://eprints.nottingham.ac.uk/id/eprint/39961

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