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Effective equations governing an active poroelastic medium

Collis, Joe; Brown, D.L.; Hubbard, Matthew E.; O'Dea, Reuben D.

Authors

Joe Collis Joe.Collis@nottingham.ac.uk

D.L. Brown

Matthew E. Hubbard Matthew.Hubbard@nottingham.ac.uk

Reuben D. O'Dea reuben.odea@nottingham.ac.uk



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.

Journal Article Type Article
Publication Date Feb 22, 2017
Journal Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Print ISSN 1364-5021
Electronic ISSN 1471-2946
Publisher Royal Society, The
Peer Reviewed Peer Reviewed
Volume 473
Issue 2198
APA6 Citation Collis, J., Brown, D., Hubbard, M. E., & O'Dea, R. D. (2017). Effective equations governing an active poroelastic medium. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473(2198), https://doi.org/10.1098/rspa.2016.0755
DOI https://doi.org/10.1098/rspa.2016.0755
Keywords Multiscale asymptotics, Fluid-structure interaction, Poroelasticity, Growing media
Publisher URL http://rspa.royalsocietypublishing.org/content/473/2198/20160755
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0





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