Effective equations governing an active poroelastic medium

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

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.

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

• Journal Article Type: Article
• Acceptance Date: Jan 16, 2017
• Publication Date: Feb 22, 2017
• Deposit Date: Jan 19, 2017
• Publicly Available 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: The Royal Society
• Peer Reviewed: Peer Reviewed
• Volume: 473
• Issue: 2198
• DOI: https://doi.org/10.1098/rspa.2016.0755
• Keywords: Multiscale asymptotics, Fluid-structure interaction, Poroelasticity, Growing media
• Public URL: https://nottingham-repository.worktribe.com/output/844753
• Publisher URL: http://rspa.royalsocietypublishing.org/content/473/2198/20160755