Effective equations governing an active poroelastic medium
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 r...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Published: |
Royal Society
2017
|
| Subjects: | |
| Online Access: | https://eprints.nottingham.ac.uk/39961/ |
| _version_ | 1848795954748063744 |
|---|---|
| author | Collis, Joe Brown, D.L. Hubbard, Matthew E. O'Dea, Reuben D. |
| author_facet | Collis, Joe Brown, D.L. Hubbard, Matthew E. O'Dea, Reuben D. |
| author_sort | Collis, Joe |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:40:18Z |
| format | Article |
| id | nottingham-39961 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:40:18Z |
| publishDate | 2017 |
| publisher | Royal Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-399612020-05-04T18:33:54Z https://eprints.nottingham.ac.uk/39961/ Effective equations governing an active poroelastic medium Collis, Joe Brown, D.L. Hubbard, Matthew E. O'Dea, Reuben D. 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. Royal Society 2017-02-22 Article PeerReviewed Collis, Joe, Brown, D.L., 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 Multiscale asymptotics Fluid-structure interaction Poroelasticity Growing media http://rspa.royalsocietypublishing.org/content/473/2198/20160755 doi: 10.1098/rspa.2016.0755 doi: 10.1098/rspa.2016.0755 |
| spellingShingle | Multiscale asymptotics Fluid-structure interaction Poroelasticity Growing media Collis, Joe Brown, D.L. Hubbard, Matthew E. O'Dea, Reuben D. Effective equations governing an active poroelastic medium |
| title | Effective equations governing an active poroelastic medium |
| title_full | Effective equations governing an active poroelastic medium |
| title_fullStr | Effective equations governing an active poroelastic medium |
| title_full_unstemmed | Effective equations governing an active poroelastic medium |
| title_short | Effective equations governing an active poroelastic medium |
| title_sort | effective equations governing an active poroelastic medium |
| topic | Multiscale asymptotics Fluid-structure interaction Poroelasticity Growing media |
| url | https://eprints.nottingham.ac.uk/39961/ https://eprints.nottingham.ac.uk/39961/ https://eprints.nottingham.ac.uk/39961/ |