Free boundary problems for Stokes flow, with applications to the growth of biological tissues

King, John; Venkataraman, Chandrasekhar

Abstract

We formulate, analyse and numerically simulate what are arguably the two simplest Stokes-flow free boundary problems relevant to tissue growth, extending the classical Stokes free boundary problem by incorporating (i) a volumetric source (the nutrient-rich case) and (ii) a volumetric sink, a surface source and surface compression (the nutrient-poor case). Both two-and three-dimensional cases are considered. A number of phenomena are identified and characterised thereby, most notably a buckling-associated instability in case (ii).

Citation

King, J., & Venkataraman, C. (2021). Free boundary problems for Stokes flow, with applications to the growth of biological tissues. Interfaces and Free Boundaries, 23(4), 433–458. https://doi.org/10.4171/IFB/459

• Journal Article Type: Article
• Acceptance Date: Jan 29, 2021
• Online Publication Date: Nov 5, 2021
• Publication Date: Nov 6, 2021
• Deposit Date: Apr 25, 2021
• Publicly Available Date: Nov 5, 2021
• Journal: Interfaces and Free Boundaries
• Print ISSN: 1463-9963
• Electronic ISSN: 1463-9971
• Publisher: European Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 23
• Issue: 4
• Pages: 433–458
• DOI: https://doi.org/10.4171/IFB/459
• Keywords: Stokes-flow; tissue growth; moving boundary problems; finite element methods
• Public URL: https://nottingham-repository.worktribe.com/output/5495856
• Publisher URL: https://www.ems-ph.org/journals/show_abstract.php?issn=1463-9963&vol=23&iss=4&rank=1