Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Chair in Applied Mathematics



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BibTex format

author = {Degond, P and Ferreira, M and Merino-Aceituno, S and Nahon, M},
journal = {SIAM: Multiscale Modeling and Simulation},
title = {A new continuum theory for incompressible swelling materials},
url = {},

RIS format (EndNote, RefMan)

AB - Swelling media (e.g. gels, tumors) are usually described by mechanical constitutive laws (e.g. Hooke or Darcy laws). However, constitutive relations of real swelling media are not well-known. Here, we take an opposite route and consider a simple packing heuristics, i.e. the particles can’t overlap. We deduce a formula for the equilibrium density under a confining potential. We then consider its evolution when the average particle volume and confining potential depend on time under two additional heuristics: (i) any two particles can’t swap their position; (ii) motion should obey some energy minimization principle. These heuristics determine the medium velocity consistently with the continuity equation. In the direction normal to the potential level sets the velocity is related with that of the level sets while in the parallel direction, it is determined by a Laplace-Beltrami operator on these sets. This complex geometrical feature cannot be recovered using a simple Darcy law.
AU - Degond,P
AU - Ferreira,M
AU - Merino-Aceituno,S
AU - Nahon,M
SN - 1540-3459
TI - A new continuum theory for incompressible swelling materials
T2 - SIAM: Multiscale Modeling and Simulation
UR -
ER -