On modelling the parallel diffusion flow in deforming porous media

Robert Cimrman and Eduard Rohan

Mathematics and Computers in Simulation (MATCOM), 2007, vol. 76, issue 1, 34-43

Abstract: We present a macroscopic model of the fluid diffusion in deformable porous media, motivated by diffusion-deformation phenomena influencing the heart muscle blood perfusion, or the mechanical properties of kidneys. The problems are described by the displacement field and by several fluid pressure fields associated with parallel porosities interpenetrating the material matrix and mutually separated by interface sectors. The model consists of the equilibrium equation, and a number of mass conservation equations, each incorporating the Darcy law of fluid diffusion. The steady state problem attains the form of the Barenblatt model of parallel flows, while, in the non-steady regime, the coupled diffusion and deformation phenomena induce the apparent viscoelastic behaviour of the bulk material. Numerical examples are given to illustrate some features of the finite element model.

Keywords: Parallel diffusion; Heart modelling; Kidney modelling; Darcy flow (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:76:y:2007:i:1:p:34-43

DOI: 10.1016/j.matcom.2007.01.034

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