Aspects of diffusive-relaxation dynamics with a nonuniform, partially absorbing boundary in general porous media

We consider the Helmholtz problem in the context of the evolution of uniform initial distribution of a physical attribute in general porous media subject to a partially absorbing boundary condition. Its spectral property as a reflection of the boundary geometry has been widely exploited, such as in...

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Bibliographic Details
Published inPhysical review letters Vol. 103; no. 11; p. 118701
Main Authors Ryu, Seungoh, Johnson, David Linton
Format Journal Article
LanguageEnglish
Published United States 11.09.2009
Subjects
Absorption
Diffusion
Models, Biological
Models, Chemical
Models, Theoretical
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Summary:We consider the Helmholtz problem in the context of the evolution of uniform initial distribution of a physical attribute in general porous media subject to a partially absorbing boundary condition. Its spectral property as a reflection of the boundary geometry has been widely exploited, such as in biological and geophysical applications. We consider the situation where the critical assumptions which enable such applications break down. Specifically, what are the consequences of an inhomogeneous absorption strength? Using perturbation theory, exact theoretical results, and numerical simulations on random sphere packs, we identify the regions of parameter space in which such inhomogeneity is important and those in which it is not. Our findings shed light on the issue that limits the mapping between the diffusion or relaxation spectrum and the underlying boundary geometry.
ISSN:0031-9007
DOI:10.1103/PhysRevLett.103.118701