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Calculation of effective diffusivities for biofilms and tissues
Author(s) -
Wood Brian D.,
Quintard Michel,
Whitaker Stephen
Publication year - 2002
Publication title -
biotechnology and bioengineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.136
H-Index - 189
eISSN - 1097-0290
pISSN - 0006-3592
DOI - 10.1002/bit.10075
Subject(s) - thermal diffusivity , simple (philosophy) , work (physics) , scale (ratio) , biological system , mass diffusivity , diffusion , biofilm , complex system , basis (linear algebra) , statistical physics , mechanics , thermodynamics , computer science , physics , mathematics , geometry , geology , biology , paleontology , philosophy , epistemology , quantum mechanics , bacteria , artificial intelligence
Abstract In this study we describe a scheme for numerically calculating the effective diffusivity of cellular systems such as biofilms and tissues. This work extends previous studies in which we developed the macroscale representations of the transport equations for cellular systems based on the subcellular‐scale transport and reaction processes. A finite‐difference model is used to predict the effective diffusivity of a cellular system on the basis of the subcellular‐scale geometry and transport parameters. The effective diffusivity is predicted for a complex three‐dimensional structure that is based on laboratory observations of a biofilm, and these numerical predictions are compared with predictions from a simple analytical solution and with experimental data. Our results indicate that, under many practical circumstances, the simple analytical solution can be used to provide reasonable estimates of the effective diffusivity. © 2002 John Wiley & Sons, Inc. Biotechnol Bioeng 77:495–516, 2002; DOI 10.1002/bit.10075