Journal
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
Volume 17, Issue 2, Pages 215-252Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202507001899
Keywords
Darcy's equation; mixture theory; interaction forces; Brinkman's equation; Biot's equations
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The celebrated equations due to Fick and Darcy are approximations that can be obtained systematically on the basis of numerous assumptions within the context of mixture theory; the equations however not having been developed in such a manner by Fick or Darcy. Relaxing the assumptions made in deriving these equations via mixture theory selectively leads to a hierarchy of mathematical models and it can be shown that popular models due to Brinkman, Biot and many others can be obtained via various approximations. It is shown that a variety of other generalizations are possible in addition to those that are currently in favor, and these might be appropriate for describing interesting technological applications.
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