On a hierarchy of approximate models for flows of incompressible fluids through porous solids Academic Article

abstract

• 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.

authors

• Rajagopal, Kumbakonam

published proceedings

• MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

author list (cited authors)

• Rajagopal, K. R.

citation count

• 196

complete list of authors

• Rajagopal, KR

publication date

• February 2007

publisher

• World Scientific Publishing  Publisher

published in

• Mathematical Models and Methods in Applied Sciences (M3AS)  Journal

keywords

• Biot's Equations
• Brinkman's Equation
• Darcy's Equation
• Interaction Forces
• Mixture Theory

Digital Object Identifier (DOI)

• 10.1142/S0218202507001899

start page

• 215

end page

• 252

volume

• 17

issue

• 2

URL

• http://dx.doi.org/10.1142/s0218202507001899