It is well known that flows of Newtonian fluids in porous matrices are governed by Darcy's low. However the law for non-Newtonian fluids has not been established. In this paper, a modified Darcy's law for non-Newtonian fluids such as pseudo-plastic fluids and a Bingham solid is derived by applying the dimensional analysis to mathematical models of the fluids assuming a flow in the porous matrices as one in both thin films and capillaries.
JSME International Journal Series C Mechanical Systems, Machine Elements and Manufacturing
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JSME international journal. Ser. A, Mechanics and material engineering
JSME international journal. Ser. 1, Solid mechanics, strength of materials