engleski

Brinkman's law for polymer fluids

Well known results on the filtration laws for Newtonian fluids, obtained by the homogenization technique, served as motivation to derive similar, analogous counterparts for the specific type of a non-Newtonian fluid. We studied stationary filtration of a polymer fluid (Ostwald-de Waele model) through the periodic porous medium. Dimensions in the periodic domain are controlled by two small parameters, one representing the period and other controlling the ratio of a solid region and a fluid region of the porous medium. We found the specific critical size of the obstacles, representing the impermeable part, for which homogenization of the nonlinear Stokes flow results in a nonlinear Brinkman-type law by means of Gamma-convergence.

polymer fluids ; filtration ; homogenization ; Brinkman's law ; drag force function ; Gamma-convergence

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