engleski

Asymptotic Analysis of the Polymer Fluid Flow through a Porous Medium

By its simplicity and its importance in the problems of fluid mechanics, Newton's model plays the major role postulating linear relationship between the viscous stress tensor and the symmetrized gradient of the velocity. In certain cases however, this model is not adequate because the viscosity simply isn't constant, but rather changes significantly with the increased shear stress.\\ Of all these so-called non-Newtonian or quasi- Newtonian fluids, we turn our attention to the ones obeying the power-law, more precisely the polymer fluids. We observe the flow through a porous domain, a periodic structure in which every cell is made of the fluid part and the impermeable part. The assumption of the periodic nature on the microscale level is fundamental to the asymptotic method called homogenization, whose main task is to determine the global filtration law. This procedure enables for the cumulative effect of the impermeable micro obstacles slowing down the fluid to be described by the effective equations given on the homogeneous domain, obstacle-free.\\ We show that the results depend on the asymptotic behaviour of one small parameter, the size of the impermeable part, during the homogenization process when number of cells tends to infinity and their size to zero. The obtained specific filtration laws are low volume fraction limit for small size obstacles and nonlinear Brinkman's law in case of the critical obstacle size.

polymer fluid; power-law; filtration; homogenization; low-volume fraction; Darcy's law; Brinkman's law; drag force function

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