engleski

Low-volume-fraction limit for polymer fluids

We consider a stationary, purely viscous polymer flow through a periodic porous medium. Fluid flow is governed by the Stokes system with shear-dependent viscosity (power-law model), while the domain is modelled as a periodic repetition of a cell consisted of a fluid part and a solid one. Solid parts of a domain present impermeable obstacles, whose impact on the fluid flow may be seen as a slowing factor through averaged quantities such as the permeability function, obtained by the homogenization process. This ef ective fi ltration law corresponds to the limit when number of cells tend to infi nity and their size to zero and as a result the influence of the microstructure is implemented in the homogenized equations through a kind of nonlinear Darcy's law. Our goal is to find explicit dependency of the permeability function on the relative size of the obstacles in the unit cell and the so-called low-volume-fraction limit as this size tends to zero. Main difficulties arise from the nonlinear character of power-law viscosity.

Polymer Fluids; Filtration; Low-volume fraction; Permeability function; Drag force function; Power-law

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