Low-volume-fraction limit for polymer fluids

作者：Fratrovic Tomislav^*; Marusic Paloka Eduard

来源：Journal of Mathematical Analysis and Applications, 2011, 373(2): 399-409.

DOI：10.1016/j.jmaa.2010.07.043

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

We study a stationary, purely viscous polymer flow through a porous medium modelled as a periodic array of cells consisted of a fluid part and a solid one. Solid parts of the domain present impermeable obstacles, whose impact on fluid flow may be seen as a slowing factor through averaged quantities such as the permeability function, obtained by the homogenization process. In that way, the influence of the microstructure is implemented in the homogenized equations through a kind of nonlinear Darcy's law. Our goal is to find more explicitly the dependence of the permeability function on the size eta of the obstacle in the unit cell and the so-called low-volume-fraction limit. Main difficulties arise from the nonlinear character of the power-law viscosity and the apparent weak convergence of the solutions involved.

• 出版日期2011-1-15