Flow of non-Newtonian polymeric solutions in fibrous media

Abstract

The equations of motion (continuity and momentum) describing the steady flow of incompressible power law liquids in a model porous medium consisting of an assemblage of long cylinders have been solved numerically using the finite difference method. The field equations as well as the pertinent boundary conditions have been re-cast in terms of the stream function and vorticity. The inter-cylinder interactions have been simulated using a simple "concentric cylinders" cell model. Extensive information on the detailed structure of the flow field in terms of the surface vorticity distribution, streamlines, and viscosity distribution on the surface of the solid cylinder as well as on the values of the pressure and friction drag coefficients under wide ranges of physical (0.4 ≤ Є ≤ 0.95; 1 ≥ n ≥ 0.4) and kinematic (0.01 ≤ Re ≤ 10) conditions have been obtained. The numerical results presented herein have been validated using the experimental results for the flow of Newtonian and power law fluids available in the literature; the match between the present predictions and the experiments was found to be satisfactory.