A scaling rule for the flow mobility of a power-law fluid through unidirectional fibrous porous media

Abstract

We propose a scaling rule for the flow mobility prediction of a power-law fluid in unidirectional fibrous porous media by separating rheological contribution from geometrical factor. Starting from the analogy to a simple circular pipe flow, we find mobility dependence on pressure drop with the help of lubrication theory for flows of a power-law fluid through arrays of square and hexagonal packing cylinders. There appears a nearly unique intersection point independent of rheological parameters in the mobility and pressure drop space, once scaled with the consistency index, and the intersection point coordinate is expressed by rheological and geometrical factors separately. Further simplification is achieved by approximating the rheological contribution by a constant that scales linearly with the consistency index. The proposed mobility estimation scheme facilitates a simple but reasonably accurate estimation and it has been verified by extensive numerical simulations for various pressure drops, rheological parameters, porosities and fibrous porous architectures. (C) 2015 Elsevier B.V. All rights reserved.