FLOW OF GENERALIZED NEWTONIAN FLUIDS ACROSS A PERIODIC ARRAY OF CYLINDERS

Traditionally, the capillary model has been used to describe the permeability-porosity relationship for porous media. Although this approach works reasonably well in flow through granular media, it fails to model the flow across aligned fibrous media, due to its inherent assumptions. A more realistic approach is chosen, using flow across regular arrays of cylinders. A closed form solution is developed by matching the analytic solution using the lubrication approach for low porosities and the analytic cell model solution for high porosities. This closed form solution is extended to generalized Newtonian fluids by linearizing the cell model solution about the Newtonian point, and extending the lubrication approach to power-law fluids. The results of the closed form solutions agree well with the numerical solution obtained by solving the Stokes equations, in square and hexagonal arrangements of cylinders for Newtonian and mildly shear-thinning fluids. A scaling is suggested which allows one to separate the effect of the fluid rheology and the porosity on the resistance to flow.