FLOW OF GENERALIZED NEWTONIAN FLUIDS ACROSS A PERIODIC ARRAY OF CYLINDERS

Traditionally, the capillary model has been used to describe the perme ability-porosity relationship for porous media. Although this approach works reasonably well in flow through granular media, it fails to mod el the flow across aligned fibrous media, due to its inherent assumpti ons. A more realistic approach is chosen, using flow across regular ar rays of cylinders. A closed form solution is developed by matching the analytic solution using the lubrication approach for low porosities a nd the analytic cell model solution for high porosities. This closed f orm solution is extended to generalized Newtonian fluids by linearizin g the cell model solution about the Newtonian point, and extending the lubrication approach to power-law fluids. The results of the closed f orm solutions agree well with the numerical solution obtained by solvi ng the Stokes equations, in square and hexagonal arrangements of cylin ders for Newtonian and mildly shear-thinning fluids. A scaling is sugg ested which allows one to separate the effect of the fluid rheology an d the porosity on the resistance to flow.