Slow flow of Boger fluids through model fibrous porous media

Abstract

The flow of viscoelastic fluids through square arrays of parallel cylinders was investigated experimentally by measuring the pressure drop and flow rate and by mapping the velocity field using particle image velocimetry. The arrays had solid volume fractions of 2½%, 5%, and 10% and the fluids were Boger fluids—specifically, two solutions of polyisobutylene in polybutene. With Reynolds numbers less than 0.1, viscosity and elasticity were the only relevant fluid properties. Measurements were made first with a glycerol/water mixture to establish an inelastic baseline. For the three arrays and two viscoelastic fluids, elastic effects started consistently at a Deborah number (De) of 0.5. For De up to 4, the flow resistance due to elasticity was up to several times that due to viscosity, which is comparable to previous findings with much higher volume fractions. But, unlike prior flows, the present ones were steady. Particle image velocimetry measurements revealed unit-cell velocity profiles, which became progressively asymmetrical as De increased. Also, flow structures related to elasticity were found in the wake regions; they were spaced periodically in the spanwise direction and offset from column to column to create a honeycomb-like pattern. Stress analyses indicate that the flow resistance due to elasticity was likely caused more by the normal stresses of N1 than by extensional stresses.