Flow of Boger fluids through packed bed of spherical and non-spherical particles: Asymptotic behaviour

The effect of fluid elasticity on frictional pressure drop during the flow of Boger fluids (constant viscosity elastic fluids) through packed bed of spherical and non-spherical particles has been examined and comprehensive data on pressure drop-flow rate behaviour were generated using spheres, cylinders, triangles, and square plates as packing material to cover the sphericity range of 0.547 <= phi <= 1. Boger fluids used in the present study were 0.01%-0.045% wt./vol. polyacrylamide in glycerol water blends. The phenomenon of drag enhancement was observed in comparison to purely viscous fluid which follows asymptotic behaviour with elasticity number (E = We/Remod). The asymptotic behaviour depicts the dominance of elasticity at low elasticity number and effect of inertia at higher Reynolds number (Re). Based on the observed experimental results, elasticity number function f (E), which well captures the dominance of elasticity at low E and inertial effects at higher Re, is incorporated in the existing Ergun equation (applicable to packed bed flow of purely viscous fluids) to predict the friction factor for Boger fluids. The developed correlation can adequately be applied to the available experimental data on non-Newtonian inelastic fluids, shear thinning viscoelastic fluids, Boger fluids as well as for non-spherical particles if the diameter of non-spherical particle is replaced with equivalent diameter, that is, volume mean diameter times sphericity (dp = deq = dv phi).