Non-newtonian effects on the drag of creeping flow through packed beds

Abstract

Slow flows of non-Newtonian fluids through packed beds of solid particles are studied numerically and analytically using the free-surface cell model to account for the interactions between particles. The flow problem of a Carreau fluid is solved by the finite difference method and that of a second-order fluid by the perturbation method. It is shown that the flow drag decreases with a decrease in the flow behavior index and with an increase in the characteristic time. The degree of this reduction is found to be more significant at low voidages. The numerical results are found to be closer to the lower bounds obtained using variational principles by earlier investigators. The perturbation solutions predict that the second normal stress difference coefficient has a significant influence on the flow resistance. The flow resistance can either increase or decrease with an increase in the Deborah number, according to the values of the second normal stress difference coefficient. The results are found to be in agreement with the experimental findings that the viscoelastic flow through packed beds can exhibit a rapid increase in the flow resistance, over and above that expected for a comparable viscous fluid, in the second normal stress difference coefficient range for most real viscoelastic fluids.