Non-steady two-phase stratified laminar flow of polymeric liquids in pipes

Abstract

A numerical method of solution is given for the non-steady two-phase stratified. laminar flow of various non-Newtonian fluids in pipes. In particular, the Ellis fluid model is chosen to illustrate inelastic shear thinning effects. It is shown that the method can be applied to the non-steady multi-phase stratified laminar flow of some non-Newtonian fluid models. An Oldroyd six constant model is used to illustrate the fully elastic flow. It is found that the presence of two phases of the same kind of immiscible liquids tends to suppress the typically viscoelastic response to time dependent situations that the same liquids would exhibit as a single phase. Overshoot of flow rates is reduced, if not completely eliminated in both the generation and decay of steady flows. In two-phase pulsatile flows, the flow enhancement is less marked and the time dependence of the individual flow rates can be significantly different. Theoretical results are used to interpret some of the flow instabilities encountered during the capillary flow of polymeric liquids.