Instabilities with reduced frictional drag in the rotating channel flow of dilute polymer solutions

Abstract

A numerical investigation is conducted on secondary flows and roll-cell instabilities in the laminar channel flow of dilute polymer solutions subjected to a steady spanwise rotation. Finite difference calculations of the full nonlinear equations of motion for a Maxwell fluid and a Rivlin-Ericksen fluid of the second grade are presented which indicate that there is a double-vortex secondary flow at weak and rapid rotation rates with an instability in the form of longitudinal roll cells at intermediate rotation rates (regimes analogous to those for a Newtonian fluid). However, for a given physical pressure gradient and rotation rate, the introduction of a minute amount of a polymeric additive to a Newtonian fluid so that the Weissenberg number is of the order of 10−5 has a stabilizing effect on rotating channel flow and gives rise to secondary flows with a substantially reduced frictional drag. Comparisions with previously conducted experimental and analytical studies are made along with a brief discussion of potential applications to the field of polymeric drag reduction.