Similarity solutions for the converging or diverging steady flow of non‐newtonian elastic power law fluids with wall suction or injection. Part I: Two‐dimensional channel flow

Abstract

AbstractSimilarity solutions are determined for the steady flow of an incompressible elastic power law fluid in a two‐dimensional channel with nonparallel walls. The possibility of wall suction or injection is considered. Solutions are found to exist only for power law indices of unity. A method is developed for estimating the pressure drop in the naturally converging flow field before the entrance to a capillary. In diverging flows a singularity is found to arise due to the elasticity of the fluid. The singularity corresponds to a Deborah number of unity. It is postulated that the singularity is, for the constitutive equation used here, a possible source of the flow instability commonly referred to as melt fracture.