Influences of Non-Newtonian Viscosity and Elasticity on Potential Flow Analogy by Hele-Shaw Cell

Abstract

The validity of potential flow analogy by the Hele-Shaw flow of non-Newtonian fluids is examined through experiments using two shear-thinning elastic polymer solutions for three different flow configurations, i.e. flows around a circular cylinder and a square cylinder and flows through an abruptly converging-diverging channel (slit). Although the polymer solutions are highly shear-thinning and elastic, their flows well reproduce the corresponding two-dimensional potential flow patterns of the respective flow configurations when the flow rate is very low. The deviation occurs at values of Reynolds number much lower than the critical value for inertia effect, and in the opposite way of the inertia effect. An analysis for inelastic non-Newtonian fluids shows that non-constant viscosity does not affect the potential flow analogy, and the potential flow patterns are observed at flows with considerable values of the first normal stress difference in shear flow. Therefore, the disturbance to the potential flow pattern is not due to the non-Newtonian viscosity or the elasticity in shear flow, but attributed to the elongational stress due to the elasticity of the polymer solutions.