Effect of elasticity of a polymer solution on the Hele-Shaw flow

Abstract

In this study, the Hele-Shaw cell is used to examine the effect of fluid elasticity on the flow patterns of two-dimensional potential flow. Flows around a circular cylinder, a square cylinder and flows through abruptly converging-diverging channels (slits) with different throat lengths are tested for water and 0.2 wt % polyacrylamide aqueous solution (PAA-solution). The viscosity of the latter is well modeled by the power law, and the first normal stress difference in the steady shear flow is around ten times higher than the shear stress. Although the PAA-solution is highly shear-thinning, the flows of PAA-solution well reproduce the two-dimensional potential flow patterns that correspond to the respective flow configurations when the flow rate is very low. The potential flow patterns of PAA solution are disturbed in the opposite way of inertia effect observed for water. The streamlines near the upstream stagnation point of cylinders are shifted upstream separating from the cylinder surface when the flow rate is higher, while streamlines in the wake approach closer to the downstream stagnation point. Streamlines of flow through the slit at flow rates higher than the potential flow region show that a pair of vortices is formed upstream the slit entrance, while the streamlines remain attached to the downstream wall after passing the slit.