Affiliations: Department of Mechanical Engineering Nagaoka
University of Technology, Kamitomiokamachi 1603-1, Nagaoka, Japan. Phone:
+81-258-47-9730; Fax: +81-258-47-9770; E-mail: [email protected]
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.
Keywords: Hele-Shaw flow, Viscoelastic fluid, Flow around a cylinder, Converging-diverging channel, Weissenberg number