The formation of vortex rings in shear-thinning liquids

Abstract

The dynamics of formation and evolution of vortex rings in non-Newtonian shear-thinning liquids generated in a piston-cylinder arrangement was studied. The ratio of the piston displacement Lm to the internal cylinder diameter D0, as well as the mean piston velocity Up determine the vortex properties and evolution. Experiments with different conditions are presented: translation velocity of the piston and stroke ratios Lm/D0. Measurements of the 2D velocity field were obtained with a PIV technique. The vortex circulation Γ was computed considering a vortex identification scheme (Q criterion). The Reynolds number was in the range 138<Re0<616. The Reynolds number for these vortices was computed in terms of the ‘power-law’ model parameters: the power index n and the consistency m. Considering different shear-thinning liquids and fixed Reynolds number, we observed that the vortex circulation decreases with the power index n. We show that the total circulation ejected from the cylinder is reduced when the thinning property of the liquid increases (decrease n); thus, the circulation confined inside the vortex ring, is reduced too. A value of the non-dimensional vortex circulation Γ/D0Up≈2 may indicate a saturation condition beyond which it is not possible to increase the vortex circulation for any Reynolds number.