Separation regimes of two spheres falling in shear-thinning viscoelastic fluids

We experimentally study the time evolution of the distance between two identical spheres settling down in polyacrylamide shear-thinning solutions in mixtures of water and glycerin. In order to analyze the behavior of the spheres under different rheological conditions, we varied the concentration of the polymer and glycerin. To examine the influence of wall effects, the experiments were performed in two containers of different size. We found that depending on the fluids' rheological properties, two different regimes are revealed for the same diluted polymer. In one of them (I), the separation between the spheres grows in time if the initial separation S-i is beyond a critical distance S-c, while the separation decreases for an initial distance shorter than S-c. In the second observed regime (II), the spheres aggregate if S-i < S-c while they remain unchanged in their separation if S-i > S-c, i.e., repulsion is not detected. The transition from one to another regime can be produced at constant polymer concentration by changing the solvent viscosity eta(s). In our experiments this shift has been done modifying the glycerin-water proportion. Although these two behaviors were reported in previous works for different viscoelastic fluids, a result that we show is that both regimes can be observed for the same polymer. The elusive regime I, in which far-field repulsion is exhibited, is of particular interest since it has been previously reported only by Riddle et al. [J. Non-Newtonian Fluid Mech. 2, 23 (1997)]. Thus, our results confirm that this behavior is also feasible.