An investigation on the motion and deformation of viscoelastic drops descending in another viscoelastic media

In the present study, an investigation of the motion and shape deformation of drops is carried out in creeping flow to highlight the effect of viscoelastic properties on the problem. A perturbation method is employed to derive an analytical solution for the general case that both interior and exterior fluids are viscoelastic, both fluids obeying the Giesekus model. An experiment is also performed for the limiting case of an immiscible drop of a 0.03% (w/w) polyacrylamide in an 80:20 glycerol/water solution falling through a viscous Newtonian silicon oil (410 cP polydimethylsiloxane oil) in order to check the accuracy of the analytical solution. It is shown that the addition of elastic properties to the interior fluid may cause a decrease in the terminal velocity of the droplet while an increase in the elastic properties of the exterior fluid results in the opposite behavior and increases the terminal velocity. The well-known spherical shape of creeping drops for Newtonian fluids is modified by elasticity into either prolate or oblate shapes. Using the analytical solution, it is shown that normal stresses play a key role on the final steady-state shape of the drops. To keep the drops spherical in viscoelastic phases, it is shown that the effect of normal stresses on the interior and exterior media can cancel out under certain conditions. The results presented here may be of interest to industries dealing with petroleum and medicine processing, paint and power-plant related fields where knowledge of the shape and terminal velocity of descending droplets is of great importance.