Drops with circular stagnation lines: combined effects of viscoelastic and inertial forces on drop shape

For viscoelastic drops falling through Newtonian fluids it is well known that, on increasing the elastic properties of the interior phase, the drop will lose its sphericity and form a dimple at the trailing end. Here we analytically determine the flow distribution around and inside a viscoelastic droplet falling within a low inertia regime. We use these solutions to theoretically investigate the motion and deformation of viscoelastic drops. The reliability of the analytical solution is confirmed with dedicated experiments which show a reasonable agreement between the two approaches. We then extend our analytical work and show that as the size of the viscoelastic drop is increased, the stagnation points at both the trailing and leading sides of the drop expand to create a region of elongational dominated flows. As the size of drop is increased further, this elongational region splits to form an additional circular stagnation line that appears on the trailing and leading sides of the drop surface in the external field.These, newly found, kinematic changes around the drop surface are shown to underpin the shape transformation, that is the appearance of both dimple and cusps, of falling viscoelastic drops.