Direct Numerical Simulations of Droplet Deformation in Low Reynolds Number Extensional Flows

We study the effect of stagnant and non-stagnant extensional flows on a suspended immiscible droplet using direct numerical simulations. We use projection method to solve the governing equations of motion, and the deformable interface is treated using level set method. This scheme is used to simulate the behavior of a droplet in a hyperbolic flow as a low Reynolds number numerical analogue of the classic four-roll mill experiments. Results indicate that the critical Capillary number of the droplet increases with reduction in Reynolds number and approaches results from the four-roll mill study which approximated a Stokesian flow. To study non-stagnant extensional flows, we simulate the motion of a Silicone oil droplet \mbox{(radius $\sim$ 2 mm)} in a Castor oil matrix through a hyperbolic converging channel. Streamwise stretching of the droplet was observed and plots of drop draw ratio vs time and position of the droplet in the flow are validated with experimental results.