Numerical and experimental studies of the flow instabilities inside and outside a rising spherical droplet

Abstract

We have analyzed how the flow related to a spherical moving droplet can be subjected to steady and unsteady instabilities. Using both experiments and direct numerical simulations, evidences are provided that the flow instability modifies the droplet drag coefficient for fixed droplet in a uniform flow or when rising in a quiescent fluid. The shape of the trajectory is also analyzed and shows path oscillations while droplet remains spherical.

We used a combination of direct numerical simulations and experiments with different fluids (n-pentane, heptane, and cyclohexane in water) to disentangle the interaction between the internal flow circulation and the outer wake flow. Thanks to DNS, we were able to identify two distinct origins yielding overall flow bifurcations. By analyzing the amplification rate of a small perturbation, we draw a stability map based on the Reynolds number, viscosity and density ratios which specifies whether the instability is originating from either inside or outside the interface. We obtain good agreement when comparing experiments on freely rising droplet and simulations of fixed droplet in a uniform flow.