On the transient flow inside and around a deforming millimetre class oil droplet falling under the action of gravity in stagnant air

The liquid flow inside, and the induced air flow around, a falling droplet in stagnant air was numerically investigated using the volume of fluid method to describe the droplet interface. The droplet consisted of oil with the same surface tension and with viscosity as parameter. It was injected into stagnant air with an initial velocity of 1 m/s; therefore, the initial Weber (We = 0.14), Reynolds (Re = 141), and Bond (Bo = 2.4) numbers remained constant during the parametric study whilst the initial Capillary (Ca) and Ohnesorge (Oh) numbers varied by an order of magnitude from 0.46 to 4.6 and from 0.044 to 0.44, respectively. We examined the effect of viscosity on the flow inside, and around, the droplet as well as on the droplet deformation and its natural frequency. This investigation showed a strong dependence of the deformation with liquid viscosity. Specifically, the droplets achieved their final deformation in under-damped, for low viscosity, and in over-damped, for high viscosity, oscillation modes...