Spreading and penetration of a micro-sized water droplet impacting onto oil layers

Abstract

This paper describes a theoretical and numerical investigation of the impact dynamics and outcomes of a microsized water droplet falling onto an oil layer. The shape of the water droplet floating on the oil layer is predicted theoretically to understand the balancing of the three interfacial tensions. Direct numerical simulations coupled with a three-phase volume-of-fluid method are performed on an axisymmetric model, considering the balancing and motion of the triple-line. The effects of the impact velocity, viscosity ratio of oil and water, height of the oil layer, and the combination of the three interfacial tensions on the impact dynamics and outcomes are systematically studied. Regime diagrams of the nonpenetration and penetration outcomes are obtained under different combinations of the flow and physical parameters. It is found that the balance among the three interfacial tensions is well maintained at the triple-line due to the low capillary number. The maximum horizontal spreading of the water droplet is proportional to the square root of the Weber number when the impact velocity is low. Moreover, the maximum penetration for high impact velocities is independent of the spreading parameter. To understand the lower transition between nonpenetration and penetration, the critical penetration distance at which the triple-line is about to collapse is obtained from simulation results as a function of the spreading parameter, and these indicate weak dependence on the viscosity ratio. A semiempirical model is used to predict the boundary of lower transitions, and these are in good agreement with the simulations results.