Numerical investigation of coalescence-induced self-propelled behavior of droplets on non-wetting surfaces

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Abstract
We numerically study the self-propelled droplet phenomenon upon droplet coalescence. The numerical method is based on a well-validated multiphase flow solver that solves the three-dimensional Navier-Stokes equations. The liquid-air interface is captured using the moment of fluid along with a direction splitting method applied to advect the interface. And an approximate projection method is used to decouple the calculation of velocity and pressure. The solver is validated by comparing with the experimental results. Our results show that the droplet jumping process can be accurately captured. The simulated droplet deformation also matches the experimental results. To investigate the jumping mechanism, we compare results between two cases with and without a contact substrate. The history of vertical momentum shows that with a contact substrate, the droplet has a longer period of acceleration. The coalesced droplet with a contact substrate also has a smaller surface area which indicates that more surface energy is converted into kinetic energy. The effects of droplet size, surface tension, and droplet density are also studied. The jumping speed generally obeys the capillary scaling law. The effect of approaching speed is also investigated. With lower approaching speed, the surface tension dominates while with higher approaching speed, the inertia force dominates the jumping process.

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