2D Lattice Boltzmann Simulation of Droplet Jumping in a Viscous Fluid

In order to investigate the coalescence and out-of-plane jumping of two incompressible droplets on a non-wetting surface surrounded by an incompressible fluid with matched viscosity in the low Ohnesorge number regime, a two-dimensional lattice Boltzmann phase-field model is implemented. An interfacial force of potential form is used to model the internal surface tension force and capture the fluid-surface interaction, viz. the contact-line dynamics. We evaluate the simulated velocity fields and interface shape evolution during coalescence and the subsequent jumping event. We confirm that the coalescence dynamics of the binary droplet system is similar to the case where the outer fluid viscosity is small compared to that of the droplet fluid, as is the case of condensed water droplet jumping on superhydrophobic surfaces in a gaseous ambient. An argument is also developed to demonstrate that the dynamics in 2D, when appropriately scaled, should be approximately equivalent to the corresponding 3D case. A simple drag model is used to capture the rapid velocity decay of the jumping droplet as it moves away from the surface into the viscous fluid. The results suggest the possibility of experimentally observing coalescence-induced droplet jumping in liquid-liquid systems that may be potentially exploited for microfluidic applications.