Modelling droplet-particle interactions on solid surfaces by coupling the lattice Boltzmann and discrete element methods

Abstract

We develop a three-dimensional numerical scheme for investigating interfacial flows coupled with frictional solid particles. Our approach combines the lattice Boltzmann method (LBM) to model the dynamics of a two-component fluid, and the discrete element method (DEM) to model normal reaction, sliding friction, and rolling friction between solid particles and between particles and solid surfaces. Key to the coupling between the fluid and particle dynamics are the momentum exchange method to transfer hydrodynamic forces between the fluids and particles, a geometric boundary condition to tune particle wettability, and a capillary force model describing surface tension forces between particles and liquid-fluid interfaces. We rigorously validate the contact forces by investigating the dynamics of a particle bouncing off a solid surface and rolling down an inclined plane, the hydrodynamic force by the Segr\`{e}-Silberberg effect, and the capillary force by particle detachment from a liquid-fluid interface. Motivated by the self-cleaning properties of lotus leaves, we apply the method to investigate how drops remove contaminant particles from surfaces. We successfully reproduce scenarios reported experimentally by Naga et al. (Soft Matter (2021) 17(7):1746-1755) by tuning the particle friction. Furthermore, the LBM-DEM approach allows us to systematically explore the effects of particle friction coefficients, drop size, and speed. Our method opens opportunities to study numerous phenomena involving particle dynamics interacting with interfacial flows, including soil erosion, capillary-driven colloidal self-assembly, and how raindrops transport microplastics in the environment. It also makes it possible to control parameters that are difficult to tune independently in experiments, including contact angles, surface tension, and friction coefficients.