Diffuse interface model to simulate the rise of a fluid droplet across a cloud of particles

A large variety of industrial and natural systems involve the adsorption of solid particles to the fluidic interface of droplets in motion. A diffuse interface model is here suggested to directly simulate the three-dimensional dynamics of a fluid droplet rising across a cloud of large particles. In this three-phase model the two solid-fluid boundaries and the fluidic boundary are replaced with smoothly spreading interfaces. A significant advantage of the method lies in the fact that the capillary effects, the three-phase flow hydrodynamics, and the inter-particle collisions are all resolved. We first report important numerical limitations associated with the inter-particle collisions in diffuse interface models. In a second stage the effect of the particle concentration on the terminal velocity of a rising fluid droplet is investigated. It is found that, in a quiescent environment, the terminal velocity of the rising the fluid droplet decreases exponentially with the particle concentration. This exponential decay is also confirmed by a simple rheological model.