Unifying the relative hindered velocity in suspensions and emulsions of nondeformable particles

Although the relative velocity of a single crystal or bubble in a quiescent fluid (melt) is well characterized, the interplay of crystals/bubbles in multiparticle systems and its effect on their settling/rising velocity is poorly quantified. We propose a theoretical model for the hindered velocity of non-Brownian emulsions and suspensions of nondeformable fluid and solid particles in the creeping flow regime. The model is based on three sets of correction: two on the drag coefficient experienced by each particle to account for both return flow and Smoluchowski effects and a correction on the rheology to account for nonlocal interactions introduced as a mean-field effective viscosity. Our model is tested against new and published experimental data over a wide range of particle volume fraction and viscosity ratio between the fluids. We find an excellent agreement between our model and experiments. The model is then applied to show that hindered settling can increase mineral residence time by up to an order of magnitude in convecting magma chambers.