Hindrance Velocity Model for Phase Segregation in Suspensions of Poly-dispersed Randomly Oriented Spheroids

Abstract:

Crystal settling and bubbles migration in magmas have significant effects on the physical and chemical evolution of magmas. The rate of phase segregation is controlled by the force balance that governs the migration of particles suspended in the melt. The relative velocity of a single particle or bubble in a quiescent infinite fluid (melt) is well characterized; however, the interplay between particles or bubbles in suspensions and emulsions and its effect on their settling/rising velocity remains poorly quantified.

We propose a theoretical model for the hindered velocity of non-Brownian emulsions of nondeformable droplets, and suspensions of spherical solid particles in the creeping flow regime. The model is based on three sets of hydrodynamic corrections: two on the drag coefficient experienced by each particle to account for both return flow and Smoluchowski effects and a correction on the mixture rheology to account for nonlocal interactions between particles. The model is then extended for mono-disperse non-spherical solid particles that are randomly oriented. The non-spherical particles are idealized as spheroids and characterized by their aspect ratio. The poly-disperse nature of natural suspensions is then taken into consideration by introducing an effective volume fraction of particles for each class of mono-disperse particles sizes.

Our model is tested against new and published experimental data over a wide range of particle volume fraction and viscosity ratios between the constituents of dispersions. We find an excellent agreement between our model and experiments. We also show two significant applications for our model:

(1) We demonstrate that hindered settling can increase mineral residence time by up to an order of magnitude in convecting magma chambers.

(2) We provide a model to correct for particle interactions in the conventional hydrometer test to estimate the particle size distribution in soils. Our model offers a greatly improved agreement with the results obtained with direct measurement methods such as laser diffraction.