The fate of particles in a volumetrically heated convective fluid at high Prandtl number

TL;DR

This paper investigates how particles behave in high Prandtl number convective fluids with internal heating, introducing a generalized Shields number to predict particle segregation and stability in geophysical systems.

Contribution

It develops a coupled model using the Shields formalism and convection scaling laws to predict particle fate, including segregation and deposit formation, in high Prandtl number convective fluids.

Findings

The sign of particle buoyancy alone does not determine particle fate.

A generalized Shields number effectively predicts particle segregation.

The model has implications for the stability of flotation crusts on rocky bodies.

Abstract

The dynamics of suspensions plays a crucial role on the evolution of geophysical systems such as lava lakes, magma chambers and magma oceans. During their cooling and solidification, these magmatic bodies involve convective viscous fluids and dispersed solid crystals that can form either a cumulate or a floating lid by sedimentation. We study such systems based on internal heating convection experiments in high Prandtl fluids bearing plastic beads. We aim to determine the conditions required to produce a floating lid or a sedimented deposit. We show that although the sign of particles buoyancy is the key parameter, it is not sufficient to predict the particles fate. To complement the model we introduce the Shields formalism and couple it with scaling laws describing convection. We propose a generalised Shields number that enables a self-consistent description of the fate of particles in the system, especially the possibility to segregate from the convective bulk. We provide a quantification of the partition of the mass of particles in the different potential reservoirs (bulk suspension, floating lid, settled cumulate) through reconciling the suspension stability framework with the Shields formalism. We illustrate the geophysical implications of the model by revisiting the problem of the stability of flotation crusts on solidifying rocky bodies.