  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.
