  This paper is the first of a two companion papers presenting a theoretical
and experimental study of the evolution of crystallizing magma oceans in
planetesimals. We aim to understand the behavior of crystals formed in a
convective magma and the implications of crystal segregation for the reservoir
thermal and structural evolution. In particular, the goal is to constrain the
possibility to form and preserve cumulates and/or flotation crusts by
sedimentation/flotation of crystals. We first use lab-scale analog experiments
to study the stability and the erosion of a floating lid composed of plastics
beads over a convective viscous fluid volumetrically heated by microwave
absorption. We propose an erosion law that depends only on two dimensionless
numbers which govern these phenomena: (i) the Rayleigh-Roberts number,
characterizing the strength of convection and (ii) the Shields number, that
encompasses the physics of the flow-particle interaction. We further consider
the formation of a cumulate at the base of the convective layer due to
sedimentation of beads that are denser than the fluid. We find that particles
deposition occurs at a velocity that scales with the Stokes velocity, a result
consistent with previous experimental studies. The theoretical framework built
on these experimental results is applied in a second paper on the evolution of
magma oceans in planetesimals and the fate of particles in this convective
environment.
