Birth and Decline of Magma Oceans in Planetesimals: 1. Experimental Study of Erosion and Deposition of Particles in an Internally Heated Convecting Fluid

This paper is the first of 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 ocean, and the implications of crystal segregation for the thermal and structural evolution of the convective system. In particular, we wish to constrain the possibility to form and preserve cumulates and/or flotation crusts by sedimentation or flotation of crystals respectively. We use lab-scale analog experiments to study the stability and the erosion of a floating lid composed of plastics beads lying over a convective viscous fluid volumetrically heated by microwave absorption. We propose a law for erosion and re-entrainment that depends only on two dimensionless numbers that govern these phenomena: (a) the Rayleigh-Roberts number, characterizing the vigor of convection and (b) 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 by sedimentation of beads that are denser than the fluid. We find that particle deposition occurs at a velocity that scales with the Stokes velocity, a result consistent with previous experimental studies. We build up a model that describes the transient evolution of the convective system's thermal state and the fraction of particles that segregated from the flow or that remain in suspension.