Birth and decline of magma oceans. Part 1: erosion and deposition of crystal layers in evolving magmatic reservoirs

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.

💡 Research Summary

This paper presents the first of a two‑part study that combines laboratory analog experiments with theoretical scaling to investigate how crystals behave in a convecting magma ocean, with particular focus on the formation and stability of floating lids and basal cumulates. The authors use a rectangular tank (30 × 30 × 5 cm) filled with a viscous mixture of glycerol and ethylene glycol, heated volumetrically by microwave absorption to generate vigorous internally heated convection (Rayleigh‑Roberts numbers Ra_H ≈ 10⁶–10⁷). Plastic beads of two size classes (radius ≈ 145 µm and 290 µm) serve as crystal analogues; their density contrast with the fluid changes sign at an inversion temperature T_inv ≈ 37.4 °C, allowing the same particles to act as buoyant lids at low temperature and as sinking particles at higher temperature.

The experimental campaign explores a matrix of surface temperatures (20–45 °C), initial lid thicknesses, and bead properties. High‑resolution temperature fields are obtained via laser‑induced fluorescence, while velocity fields are measured with particle‑image velocimetry. The authors observe a reproducible sequence: (i) rapid onset of convection, (ii) formation of a bed‑load layer at the base of the floating lid, (iii) development of dune‑like cusps that increase shear stress, (iv) triggering of erosion when the shear exceeds a critical Shields number, and (v) progressive thinning of the lid until either a steady partial thickness is reached or the lid is completely removed. The erosion rate collapses onto a simple law

  Erosion ∝ Θ · Ra_H^{‑½},

where Θ is a modified Shields number that incorporates the buoyancy of the beads and the convective shear stress. This relationship extends the classic Shields criterion (originally derived for river beds) to the case of internally heated, high‑Prandtl number convection.

In parallel, when the bulk temperature exceeds T_inv, beads become negatively buoyant and settle at the tank bottom. The measured deposition velocity matches the Stokes settling speed

  v_s = (2/9) (Δρ g r²)/η_f,

indicating that, within the experimental parameter space, convection does not significantly modify the sedimentation rate. Thus, the formation of a basal cumulate can be predicted solely from particle size, density contrast, and fluid viscosity.

Thermal modeling treats the system as a conductive lid over a convecting bulk. The internal heating defines a temperature scale ΔT_H = H h²/λ_f. In the high‑Prandtl limit, the thermal boundary layer (TBL) at the top of the convective layer has thickness δ_TBL = C_δ h Ra_H^{‑¼} and temperature drop ΔT_TBL = C_T ΔT_H Ra_H^{‑¼}, with constants C_T≈3.41 and C_δ≈7.36 derived from previous work. Energy balance for the bulk yields

  ρ_f c_p ∂T_bulk/∂t = H − Q_s,conv,

and the convective heat flux scales as

  Q_s,conv = λ_f (C_T)^{4/3}