The Physics Of Crystal Settling And Suspension In A Turbulent Magma Ocean
Authors: Tonks W B , Melosh H J 
Published: November 2023

Abstract
It is widely assumed that a magma ocean on either the Earth or the Moon would necessarily differentiate by fractional crystallization. Geochemists and petrologists making this ption, however, have so Jar fulled to take into account the physics of crystal suspension in a planetary-scale convecting system. In the first part of this paper we show that convective velocities in a deep ultramafic magma ocean on either the Earth or the Moon are sufficiently rapid to suspend large crystals. 1bis demonstration involves aspects of convective theory and the mechanics of suspension that may be unfamiliar to most planetary scientists. Indeed, the problem has more affinities to aeolian transport in a deep planetary atmosphere than to traditional studies of magma convection. A vigorously convecting system can be divided into three distinct regions: an upper conductive boundary layer, a sublayer dominated byviscous forces, and a volume of turbulent fluid whose flow is controlled by inertial forces. 1bis inertial flow zone, which does not exist in the more familiar subsolidus convection, supports large-scale turbulent eddies that are analogous to gusty winds in a planetary atmospheric convective system. The criterion for suspension is derived from empirical studies of sediment transport and is given by the Rouse number, which is the ratio between the tenninal velocity of the crystals and the turbulent friction velocity. Settling ( or flotation) only takes place for Rouse numbers greater than about. We present several studies of magma ocean evolution with realistic rheological properties and cooling histories. The results show that on both the Earth and Moon crystals up to 1-2 cm in diameter can be suspended from the onset of cooling. In the later stages of cooling, as viscosity increases, crystals of 10 cm to more than I m in diameter may be suspended A surprising feature of our analysis is that the ability of a magma ocean to suspend crystals is only weakly dependent on gravity and depth: Viscosity is the major factor determining suspension. 1bis result raises a serious problem for the lunar magma ocean hypothesis, because the differentiation of an anorthositic crust strongly suggests that crystal fractionation did occur. We offer an explanation for this apparent anomaly by appealing to the low lunar gravity. Since pressure in the Moon increases only slowly with depth, the solidus and liquidus temperatures are · nearly independent of depth. In a convecting magma ocean on the Moon adiabats lie between the solidus and liquidus at all depths, so that growing crystals circulate through the ocean for long periods of time without dissolving. Under these circumstances they may grow large enough to settle out, resulting in the observed differentiation. In contrast, on the Earth the liquidus and solidus profiles are steeper than an adiabat so crystallization only takes place over a restricted depth range near the bottom of the ocean. Convective velocities are so high that crystals liti lciiting in this zone do not have time to grow larger than a few microns and are thus incapable of settling out. In this way even a totally molten initial Earth may have fulled to differentiate by fractional crystallization.