Thermal evolution of a metal drop falling in a less dense, more viscous fluid

Abstract

The initial state of terrestrial planets was partly determined, during accretion, by the fall of metal drops in a liquid magma ocean. Here, we perform systematic numerical simulations in 2D cylindrical axisymmetric geometry of these falling dynamics and associated heat exchanges at the scale of one single drop, for various initial sizes and ambient viscosities. We explore Reynolds number in the range [0.05 − 48], viscosity ratios in the range [50 − 4000], Weber number in the range [0.04 − 5] and Peclet number in the range [70 − 850]. We show that heat exchanges between the two phases occurs predominantly at the front section of the drop. Our systematic, parametric study exhibits shows that the thermal boundary layer thickness, the depth and time for equilibration, the Nusselt number, and the magma ocean volume affected by thermal echanges, all scale as power laws of the Peclet number. Because of drop distortions, these scaling laws deviate from the classical balances considering only heat diffusion through a laminar thermal boundary layer. Finally, when considering a temperaturedependent viscosity of the ambient fluid, we show that a low viscosity layer surrounds the drop, which influences the thermal evolution of non-deformable, low Reynolds number drops only, and decreases the breakup distance for some limited breakup modes.

Dynamics of core-mantle separation: Influence of viscosity contrast and metal/silicate partition coefficients on the chemical equilibrium

“…where v is the velocity of the diapir, hmax is the mesh size and kc is the diffusion coefficient (10 -6 m 2 .s -1 , which is higher than a typical chemical diffusion, but high enough to limit numerical diffusion (see Qaddah et al, 2020). In the reference case and for the other cases within the Stokes regime, the value of Pemesh was sufficiently low (Pemesh < 10) meaning that numerical diffusion was negligible (see Mittal & Jain, 2012).…”

Conditions for Segregation of a Crystal‐Rich Layer Within a Convective Magma Ocean

“…Code Availability : The software used for this study is the commercial software COMSOL Multiphysics (version 5.4) previously validated for two phase flow applications (Qaddah et al. (2019, 2020)). User manual can be downloaded here: https://doc.comsol.com/5.4/doc/com.comsol.help.cfd/CFDModuleUsersGuide.pdf.…”

“…We used the commercial software COMSOL Multiphysics (version 5.4) that has been previously validated for two phase flow applications (Qaddah et al (2019(Qaddah et al ( , 2020). Equations 1-5 were solved using the multiphase-flow tool-suite of COMSOL Multiphysics 5.4 (Computational Fluid Dynamics and Heat transfer modules) (For more informations see the Code Availability section).…”

“…COMSOL Multiphysics is a simulation platform that provides fully coupled multiphysics and single-physics modeling capabilities. COMSOL Multiphysics (version 5.4) has been previously validated for two phase flow applications (Qaddah et al (2019(Qaddah et al ( , 2020). To compute our simulations we used the Heat Transfer (www.comsol.com/heat-transfer-module) and Computational Flow Dynamics (www.comsol.com/cfd-module) modules in addition to the main Multiphysics platform (www.comsol.com/comsol-multiphysics).…”