Phase-Change Convection

Thierry Alboussière

Crystallization

The crystallization of alloys results often in a solid-liquid region. It can be a so-called mushy zone where a network of solid structures grows in an interstitial liquid. It has sometimes been compared to a forest of trees and branches, the dendrites. The chemical composition of the liquid is depth-dependent, and so is the equilibrium solid-liquid temperature. The small size of the dendrites adapts so that chemical exchanges between solid and liquid phases can take place: those exchanges are necessary as the equilibrium composition is not identical in both phases (fractionation). A schematic view, and images, of a mushy zone are shown below

Convection at large scale develops in the mushy zone, leading to the formation of chimneys that channel the liquid out of the mush.

Crystallization experiments were run, within the PhD project of Ludovic Huguet and with colleagues from Lyon (Stéphane Labrosse, Renaud Deguen who then moved to Grenoble and master students Thomas Le Reun and Germain Lesoeur) and the USA (Mike Bergman). We have put the experiment in a centrifuge rotor to increase apparent gravity. A comparison is made with results from the literature obtained for gravity levels lower than the usual gravity.

This led to more compact mushy layers, as shown in the next figure.

Analysis and application to the inner core of the Earth can be found in this paper PDF.

Interface conditions

When the details of the crystallization zone are ignored, it is possible to derive global interface conditions at the expense of some assumptions. With Renaud Deguen, I had first developed this kind of model to explain the East-West asymmetry of the Earth inner core PDF, PDF and PDF.

With Stéphane Labrose, Adrien Morison and Roberto Agrusta, we have then extended the model to study the crystallization of the primitive Earth's mantle PDF. It can also be used to study icy planets and satellites.

In this configuration above, convection is a layer of solid silicates is surrounded (top and bottom) by a magma ocean. The parameter Φ is related to the dynamics in the liquid phase, latent heat of crystallization, gravity, viscosity of the solid phase, adiabatic and Clapeyron slopes... The value of this single parameter in the integrated boundary condition leads to a classical (close boundary) Rayleigh-Bénard convection (large values of Φ) or to open top and bottom boundaries (small values of Φ). This last option corresponds to a significant increase of heat flux.

Adrar, Mauritania

Adrar, Mauritania