Marangoni effect in metal-silicate self separation

High pressure experiments of metal silicate mixtures display a tendency for the molten metal phase to percolate through the solid silicate matrix toward the coolest regions of the sample. This simple observation carries important implications for processes leading to formation of planetary cores and present day core-mantle interactions. For the percolation to work, two ingredients are necessary, the classical wetting condition and a driving force to compact the silicate matrix. At laboratory scale experiments, gravity is negligible and the only available driving force is surface tension, and in particular its temperature dependence (the Marangoni effect). We developed a physical model to treat numerically this problem within the framework of the compaction two-phase theory proposed by Bercovici, Ricard et al. Starting from a layered situation where the metal is on the hottest side, we obtain a wetting front motion toward the cold side. Numerical experiments show that the velocity of the wetting front scales inversely with the viscosity of the matrix, and matching the experimental results allows its determination. Comparison of interfacial tension and gravity shows that the former dominates at laboratory scale and is negligible at the scale of the Earth mantle. An interesting situation may arise in 100 km sized planetesimals during their core formation: gravity dominates in the upper part and would drive downward flow of the metal whereas effects become small toward the center where the temperature gradient would push the metal upward.