A Numerical Treatment of Melt/Solid Segregation: Size of the Eucrite Parent Body and Stability of the Terrestrial Low-Velocity Zone

Crystal sinking to form cumulates and melt percolation toward segregation in magma pools can be treated with modifications of Stokes' and Darcy's laws, respectively. The velocity of crystals and melt depends, among other things, on the force of gravity (g) driving the separations and the cooling time of the environment. The increase of g promotes more efficient differentiation, whereas the increase of cooling rate limits the extent to which crystals and liquid can separate. The rate at which separation occurs is strongly dependent on the proportion of liquid that is present. As a result, cumulate formation is a process with a negative feedback; the more densely aggregated the crystals become, the slower the process can proceed. In contrast, melt accumulation is a process with a positive feedback; partial accumulation of melt leads to more rapid accumulation of subsequent melt. This positive feedback can cause melt accumulation to run rapidly to completion once a critical stability limit is passed. The observation of cumulates and segregated melts among the eucrite meteorites is used as a basis for calculating the g (and planet size) required to perform these differentiations. The eucrite parent body was probably at least 10-100 km in radius. The earth's low velocity zone (LVZ) is shown to be unstable with respect to draining itself of excess melt if the melt forms an interconnecting network. A geologically persistent LVZ with a homogeneous distribution of melt can be maintained with melt fractions only on the order of 0.1% or less