ENTRAINMENT FROM A BED OF PARTICLES BY THERMAL-CONVECTION

Differentiation in magma chambers, in the Earth's core and in the part ially molten early Earth is a competitive process between sedimentatio n and re-entrainment of crystals in the presence of convection. Previo us studies show that the particles suspended in convective layers even tually settle and do so almost as fast as in the absence of convection . However, the nature and magnitude of the competing entrainment has r emained unclear. Here we provide a simple theory and experimental evid ence showing that entrainment occurs at the crests of dunes created in the particle bed at the base of a convecting fluid. In both laminar a nd turbulent regimes, the dune formation and entrainment are driven by viscous stresses produced by thermal plumes. At sufficiently high Ray leigh numbers the particles are probably entrained by Reynolds stresse s. Entrainment in the Earth's core is hardly possible because it requi res unreasonably small crystals. Entrainment of 10(-2)-10(-1) cm diame ter crystals is very likely in magma oceans. For magma chambers entrai nment requires large viscosities (> 10(6) P) and even when it occurs, the total amount of the suspended solid fraction is very small.