Convection and Crystallization in a Liquid Cooled from above: an Experimental and Theoretical Study

Evidence from experiments and theoretical modeling suggests that systems crystallizing exclusively from the top down and rejecting a buoyant liquid effectively cease convecting once the initial superheat has been lost. We report here on a combined experimental and theoretical study designed to investigate in some detail the interaction of convection and crystallization in a fluid cooled from above. The experiments are carried out in a small tank where temperature, composition, mush thickness, and convective velocities have been monitored. After an initial period of turbulent convection removing the superheat, the bulk fluid temperature holds steady at the liquidus temperature. Further convection at Ra ∼ 10⁶ is characterized by a gentle, broad stirring of the entire tank through upward boundary layer flows hugging the tank walls, which are inferred to be sustained by a small but steady leakage of heat into the tank through the sidewalls. The thickness of the overlying mush zone increases linearly with √t and is found to be very sensitive to leakage of heat through the sidewalls. Within the uncertainty of the liquidus determination, there is no measurable undercooling and no crystallization is observed within the bulk fluid. The experimental results are investigated with a comprehensive analytical model employing sidewall heating and, among other things, either equilibrium or disequilibrium crystallization. Either crystallization model gives satisfactory agreement with the experiments. More importantly, however, once the superheat is lost all the convective motion is well explained by the unwanted sidewall heating, and if this heat source is then ‘analytically’ turned off, convection ceases upon loss of the superheat. In sum, this combined study supports the conclusion that convection in similar binary phase systems crystallizing from the top down and rejecting a buoyant liquid becomes non-turbulent or even ceases upon loss of the superheat. Transferring these results to magmatic systems, we suggest that the dynamics inside intrusive bodies upon cooling are very sensitive to the actual phase diagram, the kinetics of crystallization and the density relation between crystals and melt.