THE NUCLEATION, GROWTH AND SETTLING OF CRYSTALS FROM A TURBULENTLY CONVECTING FLUID

We present a new model to describe the thermal and compositional evolu tion of a binary alloy which is cooled from above. Explicit account is taken of the nucleation of crystals in the cold upper thermal boundar y layer, the growth of crystals in the turbulently convecting interior , and their subsequent gravitational settling to the floor of the cham ber. The crystallization of one solid phase only is considered. When t he residence time of a typical crystal within the convecting bulk is s hort compared with the overall cooling time of the fluid, the crystal size distribution loses memory of earlier conditions in the fluid and the number density simply decays exponentially with the cube of the cr ystal size. A quasi-steady state exists in which the rate of crystal p roduction is balanced by the rate of sedimentation at the floor, allow ing the volume fraction of suspended crystals to remain small until co nvection ceases to be vigorous. We focus on the situation in which the latent heat released by solidification would far exceed the heat flux extracted through convection if the melt undercooling were maintained equal to the initial temperature difference applied at the cold upper boundary. In this case, either the growth or nucleation of crystals m ust be limited in order that the fluid continues to cool. Both the gro wth-limited and nucleation-limited regimes may develop during the cool ing of an individual fluid body, depending upon the thermal boundary c ondition at the upper boundary of the convecting portion of the fluid. We calculate how the mean crystal size within the sedimented crystal pile evolves as the fluid cools. During the growth-limited regime, the mean crystal size in the crystal pile typically decreases with height , owing to the decrease in the extracted heat flux and the greater eff iciency of crystal settling as the fluid layer becomes shallower. In c ontrast, during the nucleation-limited regime, the fluid undercooling may increase significantly as the fluid cools, and inverse grading (la rge crystals over small) is possible. We discuss the possible applicat ion of our theory to the cooling of large igneous intrusions.