Boundary-layer analysis for the convection/diffusion transition in dendritic growth

The supercooling dependence of dendritic growth kinetics under the influence of convective heat transport is investigated theoretically and experimentally with emphasis on theoretical prediction of the supercooling level at which the transition from diffusion-controlled to convection-controlled dendritic growth occurs. It is shown that the crossover between diffusive and convective transport depends on the relative thickness of the Stefan length compared with the thermal boundary layer. These lengths become equal at a supercooling which may be calculated from diffusion theory and fluid mechanics. It is also shown that the crossover supercooling varies weakly with the gravitational acceleration, melt viscosity, and the volumetric expansion coefficient.