On the validity of boundary layer analysis for flow and mass transfer caused by rotation during the solution growth of large, single crystals

The rate of growth of single crystals from liquid solutions depends on coupled kinetic and transport phenomena. However, when continuum transport is limiting, the maximum crystal growth rate is determined by the rate of solute transport through the liquid phase to the growing crystal. We examine the validity of simple scaling and boundary layer theories to assess the behavior of a model solution crystal growth system, namely the growth of potassium titanyl phosphate (KTP) from high-temperature solutions. The approximation of the transport to a crystal rotating steadily in a supersaturated solution is based on the classical analytical solution for flow driven by a semi-infinite rotating disk and associated mass transfer. Our results indicate that this boundary layer analysis is reasonable as long as the solution container is very large, the geometry of the system is nearly axisymmetric, and the imposed flows are predominantly steady. For many practical systems, these conditions do not hold and such boundary layer analyses are expected to be in considerable error.