Momentum and mass transfer in supersaturated solutions and crystal growth from solution

The physical properties of supersaturated solutions such as solution density ϱ, shear viscosity η and solute diffusivity D are strongly dependent on solute concentration c∞: ϱ = ϱ(c∞), η = η(c∞) and D = D(c∞). The concentration dependence of the properties has been taken into account in the rederivation of the generalized momentum and mass transport equations governing crystal growth from solutions. The non-linear ordinary differential equations obtained for the steady regime of isothermal crystal growth were analyzed. The exact simultaneous solutions obtained for the rederived transport equations resulted in the following conclusions: (a) There exists a restriction imposed on the Schmidt number for supersaturated solutions: Sc∞ ⪢ 49. Only under this restriction the generalized momentum and mass transfer equations have simultaneous consistent solutions. (b) The solution-crystal interface profile “thickness” ·int(x1) is proportional to the diffusion boundary layer (DBL) thickness: ·int(x1) ≈ 0.24·diff(x1). (c) The ratio of solute flux along the solution-crystal interface to the flux along the DBL edge is the increasing function of and is dependent only on Sc∞.