Concentration dependence of solution shear viscosity and solute mass diffusivity in crystal growth from solutions.

Abstract

The physical properties of a supersaturated binary solution such as its density \ensuremath{\rho}, shear viscosity \ensuremath{\eta}, and solute mass diffusivity D are dependent on the solute concentration c: \ensuremath{\rho}=\ensuremath{\rho}(c), \ensuremath{\eta}=\ensuremath{\eta}(c), and D=D(c). The diffusion boundary layer equations related to crystal growth from solution are derived for the case of natural convection with a solution density, a shear viscosity, and a solute diffusivity that are all dependent on solute concentration. The solution of these equations has demonstrated the following. (a) At the vicinity of the saturation concentration ${\mathit{c}}_{\mathit{s}}$ the solution shear viscosity \ensuremath{\eta} depends on \ensuremath{\rho} as ${\mathrm{\ensuremath{\eta}}}_{\mathit{s}}$=\ensuremath{\eta}(${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$)\ensuremath{\propto}${\mathrm{\ensuremath{\rho}}}^{1/2}$(${\mathit{c}}_{\mathit{s}}$). This theoretically derived result has been verified in experiments with several aqueous solutions of inorganic and organic salts. (b) The maximum solute mass transfer towards the growing crystal surface can be achieved for values of c where the ratio of d ln[D(c)/dc] to ln[\ensuremath{\eta}(c)/dc] is a maximum.