Hydromechanics for crystal growth from water-salt solutions

Abstract

This paper presents an overview of the current state of technological problem solving related to controlling of hydrodynamics and mass transfer in crystallizers of complex design (continuous-flowing and non-flowing) during the growth of crystals with technologically important properties (potassium dihydrogen phosphate - KDP and a mixed crystal of nickel and cobalt - KCNSH) from special water-salt solutions. Unlike crystallizers of standard designs for crystal growth from a melt (by Czochralski, Bridgman, etc.), there are also crystallizers of different design for crystal growth from water-salt solutions. According to the designers, the necessary crystal growth conditions are maintained in these crystallizers by creating the best characteristics of the flow, i.e., by controlling its velocity and direction, as well saline saturation solution and temperature. In this work, hydromechanical problems are solved for continuous-flowing and non-flowing crystallizers. The flow visualization through its physical model reveals a multi-vortex and unsteady flow structure due to mixer action, three-dimensional solution inflow and outflow and spatial crystal placement. For this reason, primary attention is given to the studies devoted to the development and application of the mathematical models for hydromechanics and heat and mass transfer based on the complete Navier-Stokes equations in the Boussinesq’s approximation for laminar regimes, as well as to the standard (k-ε)-turbulence model for turbulent regimes. The hydromechanical features associated with the three-dimensional flow complexity are discussed for continuous-flow crystallizers. The possibilities of maintaining the required saline saturation near the growing crystal over a long period of time are analyzed for non-flowing crystallizers. Mathematical models of convective mass transfer are considered in a "solution-crystal" conjugate formulation. The local features of hydrodynamics and mass transfer conditions in solution (saline solution saturation near growing crystal) are analyzed.