A new theoretical approach to model crystal growth from solution

A description of crystal growth in supersaturated solutions is suggested, based on conventional theories of mass diffusion and integration of solute molecules into the crystal lattice. In this approach, the integration step is preceded by two other steps (solute diffusion and adsorption) occurring concurrently over the adsorption layer. The new arrangement of the processes involved and the estimation of crystallization kinetics as a function of what is adsorbed are thought as being the main differences relative to established models. The physical concepts are presented in the first part of the paper, following a methodology comparable to well-known derivations of adsorption isotherms. Supported on that theoretical background, shell mass conservation balances are formulated, with resulting second-order differential equations for the concentration profile around the crystals. The model-characteristic equations are then derived for different crystal geometries, diffusional resistances and kinetic orders. Finally, a simplified growth rate equation is deduced, providing a generic way of relating the crystallization variables.