Multi-Component Diffusion in the Vicinity of a Growing Crystal

Abstract

Co-crystallization from multi-component solutions occurs in many solids formation processes. The measurement or simulative description of concentration courses in the fluid vicinity of a growing crystalline substrate is difficult for such systems. These are relevant with respect to developing concentrations of crystallizing components at the solid-liquid interface due to diffusion fluxes in the solution. Concentrations may change such that unintended crystalline states can develop. With Fickian multi-component diffusion modeling we are able to simulate the timely evolution of the concentrations in the diffusion boundary layer during crystallization of various solid entities. Not only single solvate crystallization is modeled but also co-crystallization from multi-component solutions with different solvate states. The simulations are run with the assumption that diffusion limitation dominates. However, the model can be easily adapted to integration limitation. The interdependence of two diffusing components is taken into account in Fick’s multicomponent diffusion with a diffusion coefficient between these two components. We show that the consideration of so called cross-diffusion effects between dissolved materials can be neglected during crystallization of single decahydrates and during co-crystallization of anhydrous electrolytes. The presented model is also capable of fitting crystal growth kinetics with single point desupersaturation measurements in a thin film. In addition to the study of the kinetic parameters, the simulation allows the determination of the spatial concentration evolution from the single point concentration measurements.