The interface concentration, a crystal dissolution rate study

grantor: University of TorontoStatistical Rate Theory has been previously proposed as a method for predicting the rate of molecular transport between thermodynamic phases. Herein, this theory is applied to formulate an expression for the steady state KAlum dissolution rate in a rotating disk apparatus. When this rate expression is combined with the application of a new solution to the steady state convection-diffusion equation, one finds that a prediction of the rate, and hence the concentration throughout the fluid phase, can be made. To evaluate these predictions, the imposition of equilibrium at the interface has been avoided. This has lead to the development of two new expressions: one for the interface concentration and the other for the diffusion layer thickness, both of which differ from those obtained by previous methods. The results demonstrate that the predicted interface concentration is lower than the saturation value, indicating nonequilibrium at the interface. It was also found that the interface concentration is (a) related to the molecular thermal speed and (b) decreases with increasing dissolution rate. Also, the predicted diffusion layer thickness was found to be a function of temperature for all rotation rates. The mathematical form of a new variable, the steady state exchange rate, was formulated and investigated. Its complete expression has been found to be a function of two constants: (a) the equilibrium exchange rate and (b) a fraction of the average fluid velocity at the entrance to the diffusion layer that the fluid still has when it is one mean free path away from the crystal surface. Finally, through nondimensional analysis, a new dimensionless similarity parameter has been defined. Except for zero rotation, this number implies that the non-linear interfacial transport rate is within an order of magnitude of the diffusion rate independent of temperature.M.A.Sc