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Mechanism of dissolution. I. Mathematical interpretation of concentration gradients developed during dissolution of a solid.

The dissolution of m-acetotoluide from fused disks was studied using a column dissolution model. This model allowed the study of dissolution under both ascending and descending conditions. Fick's second law of diffusion was solved for the case of D = f(c) and theoretical concentrations calculated assuming the existence of a saturated layer at the solid-liquid interface. Excellent agreement between the theoretical and experimental values for dissolution and diffusion indicated that diffusion control of the dissolution process was obtained in the ascending model. The descending model produced mass transfer rates far in excess of any that could be predicted by molecular diffusion alone. An effective interfacial concentration, less than saturation, was developed in the descending model which could be determined experimentally and which, when used to calculate the total amount dissolved, gave excellent correlation with experimental results. A random-walk model with autocorrelation, which gives rise to the telegraph equation, was used to describe the concentration gradient developed in the descending model.