Modeling of the dissolution phenomena of solid particles into an infinitely large medium from the analytical solutions of reaction–diffusion equations

Abstract

Mathematical solutions of the concentration of dissolved component in surrounding fluid were obtained for analyses of the dissolution phenomena of spherical, cylindrical, and slab-type particles. Calculation of the surface flux enabled material balance equations to be derived for the prediction of transient particle size. For the spherical particle, the resulting differential equation was solved numerically to compare with the analytical solution. For the cylindrical particle, the Weber transform was applied to predict the radius of the infinitely long cylinder as a function of time. After obtaining an analytical solution for the thickness of the dissolving slab, the result was compared with those of the sphere and cylinder. The spherical particle exhibited the shortest complete dissolution time (CDT), due to having the greatest surface-to-volume ratio. When external film resistance was important for the mass transfer, the Biot number was included in the governing equation, and to predict the particle size during dissolution, the concentration in the fluid phase could be derived by the combination of variables, or the Weber-type transform. When first-order or zero-order reaction occurs in the surrounding fluid, the concentration could also be predicted by the Laplace transform, and the particle size could be calculated for the solid particles. Similar to the simple diffusion process, CDT was predicted to increase in the order sphere < cylinder < slab. The experimental data of the dissolution of polymeric fiber was compared with the modeling result to estimate the diffusivity and solubility factor, which varied with the pH of the surrounding fluid.