Analytical Solutions of Shrinking Sphere Models for Batch Reactions
by
Rose Davies
School of Engineering and Advanced Technology, Massey University
Coauthors: Richard G. Haverkamp

Two shrinking sphere models are presented for the reaction of spherical particles controlled by mass transfer where reactants and products are contained in a closed system, such as a batch digestion of a mineral. The models have been developed with a pseudo steady state (PSS) approximation where the concentration profile through the diffusion layer of particles is assumed to reach steady state quickly in response to the changes in the product species concentration in the solvent of the closed system. One of the two models is for planar diffusion through the diffusion layer while the other accounts for diffusion through a spherical shell diffusion layer. Analytical solutions have been obtained with these two models. The results of the calculations show that this spherical diffusion shell results in much shorter dissolution times for small particles and show that those two forms give very similar results when the particle size is relatively large. The analytical solutions from the two forms of the model enable reaction profiles to be modelled for many systems with different physical properties of particles and reactors. The solutions are compared with experimental data.

Date received: November 5, 2009