Mass-transfer calculation methods for transient diffusion within particles

Modeling of diffusion within spherical particles is often an important part of modeling of many processes relevant to chemical engineering such as adsorption. The accurate solution of the differential equations describing diffusion is quite a complicated task involving calculation of infinite series. A rational approximation to the diffusion equation is presented in this article leading to a solution that is both very easy to use and very accurate. The present method was compared to the exact solution for diffusion and adsorption in spheres, and it was found that the present solution is practically indistinguishable from the exact solution. This method is also applicable to multicomponent systems in a straightforward manner.