Document Type


Subject Area(s)

Chemical Engineering


This paper describes a new approach to solving the equations comprising the shrinking core model for diffusion and reaction of a chemical species in a solid spherical particle. The reactant adsorbs on the particle surface, diffuses into the particle's interior, and reacts with the particle to form a solid product. The shrinking core model assumes a fast reaction rate compared to reactant diffusion so that the reaction is localized in the interfacial zone between the unreacted solid core and the surrounding shell of reacted product. Analytical solutions of the governing conservation equations usually invoke the pseudo-steady state (PSS) approximation which neglects the transient mass accumulation and diffusion-induced convection terms in the continuity equation for the diffusing reactant. However, small particle radii and slow reactant diffusion cast doubt on the validity of the PSS approximation. Dimensional analysis reveals an approximation that is less restrictive than PSS, yet enables a semi-analytical solution for the diffusing reactant distribution and interface velocity. For sufficiently large values of the surface mass fraction of the diffusing reactant, the PSS approximation leads to serious errors in the time dependence of the interface position and fractional conversion. However, our estimate of the surface mass fraction of hydrogen in LaNi5 particles suggests the validity of the PSS approximation for hydriding of metal alloy particles. The shrinking core model thus enables an estimate of hydrogen diffusivity in metal alloy particles.