Concentration profile for linear driving force model for diffusion in a particle

The linear driving force (LDF) model for diffusion rates in a particle has been a key tool in adsorber studies and design since Glueckauf first proposed it in 1955. The general profiles, q(t, r) = A(t)+B(t)rⁿ where n is an integer≥2, lead directly to the LDF model. The parabolic profile is only one specific solution for this model. For the transient volume-average uptake, it is proven that only n = 2 or 5 yield results identical to those of the LDF model. From the transient concentration distribution in the particle, however, only n = 5 can represent the LDF results. Hence, the 5th-order binomial concentration profile, rather than the parabolic profile, is the correct representation of the LDF model.