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To match the dynamics of a linear driving force model and the diffusion equation is of great practical importance in the design and optimization of adsorption separation processes. A frequency response analysis is applied to show that it is not possible to arrive at an equivalence based on a single parameter. Using this as the basis, a universal equivalence for the linear problem is constructed and closed form analytical expressions for the two parameters are derived for the sphere and slab geometries. The two parameters represent the increased effective mass transfer coefficient and a reduction in the active volume of the particle, both corresponding to the internal concentration profiles of the diffusion equation at cyclic steady state.

Exact equivalence at cyclic steady state between isothermal diffusion and linear driving force models for linear adsorption systems