New analytical solution for nonlinear adsorption and diffusion in a single particle

Abstract

A new analytical solution for the fractional uptake in a single particle was obtained that obviates the use of the assumption Q ̄ =f( C ̄ ) that has been used by others to make the mathematics more tractable. This new solution utilizes the summation of the gas and adsorbed phases approach to describe the simultaneous intraparticle gas and surface diffusion rates. The resulting uptake curves predicted from the new expression compare very well with those obtained from the exact numerical solution for a wide range of systems and conditions. An expression for the rate of accumulation of the adsorbed species was also derived that should find use in adsorption process modeling, as it accounts for both pore and surface diffusion in a simple formulation. Overall, this analysis reveals the validity of the above assumption even for systems that exhibit highly nonlinear adsorption isotherms; hence, it should be useful as a major simplification in other derivations dealing with nonlinear adsorption and diffusion.