A new closed-form approximate solution to diffusion with quadratic Fujita's non-linearity: the case of diffusion controlled sorption kinetics relevant to rectangular adsorption isotherms

A new approximate solution relevant to case of rectangular (Langmuirian) adsorption isotherms has been developed on the basis of the integral-balance method with double integration technique. The solution is based on the model developed by Ruthven for slab and spherical adsorption pellets where the adsorption is controlled by the diffusion in macropores. This model results in a concentration-dependent diffusion coefficient with a quadratic nonlinearity of Fujita's type. The new approximate solution utilizes the concept of finite penetration depth of the diffusant penetration and almost shockwave shape of the concentration profiles. The solution is based on an assumed parabolic profile with unspecified exponent. The solution analysis allowed determining the optimal exponents of the concentration profile as a function of the nonlinearity parameter of the Fujita's concentration relationship. The approximate solutions have been compared to existing results from the literature and especially the data published by Ruthven and Crank, for concentration distributions and fractional uptakes in an adsorbent slab pellet.