Wave mechanism of mass transfer for kinetics of adsorption in biporous media

For the first time, the process of adsorption kinetics in biporous media is considered under conditions of temporal nonlocality. In this case transition to equilibrium between each small element of the medium and the ambient volume occurs with a finite velocity. Mass transfer is studied in the context of phenomenological theory for sorption in a biporous cylindrical granule. We show that under temporal nonlocality the process is described by an integer–differential equation, and the concentration distribution in the cross-section of the biporous granule exhibits both wave and diffusion properties. We find the analytical solutions of the equation when the transfer stage in the transport pores is the rate-limiting one. We show that near thermodynamic equilibrium, the main contribution is made by the diffusion component, and the concentration distribution weakly depends on the condition of temporal nonlocality. In contrast, at a time comparable with a time of relaxation to local equilibrium, the contribution of hyperbolic component prevails. The concentration profile in this case has a sharp front moving away from the granule surface with a constant velocity contrary to the classical theory. In this way, the condition of local nonequilibrium determines the wave mechanism of mass transfer in the processes of adsorption in biporous media. We propose new experiments to check the validity of our hyperbolic model of mass transfer and discuss the adequacy of the theoretical approach.