Transient anomalous diffusion regimes in reversible adsorbing systems

Diffusion in Heterogenous Media and Sorption—Desorption Processes

We investigate particle diffusion in a heterogeneous medium limited by a surface where sorption–desorption processes are governed by a kinetic equation. We consider that the dynamics of the particles present in the medium are governed by a diffusion equation with a spatial dependence on the diffusion coefficient, i.e., K(x) = D|x|−η, with −1 < η and D = const, respectively. This system is analyzed in a semi-infinity region, i.e., the system is defined in the interval [0,∞) for an arbitrary initial condition. The solutions are obtained and display anomalous spreading, that is, the dynamics may be viewed as anomalous diffusion, which in turn is related, and hence, the model can be directly applied to several complex systems ranging from biological fluids to electrolytic cells.

Interplay of adsorption and surface mobility in tracer diffusion in porous media

We model the diffusion of a tracer that interacts with the internal surface of a porous medium formed by a packing of solid spheres. The tracer executes a lattice random walk in which hops from surface to bulk sites and hops on the surface have small probabilities compared to hops from bulk sites; those probabilities are related to bulk and surface diffusion coefficients and to a desorption rate. A scaling approach distinguishes three regimes of steady state diffusion, which are confirmed by numerical simulations. If the product of desorption rate and sphere diameter is large, dominant bulk residence is observed and the diffusion coefficient is close to the bulk value. If that product is small and the surface mobility is low, the tracers are adsorbed most of the time but most hops are executed in the bulk. However, for high surface mobility, there is a nontrivial regime of dominant surface displacement, since the connectivity of solid walls allows the tracers to migrate to long distances while they are adsorbed. In this regime, we observe rounded tracer paths on the sphere walls, which are qualitatively similar to those of a recent experiment on polystyrene particle diffusion. The calculated average residence times are proportional to the bulk and surface densities of an equilibrium ensemble of noninteracting tracers, and the relation between those densities sets the adsorption isotherm. Simulations performed with initially uniform (nonequilibrium) distribution of tracers in the pores show other nontrivial results in cases of dominant surface residence: slow increase of the mean-square displacement at short times, since the tracer has not explored a homogeneous medium, and a remarkable slowdown between the first encounter with a solid wall and the first hop from that point. Relations between our results and other models of diffusion and adsorption in porous media are discussed.