Exact calculation of the tortuosity in disordered linear pores in the Knudsen regime

The squared reciprocal tortuosity kappa-2=D/D0 for linear diffusion on lattices and in pores in the Knudsen regime is calculated analytically for a large variety of disordered systems. Here, D0 and D are the self-diffusion coefficients of the smooth and the corresponding disordered system, respectively. To this end, a building-block principle is developed that composes the systems into substructures without cross correlations between them. It is shown how the solutions of the different building blocks can be combined to gain D/D0 for pores of high complexity from the geometrical properties of the systems, i.e., from the volumes of the different substructures. As a test, numerical simulations are performed that agree perfectly with the theory.