Tortuosity in the Brick and Mortar Model Based on Chemical Conduction

Diffusion is a reoccurring phenomena in many fields and is affected by the geometry in which it takes place. Here we investigate the effects of geometry on diffusion in a Brick and Mortar model system. The tortuous effects are evaluated based on generalized Fick's law, i.e. diffusion driven by differences in chemical potential. The presented formalism gives a general (semi-) exact analytic expression for the tortuosity using impermeable bricks, which is successfully validated against standard techniques and finite element method results. The approach allows for anisotropic properties of the mortar, which we show can be significant and is not captured with known analytic techniques. Based on the introduced concept of chemical conductivity we also find generalized Fick's law consistent with Ohm's and Fourier's law in terms of their constituent parts, which further makes the main results for Brick and Mortar structures directly applicable to diffusion of either charge, heat, or mass.