Tortuosity

Tortuosity is a geometric measure of how winding a path is compared with the straight-line distance between two points. In most contexts it is defined as the ratio τ = L_eff / L_free, where L_eff is the actual length of a transport path and L_free is the direct distance between its endpoints. The value is dimensionless and satisfies τ ≥ 1, with higher values indicating more convoluted paths.

In porous media, tortuosity describes how pore structure hinders diffusive and advective transport. It factors into models of diffusion, electrical conductivity, and fluid flow, where transport coefficients in a porous medium are often expressed as the product of a porosity factor and a tortuosity factor (for example, D_eff ≈ D_0 ε / τ in simple homogenization schemes). Tortuosity tends to increase with poorer connectivity, greater pore-scale curvature, and anisotropy, and it often depends on the scale and the method used to measure it.

Measurement and estimation of tortuosity employ several approaches. Imaging-based reconstruction from micro-CT or similar techniques can reveal pore paths for geometric calculations. Tracer diffusion experiments and impedance or conductivity measurements provide hydrodynamic or transport-based estimates. Different communities may emphasize geometric versus transport-based definitions, yielding related but not identical tortuosity values.

Applications of tortuosity span disciplines. In geology and hydrogeology, it influences groundwater diffusion and contaminant migration. In chemical engineering and energy storage, it affects ion transport in porous electrodes and membranes. In physiology and medicine, tissue tortuosity describes the twisted architecture of vessels and capillaries, impacting oxygen delivery, nutrient transport, and drug diffusion.