Tortuosity of porous particles

Tortuosity is often used as an adjustable parameter in models of transfer properties through porous media. This parameter, not reducible to classical measured microstructural parameters like specific surface area, porosity, or pore size distribution, reflects the efficiency of percolation paths, which is linked to the topology of the material. The measurement of the effective conductivity of a bed of particles saturated with an electrolyte is a simple way to evaluate tortuosity. Nevertheless, it received only little attention because of the real difficulties in both getting reliable results and interpreting data. Notably, the discrimination between the contribution of interparticle and intraparticle porosities to the tortuosity is not resolved. To our knowledge, there is no model able to fit the experimental data of the tortuosity of a suspension, and a fortiori of a particle bed, in the whole porosity range. Only empirical expressions have been proposed, but they do not allow deriving intratortuosity of a porous particle. For a dilute system, Maxwell's equation predicts the effective conductivity of suspensions of spherical particles as a function of the bulk electrolyte conductivity and of particle conductivity. The intraparticle tortuosity can be derived from the particle conductivity obtained from the Maxwell equation applied to data at infinite dilution of particles. Then, by assuming that the Maxwell equation is a first-order approximation of the conductivity as a function of porosity, we propose an explicit relation of the tortuosity tau of a suspension of porous particles, obtained by conductivity measurement, as tau = tau(epsilon, epsilon(p), tau(p)), where epsilon is the total porosity of the suspension, tau(p) is the intraparticle tortuosity, and epsilon(p) is the particle porosity. This relationship fits the experimental data in the whole porosity range and can be used to determine tau(p) from an experiment at only one porosity. Finally, the obtained values of tau(p) for a set of porous particles used in chromatography are discussed and compared to the data available in the literature.