Tortuosity evaluation for characterization of transport phenomena in pure-crystalline metal lattices and porous media

A precise knowledge of tortuosity and connectivity of regular structures of particles is of great interest in a plenty of fields, especially in the estimation of the transport properties of hydrogen in metal lattices in terms, for example, of the effective diffusivity. For this purpose, the present chapter reports a systematic evaluation of tortuosity and connectivity, which can be generally applied to other types of structures, too. In particular, several mono- and bidisperse structures of overlapping and detached spherical particles are considered: simple cubic (SC), face-centered cubic (FCC), body-centered cubic (BCC), tetragonal, and CaF2-like structures. This analysis is carried out using a computational fluid dynamics (CFD) approach, by means of which the dependence of the so-called diffusive tortuosity on the characteristic geometrical parameters is evaluated. Once tortuosity is evaluated, the structure connectivity is quantified by an appropriate connectivity factor, which is defined as the inverse of tortuosity. As one of the major results among others, it is shown that the regular structures of spherical particles have a limit porosity-called Limit Porosity Value-below which the tortuosity becomes infinite (i.e., zero-connectivity), since the inner pores are completely disconnected to each other. The extension of this concept to bidisperse and, more generally, multidisperse structures leads to so-called morphology maps, which is a sort of phase diagram showing the connectivity level of a structure. An example of morphology map is reported here for the CaF2-like structure. The proposed analysis allows comparing the morphology of different porous and dense materials, applicable in the fields of catalysis, transport in porous media and membranes.