Tortuosity and connectivity evaluation by CFD simulation for morphological characterization of membranes and catalytic structures. Case study: CaF2-like structure

A systematic methodology to characterise porous structure of membranes and catalysts in terms of tortuosity and connectivity is presented. The considered case study is the CaF2-like structure of bidisperse spherical particles (i.e., inner and outer particles with different diameters), which are allowed to overlap. Consequently, the morphology of the resulting structure is shown to be completely determined by two geometrical parameters (two degrees of freedom). For this investigation, a Morphology Map is developed, it being a plot mapping void connection as a function of the characteristic geometrical parameters. Within such a map, we introduce the so-called Minimum Connection Curve, which is a characteristic curve representing the boundary between the connected region and the disconnected one (zero connectivity). It is then found that the CaF2-like structure has three specific points where there is an abrupt change in the morphology behaviour, also correlated to the normalised surface area. Then, the structure tortuosity and connectivity are systematically evaluated in a wide range of geometrical conditions of the two parameters characterising the considered structure. As a result, it is shown that it is not possible to express these parameters as a unique function of porosity. However, both tortuosity and connectivity are found to be correlated with a good approximation in a certain range of porosity values with a geometrical parameter that we called Effective Porosity, which is the porosity available for diffusion at the minimum connection conditions. Convenient empirical correlations are eventually provided to allow readers to evaluate tortuosity and connectivity in a wide range of values.