Role of the bi-dispersion of particle size on tortuosity in isotropic structures of spherical particles by three-dimensional computer simulation

Abstract

In this study, the effect of the bi-dispersion of the particle size on tortuosity is investigated. To do that, three-dimensional computer simulations are carried out on isotropic structures of non-overlapping spherical particles. The validity of the calculation methodology is provided by investigating different diffusion directions of the FCC structure (〈1 0 0〉, 〈1 1 0〉 and 〈1 1 1〉) and mesh settings. Then, the functionality of tortuosity with porosity is first evaluated for several mono-disperse structures—i.e., the Simple Cubic (SC), Body-Centred Cubic (BCC), Face-Centred Cubic (FCC) and the so-called “Tetragonal” structure – introducing also a suitable empirical correlation with just one adjustable parameter. Afterwards, two bi-disperse structures – NaCl and CaF2 – are investigated, highlighting the effect of the bi-dispersion on tortuosity in terms of several geometrical parameters (inter-particle distance and particle diameters). As the main novel result, it is found that the functionality of tortuosity with porosity presents a lower bound curve (here-called Minimum Tortuosity Curve, MTC) for each structure investigated. In particular, it is proposed that this curve might be generally achieved by considering the particle diameters in the minimum porosity configurations (i.e., maximum packing degree) and allowing just the inter-particle distance to change. This concept is used to explain the reason why the mono-disperse structure with the highest minimum porosity have also the highest tortuosity-curve. Furthermore, for the NaCl structure, it is found a small porosity range in which tortuosity slightly increases with increasing porosity. This peculiar behaviour, observed for the first time, is attributed to the particular approach of the NaCl structure to the FCC one as the second particle decreases. Finally, after presenting a brief geometrical comparison between FCC, NaCl and CaF2 in terms of cross-sectional area profiles, an overall correlation is proposed to calculate the porosity–tortuosity ratio.