Specific surface area versus porosity from digital images: High-porosity granular samples

We micro-CT-scanned several granular packs, including glass beads of two different particle sizes and their mixtures, a natural dune sand, as well as two sieved samples of this sand and their mixtures. After segmenting these digital volumes into grains and pores, we computed their porosity (φ) and specific surface area (S). Moreover, we subsampled these segmented volumes and computed the respective φ and S of the subvolumes as well. The resulting data pairs exhibited fairly tight S versus φ trends. These trends, as observed among different samples, present a somewhat inconsistent picture. In some granular digital samples, S increases with increasing φ, while in others the opposite behavior is observed. To explain these behaviors, we analytically model the evolution of the pore-space geometry as that of a binary mixture of large and small particles. Where the small particles gradually fill the pores of an undisturbed large-particle frame, S becomes larger as φ reduces. The opposite behavior takes place where the disparate large particles are embedded into the continuum of the small particles. The smaller the number of the large particles the higher the porosity and the larger the specific surface area. Where the particles in a pack are of uniform size, S reduces with increasing φ. This theory quantitatively supports the observed experimental relations. The observed consistency between the experiment and theory means that the behaviors observed on microscopic samples are applicable at a much larger spatial scale.