Revealing void anisotropies in vertically-vibrated granular sphere packings with various structural characterizations

We utilize magnetic resonance imaging (MRI) techniques to study granular sphere packings prepared with vertical vibration, and reveal the extremely slight global anisotropies of the void phase with systematic analyses on Delaunay pores and chords. Unexpectedly, the global orientational orders of the eigenvectors of tensors quantifying (i) pore throats, (ii) chords going through individual pores, (iii) shape of Voronoi cells and (iv) contact fabrics have consistent evolution laws when packing fraction changes, but the orientational order of the eigenvectors of a pore volume tensor exhibits a peculiarly different trend. With an orientation-dependent spatial correlation function, we attribute their different behaviors to the fact that different anisotropy variables probe the void phase at different length scales, so that their dependences on packing fraction are different. The segmentation of the void region into pores sensitively captures a unique and intricate structural anisotropy at an intermediate length scale.