Modes of wall induced granular crystallisation in vibrational packing

Abstract

Granular crystallisation is an important phenomenon whereby ordered packing structures form in granular matter under vibration. However, compared with the well-developed principles of crystallisation at the atomic scale, crystallisation in granular matter remains relatively poorly understood. To investigate this behaviour further and bridge the fields of granular matter and materials science, we simulated mono-disperse spheres confined in cylindrical containers to study their structural dynamics during vibration. By applying adequate vibration, disorder-toorder transitions were induced. Such transitions were characterised at the particle scale through bond orientation order parameters. As a result, emergent crystallisation was indicated by the enhancement of the local order of individual particles and the number of ordered particles. The observed heterogeneous crystallisation was characterised by the evolution of the spatial distributions via coarse-graining the order index. Crystalline regimes epitaxially grew from templates formed near the container walls during vibration, here termed the wall effect. By varying the geometrical dimensions of cylindrical containers, the obtained crystallised structures were found to differ at the cylindrical wall zone and the planar bottom wall zone. The formed packing structures were quantitatively compared to X-ray tomography results using again these order parameters. The findings here provide a microscopic perspective for developing laws governing structural dynamics in granular matter.

The effects of packing structure on the effective thermal conductivity of granular media: A grain scale investigation

“…This contrast can be attributed to the different completeness of ordering in these two regions. As mentioned before, due to the curved cylinder wall, distortion occurs in the side region [53], making the ordered packing structures deviate from perfect FCC and HCP and become looser as well as less symmetric. In summary, two grain-scale mechanisms to enhance the macroscopic eff are identified regarding to the ordered packing structure.…”

“…By vibrational agitation of granular media disorder-to-order transitions are provoked. Grains gradually rearrange themselves into structured clusters to achieve dynamic efficiency [41,53]. Not only can the packing fraction be varied, but also the order level of the packing structure significantly increases during vibration.…”

“…These packings are then subjected to continuous mechanical vibration by sine wave agitation of the bottom surface. As a result, grains are excited and relocate into new positions, forming structured clusters that grow and finally reach quasi-equilibrium states [53]. Three types of granular media are simulated and their geometrical dimensions are summarised in Table 2.…”

“…In such measurement, the neighbour configuration of each grain is first represented by a set of vectors pointing from a given grains to its neighbours, i.e., 12 nearest grains in current study, and then the cosine similarity between the vector set of a particular grain and those vector sets of its neighbours is used to evaluate the resemblance between the neighbour configurations of these grains. Thus, the order level of grain-scale packing structure is positively described by the aforementioned resemblance, with values ranging from 0 to 12 [39,[53][54][55]. Voronoi tessellation [56] is employed to obtain the effective volume V and packing fraction V of individual grains.…”

“…As shown in Figure 5, the mean values of both of 6 and V monotonically increase with vibration, which implies a cooperative process between densification and ordering in granular media. The reason for the sudden increase of V in D50 can be explained by the geometrical effect in the ordering process [53]. The large cylinder diameter promotes the growth of perfect HCP and FCC clusters, while the small one causes distortion in the ordered clusters with imperfection.…”