Shaking-induced crystallization of dense sphere packings

Crystallization in load-controlled shearing flows of monosized spheres

Identical, inelastic spheres crystallize when sheared between two parallel, bumpy planes under a constant load larger than a minimum value. We investigate the effect of the inter-particle friction coefficient of the sheared particles on the flow dynamics and the crystallization process with discrete element simulations. If the imposed load is about the minimum value to observe crystallization in frictionless spheres, adding small friction to the granular assembly results in a shear band adjacent to one of the planes and one crystallized region, where a plug flow is observed. The ordered particles are arranged in both face-centered cubic and hexagonal-closed packed phases. The particles in the shear band are in between the crystalline state and the fluid state, but the latter is never reached, which results in a large shear resistance. As the particle friction increases, the shear band disappears, and the ordering in the core region is destroyed. A significant portion of the particles are in a fluid state with a zero shear rate, leading to a substantial and unexpected reduction in the shear resistance with respect to the frictionless case. If the imposed load is increased well above the minimum from the onset of crystallization, we observe the formation of one shear band in the core, where the particles are again between the crystalline state and the fluid state, surrounded by two crystallized regions near the boundaries, in which most of the particles are in the face-centered cubic phase and translate as a rigid body with the boundaries themselves. In this case, the macroscopic shear resistance is independent of the particle friction.

Structural evolution of granular cubes packing during shear-induced ordering

Packings of granular particles may transform into ordered structures under external agitation, which is a special type of out-of-equilibrium self-assembly. Here, evolution of the internal packing structures of granular cubes under cyclic rotating shearing has been analyzed using magnetic resonance imaging techniques. Various order parameters, different types of contacts and clusters composed of face-contacting cubes, as well as the free volume regions in which each cube can move freely have been analyzed systematically to quantify the ordering process and the underlying mechanism of this granular self-assembly. The compaction process is featured by a first rapid formation of orientationally ordered local structures with faceted contacts, followed by further densification driven by free-volume maximization with an almost saturated degree of order. The ordered structures are strongly anisotropic with contacting ordered layers in the vertical direction while remaining liquid-like in the horizontal directions. Therefore, the constraint of mechanical stability for granular packings and the thermodynamic principle of entropy maximization are both effective in this system, which we propose can be reconciled by considering different depths of supercooling associated with various degrees of freedom.

Flow-induced surface crystallization of granular particles in cylindrical confinement

An interesting phenomenon that a layer of crystallized shell formed at the container wall during an orifice flow in a cylinder is observed experimentally and is investigated in DEM simulation. Different from shear or vibration driven granular crystallization, our simulation shows during the flow the shell layer is formed spontaneously from stagnant zone at the base and grows at a constant rate to the top with no external drive. Roughness of the shell surface is defined as a standard deviation of the surface height and its development is found to disobey existed growth models. The growth rate of the shell is found linearly proportional to the flow rate. This shell is static and served as a rough wall in an orifice flow with frictionless sidewall, which changes the flow profiles and its stress properties, and in turn guarantees a constant flow rate.

Self-assembly of granular spheres under one-dimensional vibration

The self-assembly of uniform granular spheres is related to the fundamentals of granular matter such as the transitions of phases, order/disorder and jamming states. This paper presents a DEM (discrete element method) study of the continuous self-assembly of uniform granular spheres from random close packing (RCP) to partially and nearly fully ordered packings under one-dimensional (1D) sinusoidal vibration without other interventions. The effects of the vibration amplitude and frequency are investigated in a wide range. The structures of the packings are characterized in terms of packing fraction and other microscopic structural parameters, including the coordination number, bond-orientational orders, and, in particular, ordered clusters, by adaptive common neighbor analysis (a-CNA). It is shown that 1D vibrations can also lead to the self-assembly of uniform granular spheres with packing fractions exceeding the RCP limit, and FCC (face centered cubic) and HCP (hexagonal close packed) structures coexist in the self-assembled packings while their total fraction can reach nearly 100%. The structures of these packings can be better correlated with the vibration velocity amplitude rather than the commonly used vibration intensity. The dynamics of such self-assembly is also preliminarily analyzed. Our study not only presents the conditions for the self-assembly of uniform granular spheres under 1D vibration, but also characterizes the order-disorder transitions during the process, which can improve our understanding of the fundamentals of granular materials and jamming states.

A neutron tomography study: probing the spontaneous crystallization of randomly packed granular assemblies

We study the spontaneous crystallization of an assembly of highly monodisperse steel spheres under shaking, as it evolves from localized icosahedral ordering towards a packing reaching crystalline ordering. Towards this end, real space neutron tomography measurements on the granular assembly are carried out, as it is systematically subjected to a variation of frequency and amplitude. As expected, we see a presence of localized icosahedral ordering in the disordered initial state (packing fraction ≈ 0.62). As the frequency is increased for both the shaking amplitudes (0.2 and 0.6 mm) studied here, there is a rise in packing fraction, accompanied by an evolution to crystallinity. The extent of crystallinity is found to depend on both the amplitude and frequency of shaking. We find that the icosahedral ordering remains localized and its extent does not grow significantly, while the crystalline ordering grows rapidly as an ordering transition point is approached. In the ordered state, crystalline clusters of both face centered cubic (FCC) and hexagonal close packed (HCP) types are identified, the latter of which grows from stacking faults. Our study shows that an earlier domination of FCC gives way to HCP ordering at higher shaking frequencies, suggesting that despite their coexistence, there is a subtle dynamical competition at play. This competition depends on both shaking amplitude and frequency, as our results as well as those of earlier theoretical simulations demonstrate. It is likely that this involves the very small free energy difference between the two structures.

Patterning the insect eye: From stochastic to deterministic mechanisms

While most processes in biology are highly deterministic, stochastic mechanisms are sometimes used to increase cellular diversity. In human and Drosophila eyes, photoreceptors sensitive to different wavelengths of light are distributed in stochastic patterns, and one such patterning system has been analyzed in detail in the Drosophila retina. Interestingly, some species in the dipteran family Dolichopodidae (the “long legged” flies, or “Doli”) instead exhibit highly orderly deterministic eye patterns. In these species, alternating columns of ommatidia (unit eyes) produce corneal lenses of different colors. Occasional perturbations in some individuals disrupt the regular columns in a way that suggests that patterning occurs via a posterior-to-anterior signaling relay during development, and that specification follows a local, cellular-automaton-like rule. We hypothesize that the regulatory mechanisms that pattern the eye are largely conserved among flies and that the difference between unordered Drosophila and ordered dolichopodid eyes can be explained in terms of relative strengths of signaling interactions rather than a rewiring of the regulatory network itself. We present a simple stochastic model that is capable of explaining both the stochastic Drosophila eye and the striped pattern of Dolichopodidae eyes and thereby characterize the least number of underlying developmental rules necessary to produce both stochastic and deterministic patterns. We show that only small changes to model parameters are needed to also reproduce intermediate, semi-random patterns observed in another Doli species, and quantification of ommatidial distributions in these eyes suggests that their patterning follows similar rules.

A simple model is able to account for a diversity of photoreceptor patterns in different fly species, ranging from highly deterministic to fully random.