Un-jamming due to energetic instability: statics to dynamics

Jamming/un-jamming, the transition between solid- and fluid-like behavior in granular matter, is an ubiquitous phenomenon in need of a sound understanding. As argued here, in addition to the usual un-jamming by vanishing pressure due to a decrease of density, there is also yield (plastic rearrangements and un-jamming that occur) if, e.g., for given pressure, the shear stress becomes too large. Similar to the van der Waals transition between vapor and water, or the critical current in superconductors, we believe that one mechanism causing yield is by the loss of the energy’s convexity (causing irreversible re-arrangements of the micro-structure, either locally or globally). We focus on this mechanism in the context of granular solid hydrodynamics (GSH), generalized for very soft materials, i.e., large elastic deformations, employing it in an over-simplified (bottom-up) fashion by setting as many parameters as possible to constant. Also, we complemented/completed GSH by using various insights/observations from particle simulations and calibrating some of the theoretical parameters—both continuum and particle points of view are reviewed in the context of the research developments during the last few years. Any other energy-based elastic-plastic theory that is properly calibrated (top-down), by experimental or numerical data, would describe granular solids. But only if it would cover granular gas, fluid, and solid states simultaneously (as GSH does) could it follow the system transitions and evolution through all states into un-jammed, possibly dynamic/collisional states—and back to elastically stable ones. We show how the un-jamming dynamics starts off, unfolds, develops, and ends. We follow the system through various deformation modes: transitions, yielding, un-jamming and jamming, both analytically and numerically and bring together the material point continuum model with particle simulations, quantitatively. Graphic abstract

Modeling Separation Process for Sunflower Seed Mixture on Vibro-Pneumatic Separators

Aim of the research is to increase the efficiency of the mechanical and technological process of separation of sunflower seed mixture on vibro-pneumatic separators, the principle of which is based on the interaction of seed flow with the surface having fluctuation-type vibration load by substantiating their efficient processing and technological parameters. A system of differential equations of sunflower seeds motions, as a granular gas, under the action of a vibrating surface was developed, taking into account the elastic-damping interaction and physical and mechanical properties of seeds. The presented system of differential equations is the basis of the physical and mathematical means of numerical modeling of this process, which was implemented in the software package STAR-CCM +. To build physical and mathematical models, it was assumed that sunflower seeds are presented in the form of ellipsoids with a certain density and effective diameter. As a result of numerical simulation of the process of moving sunflower seeds under the action of a vibrating sieve, dependences of the change in total concentration θ and productivity q on seed supply Q, sieve angle α, sieve frequency ψ and sieve amplitude A were obtained. As a result of numerical simulation of the process of moving sunflower seeds under the action of a vibrating surface, dependences of the change of filling factor χ, distribution coefficient δ and productivity q on seed supply Q, vibration surface angles α and β, oscillation frequency ψ, oscillation amplitude A and set air velocity V were obtained. Theoretical provisions were implemented and tested in the development of an adaptive vibrating screen separator of sunflower seeds (Ukrainian patent #120235).

Rarefied particle motions on hillslopes – Part 2: Analysis

We examine a theoretical formulation of the probabilistic physics of rarefied particle motions and deposition on rough hillslope surfaces using measurements of particle travel distances obtained from laboratory and field-based experiments, supplemented with high-speed imaging and audio recordings that highlight effects of particle–surface collisions. The formulation, presented in a companion paper (Furbish et al., 2021a), is based on a description of the kinetic energy balance of a cohort of particles treated as a rarefied granular gas, as well as a description of particle deposition that depends on the energy state of the particles. Both laboratory and field-based measurements are consistent with a generalized Pareto distribution of travel distances and predicted variations in behavior associated with the balance between gravitational heating due to conversion of potential to kinetic energy and frictional cooling due to particle–surface collisions. For a given particle size and shape these behaviors vary from a bounded distribution representing rapid thermal collapse with small slopes or large surface roughness, to an exponential distribution representing approximately isothermal conditions, to a heavy-tailed distribution representing net heating of particles with large slopes. The transition to a heavy-tailed distribution likely involves an increasing conversion of translational to rotational kinetic energy leading to larger travel distances with decreasing effectiveness of collisional friction. This energy conversion is strongly influenced by particle shape, although the analysis points to the need for further clarity concerning how particle size and shape in concert with surface roughness influence the extraction of particle energy and the likelihood of deposition.