Free cooling phase-diagram of hard-spheres with short- and long-range interactions

Abstract

We study the stability, the clustering and the phase-diagram of free cooling granular gases. The systems consist of mono-disperse particles with additional non-contact (long-range) interactions, and are simulated here by the event-driven molecular dynamics algorithm with discrete (short-range shoulders or wells) potentials (in both 2D and 3D). Astonishingly good agreement is found with a mean field theory, where only the energy dissipation term is modified to account for both repulsive or attractive non-contact interactions. Attractive potentials enhance cooling and structure formation (clustering), whereas repulsive potentials reduce it, as intuition suggests. The system evolution is controlled by a single parameter: the non-contact potential strength scaled by the fluctuation kinetic energy (granular temperature). When this is small, as expected, the classical homogeneous cooling state is found. However, if the effective dissipation is strong enough, structure formation proceeds, before (in the repulsive case) non-contact forces get strong enough to undo the clustering (due to the ongoing dissipation of granular temperature). For both repulsive and attractive potentials, in the homogeneous regime, the cooling shows a universal behaviour when the (inverse) control parameter is used as evolution variable instead of time. The transition to a non-homogeneous regime, as predicted by stability analysis, is affected by both dissipation and potential strength. This can be cast into a phase diagram where the system changes with time, which leaves open many challenges for future research.

Steady state rheology of homogeneous and inhomogeneous cohesive granular materials

“…2 ) among all the particles which is of significance of determining how "hot" the system is [13,34,72,75]:…”

Freely cooling granular gases with short-ranged attractive potentials

“…24 As a final remark, the addition of short-ranged attraction will have more of an effect on the granular gas than to simply hasten the formation of instabilities, which is also discussed independently in a paper by Gonzalez, Thornton, and Luding. 36 For example, it is well-known that at late times, the traditional granular gas shows a strong correlation between regions of high density and low temperature. 24,37 Even relatively weak cohesion would change the behavior of these regions, collapsing and arresting them in large aggregate structures with tensile strength.…”

Meso-scale transport in sticky granular fluids

“…One interesting phenomenon caused by dissipation at low and moderate densities, occurring at a scale considerably larger than the particles, is the so-called clustering (hydrodynamic) instability (Luding 2009;Gonzalez, Thornton & Luding 2014): in an initially homogeneous system, large-scale structures form in the presence of strong enough dissipation for a given system size and density, see figure 1(b). The associated large time of (free) motion between collisions of clusters, allows mass, momentum and energy to be transported much faster with the clusters, which changes mixing from diffusive to ballistic (https://www2.msm.ctw.utwente.nl/sluding/pictures/cooling.html).…”

“…In contrast, attractive forces, with cohesive (surface) energy φ < 0, can enhance structure formation by favouring collisions, enhancing dissipation and keeping particles together. Both forces can be unified into one framework and the onset of structure formation can be predicted by hydrodynamic stability analysis in a phase diagram with parameters dissipation and repulsion/cohesion (Gonzalez et al 2014). The relevant dimensionless number is the relative strength of the interaction potential energy to the fluctuations of kinetic energy, Γ = φ/T g .…”