Effective potentials in a bidimensional vibrated granular gas

Abstract

We present a numerical study of the spatial correlations of a quasi-two-dimensional granular fluid kept in a nonstatic steady state via vertical shaking. The simulations explore a wide range of vertical accelerations, restitution coefficients, and packing fractions, always staying below the crystallization limit. From the simulations we obtain the relevant pair distribution functions (PDFs), and effective potentials for the interparticle interaction are extracted from these PDFs via the Ornstein-Zernike equation with the Percus-Yevick closure. The correlations in the granular structures originating from these effective potentials are checked against the originating PDF using standard Monte Carlo simulations, and we find in general an excellent agreement. The resulting effective potentials show an increase of the spatial correlation at contact with the decreasing values of the restitution coefficient, and a tendency of the potentials to display deeper wells for more dissipative dynamics. A general exception to this trend appears for a range of values of the forcing, which depends on the restitution coefficient, but not on the density, where resonant bouncing increases correlations, resulting in deeper potential wells. The nature of these resonances is explored and shown to be the result of synchronization in the parabolic flights of the particles.

Granular beads in a vibrating, quasi two-dimensional cell: The true shape of the effective pair potential

“…4 of Ref. [15] as far as the shape of the functions is concerned, but the reduced potentials in Ref. [15] are more strongly attractive, with a minimum value around −1 to −1.5, which is approximately three times deeper than the minima of our results for βu(r) at φ = 0.4.…”

“…[15] as far as the shape of the functions is concerned, but the reduced potentials in Ref. [15] are more strongly attractive, with a minimum value around −1 to −1.5, which is approximately three times deeper than the minima of our results for βu(r) at φ = 0.4. We presume that the reason for this quantitative disagreement might be a difference between the particle-wall restitution coefficients ǫ w of our Granular Dynamics simulations and those that were used in Ref.…”

“…We will therefore use the notation HNC Inversion (HNCI) and PY Inversion (PYI) for the numerical schemes that are obtained when only the initialization steps of IHNCI or IPYI are executed, and the subsequent MC simulations and iterative potential corrections are omitted. The so-obtained PYI method has already been used [11,15] to calculate effective potentials of granular beads in vibrated quasi-two-dimensional cells, but we are going to demonstrate in Sec. IV that the results from PYI and HNCI are not reliable as they contain a large systematic error.…”

“…Effective potentials have been calculated for experimentally observed quasi two-dimensional systems of granular spheres under mechanical agitation [11] or under the effects of external, oscillating magnetic fields [12,13], by measuring the radial distribution function and inverting it by means of the Percus-Yevick (PY) integral equation [14]. Following the same approach, Velázquez-Pérez and co-workers have studied the effect of the interparticle coefficient of restitution on the shape of the effective potential, reporting an increment of the effective particle attraction with decreasing values of the coefficient of restitution [15]. In their paper, they present a complicated shape of the attractive effective potential as a function of the particle separation distance.…”

Colloidal Soft Matter Physics

“…Colloids and granular media are aggregates of matter that typically exemplify the differences between systems in and out of thermodynamic equilibrium, respectively. Despite the differences in size and in their phase behavior, there are many similarities between the phenomenologies of both systems, for example, they exhibit very similar dynamics [137] and rheological properties [138] and it is even possible to determine effective potentials between grains [139], which allows us treating them with the same or very similar theoretical and computational modeling tools. A crucial characteristic of granular matter, and one that makes it different from equilibrium thermodynamic systems, is the high dissipation of energy when its particles interact at contact.…”