Towards dense, realistic granular media in 2D

Abstract

The development of an applicable theory for granular matter -with both qualitative and quantitative value -is a challenging prospect, given the multitude of states, phases and (industrial) situations it has to cover. Given the general balance equations for mass, momentum, and energy, the limiting case of dilute and almost elastic granular gases, where kinetic theory works perfectly well, is the starting point.In most systems, low density coexists with very high density, where the latter is an open problem for kinetic theory. Furthermore, many additional non-linear phenomena and material properties are important in realistic granular media, involving, e.g.: (i) multi-particle interactions and elasticity (ii) strong dissipation, (iii) friction, (iv) long-range forces and wet contacts (v) wide particle size-distributions, and (vi) various particle shapes. Note that, while some of these issues are more relevant for high density, others are important for both low and high densities; some of them can be dealt with by means of kinetic theory, some can not. This paper is a review of recent progress towards more realistic models for dense granular media in 2D, even though most of the observations, conclusions, and corrections given are qualitatively true also in 3D. Starting from an elastic, frictionless and monodisperse hard sphere gas, the (continuum) balance equations of mass, momentum and energy are given. The equation of state, the (Navier-Stokes level) transport coefficients and the energy-density dissipation rate are considered. Several corrections are applied to those constitutive material laws -one by one -in order to account for the realistic physical effects and properties listed above.

Microstructure and macroscopic properties of polydisperse systems of hard spheres

“…Systems with monodisperse size distributions are widely used since kinetic theory predicts their physical behaviour [2,115,116], and it is the natural benchmark against which to compare. Bi-disperse size distributions are often used for theo- retical models [114,117,118], and can often be a good approximation to physically realistic size distributions.…”

“…Figure 3.5 shows the particle systems with different particle size distributions for N = 125001 and volume fraction (the ratio between the volume of the particles and the volume of the system) ν = 0.62. Note, that particles of the monodisperse case are ordered (near to walls), since the volume fraction is above 0.55 [116,119,120].…”

“…The hard-sphere model can be applied with some success for various physical phenomena and systems, like e.g., disorder-order transitions, the glass transition, dense granular flows and simple gases and liquids [2,116,[138][139][140][141][142].…”

“…There exists no unique equation of state, valid for the intermediate densities, where the system changes from the disordered to the ordered state, since the system displays hysteresis and rate-dependence; for various theoretical approaches see Refs. [116,[151][152][153][154][155][156][157][158][159][160] and references therein.…”

Simulating granular materials by energy minimization

“…The soft-particle simulations are performed with the open access particle mechanics simulator MercuryDPM [21][22][23][24]. In all test cases, we use a uniform distribution of particle radii between r min and 2r min , to prevent crystallization [25], i.e., long-range order and an associated increase in packing efficiency and thus reduction of potential energy [26].…”