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Register a new userGranular beads in a vibrating, quasi two-dimensional cell: The true shape of the effective pair potential
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Gustavo M. Rodr\\'iguez-Li\\~n\\'an
Publication date
2018
fields
Physics
and research's language is
English
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Steady-state pair correlations between inelastic granular beads in a vertically shaken, quasi two-dimensional cell can be mapped onto the particle correlations in a truly two-dimensional reference fluid in thermodynamic equilibrium. Using Granular Dynamics simulations and Iterative Ornstein--Zernike Inversion, we demonstrate that this mapping applies in a wide range of particle packing fractions and restitution coefficients, and that the conservative reference particle interactions are simpler than it has been reported earlier. The effective potential appears to be a smooth, concave function of the particle distance $r$. At low packing fraction, the shape of the effective potential is compatible with a one-parametric fit function proportional to $r^{-2}$.
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The Navier--Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture of inelastic hard spheres are determined from the Boltzmann kinetic equation. A normal or hydrodynamic solution to the Boltzmann equation is obtained via the Chapman--Enskog method for states near the local version of the homogeneous time-dependent state. The mass, momentum, and heat fluxes are determined to first order in the spatial gradients of the hydrodynamic fields, and the associated transport coefficients are identified. As expected, they are given in terms of the solutions of a set of coupled linear integral equations. In addition, in contrast to previous results obtained for low-density granular mixtures, there are also nonzero contributions to the first-order approximations to the partial temperatures $T_i^{(1)}$ and the cooling rate $zeta^{(1)}$. Explicit forms for the diffusion transport coefficients, the shear viscosity coefficient, and the quantities $T_i^{(1)}$ and $zeta^{(1)}$ are obtained by assuming the steady-state conditions and by considering the leading terms in a Sonine polynomial expansion. The above transport coefficients are given in terms of the coefficients of restitution, concentration, and the masses and diameters of the components of the mixture. The results apply in principle for arbitrary degree of inelasticity and are not limited to specific values of concentration, mass and/or size ratios. As a simple application of these results, the violation of the Onsager reciprocal relations for a confined granular mixture is quantified in terms of the parameter space of the problem.
We present experimental results on the shape of arches that block the outlet of a two dimensional silo. For a range of outlet sizes, we measure some properties of the arches such as the number of particles involved, the span, the aspect ratio, and the angles between mutually stabilizing particles. These measurements shed light on the role of frictional tangential forces in arching. In addition, we find that arches tend to adopt an aspect ratio (the quotient between height and half the span) close to one, suggesting an isotropic load. The comparison of the experimental results with data from numerical models of the arches formed in the bulk of a granular column reveals the similarities of both, as well as some limitations in the few existing models.
A Molecular Dynamics approach has been used to compute the shear force resulting from the shearing of disks. Two-dimensional monodisperse disks have been put in an horizontal and rectangular shearing cell with periodic boundary conditions on right and left hand sides. The shear is applied by pulling the cover of the cell either at a constant rate or by pulling a spring, linked to the cover, with a constant force. Depending on the rate of shearing and on the elasticity of the whole set up, we showed that the measured shear force signal is either irregular in time, regular in time but not in shape, or regular in shape.
This paper continues the investigation of the exponentially repulsive EXP pair-potential system of Paper I with a focus on isomorphs in the low-temperature gas and liquid phases. As expected from the EXP systems strong virial potential-energy correlations, the systems reduced-unit structure and dynamics are isomorph invariant to a good approximation. Three methods for generating isomorphs are compared: the small-step method that is exact in the limit of small density changes and t
We report the observation of the homogenous nucleation of crystals in a dense layer of steel spheres confined between two horizontal plates vibrated vertically. Above a critical vibration amplitude, two-layer crystals with square symmetry were found to coexist in steady state with a surrounding granular liquid. By analogy to equilibrium hard sphere systems, the phase behavior can be explained through entropy maximization. However, dramatic non-equilibrium effects are present, including a significant difference in the granular temperatures of the two phases.
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