Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHydrodynamics of granular gases of inelastic and rough hard disks or spheres. I. Transport coefficients
109
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The transport coefficients for dilute granular gases of inelastic and rough hard disks or spheres with constant coefficients of normal ($alpha$) and tangential ($beta$) restitution are obtained in a unified framework as functions of the number of translational ($d_t$) and rotational ($d_r$) degrees of freedom. The derivation is carried out by means of the Chapman--Enskog method with a Sonine-like approximation in which, in contrast to previous approaches, the reference distribution function for angular velocities does not need to be specified. The well-known case of purely smooth $d$-dimensional particles is recovered by setting $d_t=d$ and formally taking the limit $d_rto 0$. In addition, previous results [G. M. Kremer, A. Santos, and V. Garzo, Phys. Rev. E 90, 022205 (2014)] for hard spheres are reobtained by taking $d_t=d_r=3$, while novel results for hard-disk gases are derived with the choice $d_t=2$, $d_r=1$. The singular quasismooth limit ($betato -1$) and the conservative Pidducks gas ($alpha=beta=1$) are also obtained and discussed.
rate research
Read More
Conditions for the stability under linear perturbations around the homogeneous cooling state are studied for dilute granular gases of inelastic and rough hard disks or spheres with constant coefficients of normal ($alpha$) and tangential ($beta$) restitution. After a formally exact linear stability analysis of the Navier--Stokes--Fourier hydrodynamic equations in terms of the translational ($d_t$) and rotational ($d_r$) degrees of freedom, the transport coefficients derived in the companion paper [A. Megias and A. Santos, Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. I. Transport coefficients, Phys. Rev. E 104, 034901 (2021)] are employed. Known results for hard spheres [V. Garzo, A. Santos, and G. M. Kremer, Phys. Rev. E 97, 052901 (2018)] are recovered by setting $d_t=d_r=3$, while novel results for hard disks ($d_t=2$, $d_r=1$) are obtained. In the latter case, a high-inelasticity peculiar region in the $(alpha,beta)$ parameter space is found, inside which the critical wave number associated with the longitudinal modes diverges. Comparison with event-driven molecular dynamics simulations for dilute systems of hard disks at $alpha=0.2$ shows that this theoretical region of absolute instability may be an artifact of the extrapolation to high inelasticity of the approximations made in the derivation of the transport coefficients, although it signals a shrinking of the conditions for stability. In the case of moderate inelasticity ($alpha=0.7$), however, a good agreement between the theoretical predictions and the simulation results is found.
We report the emergence of a giant Mpemba effect in the uniformly heated gas of inelastic rough hard spheres: The initially hotter sample may cool sooner than the colder one, even when the initial temperatures differ by more than one order of magnitude. In order to understand this behavior, it suffices to consider the simplest Maxwellian approximation for the velocity distribution in a kinetic approach. The largeness of the effect stems from the fact that the rotational and translational temperatures, which obey two coupled evolution equations, are comparable. Our theoretical predictions agree very well with molecular dynamics and direct simulation Monte Carlo data.
The expansion of the velocity distribution function for the homogeneous cooling state (HCS) in a Sonine polynomial series around a Maxwellian is shown to be divergent, though Borel resummable. A convergent expansion for the HCS has been devised and employed to obtain the HCS velocity distribution function and (using it) the linear transport coefficients for a three dimensional monodisperse granular gas of smooth inelastic spheres, for all physical values of the coefficient of normal restitution. The results are in very good agreement with findings of DSMC simulations.
The smallest maximum kissing-number Voronoi polyhedron of 3d spheres is the icosahedron and the tetrahedron is the smallest volume that can show up in Delaunay tessalation. No periodic lattice is consistent with either and hence these dense packings are geometrically frustrated. Because icosahedra can be assembled from almost perfect tetrahedra, the terms icosahedral and polytetrahedral packing are often used interchangeably, which leaves the true origin of geometric frustration unclear. Here we report a computational study of freezing of 4d hard spheres, where the densest Voronoi cluster is compatible with the symmetry of the densest crystal, while polytetrahedral order is not. We observe that, under otherwise comparable conditions, crystal nucleation in 4d is less facile than in 3d. This suggest that it is the geometrical frustration of polytetrahedral structures that inhibits crystallization.
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.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
