Effective two-dimensional model for granular matter with phase separation

Abstract

Granular systems confined in vertically vibrated shallow horizontal boxes (quasi two-dimensional geometry) present a liquid to solid phase transition when the frequency of the periodic forcing is increased. An effective model, where grains move and collide in two-dimensions is presented, which reproduces the aforementioned phase transition. The key element is that besides the two-dimensional degrees of freedom, each grain has an additional variable $\epsilon$ that accounts for the kinetic energy stored in the vertical motion in the real quasi two-dimensional motion. This energy grows monotonically during free flight, mimicking the energy gain by collisions with the vibrating walls and, at collisions, this energy is instantaneously transferred to the horizontal degrees of freedom. As a result, the average values of $\epsilon$ and the kinetic temperature are decreasing functions of the local density, giving rise to an effective pressure that can present van der Waals loops. A kinetic theory approach predicts the conditions that must satisfy the energy grow function to obtain the phase separation, which are verified with molecular dynamics simulations. Notably, the effective equation of state and the critical points computed considering the velocity--time-of-flight correlations differ only slightly from those obtained by simple kinetic theory calculations that neglect those correlations.

References in corpus (15)

• Clustering, Order, and Collapse in a Driven Granular Monolayer
• Crystallization of a quasi-two-dimensional granular fluid
• Caging dynamics in a granular fluid
• Statistical mechanics of fluidized granular media: short range velocity correlations
• Non-equilibrium two-phase coexistence in a confined granular layer
• The dynamics of thin vibrated granular layers
• Fluctuations and Criticality of a Granular Solid-Liquid-like Phase Transition
• Hydrodynamic modes in a confined granular fluid
• Coarsening of granular clusters: two types of scaling behaviors
• Capillary-like Fluctuations of a Solid-Liquid Interface in a Non-Cohesive Granular System
• Effect of inelasticity on the phase transitions of a thin vibrated granular layer
• Universality and criticality of a second-order granular solid-liquid-like phase transition
• Heated granular fluids: the random restitution coefficient approach
• Shear viscosity of a model for confined granular media
• Critical Phenomena in Quasi-Two-Dimensional Vibrated Granular Systems

Cited by in corpus (14)

• Enskog kinetic theory for a model of a confined quasi-two-dimensional granular fluid
• Understanding the instability of a vibrated granular monolayer
• Energy nonequipartition in a collisional model of a confined quasi-two-dimensional granular mixture
• Homogeneous dynamics in a vibrated granular monolayer
• Navier--Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture
• Hyperuniform interfaces in non-equilibrium phase coexistence
• Non-equilibrium coexistence between a fluid and a hotter or colder crystal of granular hard disks
• Dynamics of an inelastic tagged particle under strong confinement
• Diffusion of impurities in a moderately dense confined granular gas
• Dynamical and structural properties of an absorbing phase transition: a case study from granular systems
• Granular beads in a vibrating, quasi two-dimensional cell: The true shape of the effective pair potential
• Kinetic model for a confined quasi-two-dimensional gas of inelastic hard spheres
• Phase separation in a chiral active fluid of inertial self-spinning disks
• Conservation laws and slow dynamics determine the universality class of interfaces in active matter