Homogeneous steady states in a granular fluid driven by a stochastic bath with friction

Abstract

The homogeneous state of a granular flow of smooth inelastic hard spheres or disks described by the Enskog-Boltzmann kinetic equation is analyzed. The granular gas is fluidized by the presence of a random force and a drag force. The combined action of both forces, that act homogeneously on the granular gas, tries to mimic the interaction of the set of particles with a surrounding fluid. The first stochastic force thermalizes the system, providing for the necessary energy recovery to keep the system in its gas state at all times, whereas the second force allows us to mimic the action of the surrounding fluid viscosity. After a transient regime, the gas reaches a steady state characterized by a \emph{scaled} distribution function $φ$ that does not only depend on the dimensionless velocity $\mathbf{c}\equiv \mathbf{v}/v_0$ ($v_0$ being the thermal velocity) but also on the dimensionless driving force parameters. The dependence of $φ$ and its first relevant velocity moments $a_2$ and $a_3$ (which measure non-Gaussian properties of $φ$) on both the coefficient of restitution $\al$ and the driven parameters is widely investigated by means of the direct simulation Monte Carlo method. In addition, approximate forms for $a_2$ and $a_3$ are also derived from an expansion of $φ$ in Sonine polynomials. The theoretical expressions of the above Sonine coefficients agree well with simulation data, even for quite small values of $α$. Moreover, the third order expansion of the distribution function makes a significant accuracy improvement for larger velocities and inelasticities. Results also show that the non-Gaussian corrections to the distribution function $φ$ are smaller than those observed for undriven granular gases.