Rheology of granular particles immersed in a molecular gas under uniform shear flow

Abstract

Non-Newtonian transport properties of a dilute gas of inelastic hard spheres immersed in a molecular gas are determined. We assume that the granular gas is sufficiently rarefied and hence, the state of the molecular gas is not disturbed by the presence of the solid particles. In this situation, one can treat the molecular gas as a bath (or thermostat) of elastic hard spheres at a given temperature. Moreover, in spite of the fact that the number density of grains is quite small, we take into account their inelastic collisions among themselves in its kinetic equation. The system (granular gas plus a bath of elastic hard spheres) is subjected to a simple (or uniform) shear flow (USF). In the low-density regime, the rheological properties of the granular gas are determined by solving the Boltzmann kinetic equation by means of Grad's moment method. These properties turn out to be highly nonlinear functions of the shear rate and the remaining parameters of the system. Our results show that the kinetic granular temperature and the non-Newtonian viscosity present a discontinuous shear thickening (DST) effect for sufficiently high values of the mass ratio $m/m_g$ ($m$ and $m_g$ being the mass of grains and gas particles, respectively). This effect becomes more pronounced as the mass ratio $m/m_g$ increases. In particular, in the Brownian limit ($m/m_g\to \infty$) the expressions of the non-Newtonian transport properties derived here are consistent with those previously obtained by considering a coarse-grained approach where the effect of gas phase on grains is through an effective force. Theoretical results are compared against computer simulations showing an excellent agreement.

18 pages, 9 figures; to be published in Physical Review E

References in corpus (12)

• Inherent Rheology of a Granular Fluid in Uniform Shear Flow
• Granular Brownian motion
• Thinning or thickening? Multiple rheological regimes in dense suspensions of soft particles
• Revisiting ignited-quenched transition and the non-Newtonian rheology of a sheared dilute gas-solid suspension
• Enskog kinetic theory of rheology for a moderately dense inertial suspension
• Generalized Langevin equation with shear flow and its fluctuation-dissipation theorems derived from a Caldeira-Leggett Hamiltonian
• Kinetic theory of granular particles immersed in a molecular gas
• Granular fluid thermostatted by a bath of elastic hard spheres
• Non-Newtonian rheology in inertial suspensions of inelastic rough hard spheres under simple shear flow
• Diffusion of intruders in granular suspensions: Enskog theory and random walk interpretation
• Tracer diffusion coefficients in a moderately dense granular suspension. Stability analysis and thermal diffusion segregation
• Rheology of a dilute binary mixture of inertial suspension under simple shear flow

Cited by in corpus (2)

• Kinetic Theory and Memory Effects of Homogeneous Inelastic Granular Gases under Nonlinear Drag
• Kinetic theory of discontinuous shear thickening of a moderately dense inertial suspension of frictionless soft particles