Rheology of a dilute binary mixture of inertial suspension under simple shear flow

Abstract

The rheology of a dilute binary mixture of inertial suspension under simple shear flow is analyzed in the context of the Boltzmann kinetic equation. The effect of the surrounding viscous gas on the solid particles is accounted for by means of a deterministic viscous drag force plus a stochastic Langevin-like term defined in terms of the environmental temperature $T_{\text{env}}$. Grad's moment method is employed to determine the temperature ratio and the pressure tensor in terms of the coefficients of restitution, concentration, the masses and diameters of the components of the mixture, and the environmental temperature. Analytical results are compared against event-driven Langevin simulations for mixtures of hard spheres with the same mass density $m_1/m_2=({\sigma }^{(1)}/{\sigma }^{(2)}{)}^3$, $m_i$ and ${\sigma }^{(1)}$ being the mass and diameter, respectively, of the species $i$. It is confirmed that the theoretical predictions agree with simulations of various size ratios ${\sigma }^{(1)}/{\sigma }^{(2)}$ and for elastic and inelastic collisions in the wide range of parameters' space. It is remarkable that the temperature ratio $T_1/T_2$ and the viscosity ratio ${\eta }_1/{\eta }_2$ (${\eta }_i$ being the partial contribution of the species $i$ to the total shear viscosity $\eta ={\eta }_1+{\eta }_2$) discontinuously change at a certain shear rate as the size ratio increases; this feature (which is expected to occur in the thermodynamic limit) cannot be completely captured by simulations due to small system size. In addition, a Bhatnagar--Gross--Krook (BGK)-type kinetic model adapted to mixtures of inelastic hard spheres is exactly solved when $T_{\text{env}}$ is much smaller than the kinetic temperature $T$. A comparison between the velocity distribution functions obtained from Grad's method, BGK model, and simulations is carried out.

arXiv comment39 pages, 22 figures

References in corpus (37)

• Discontinuous Shear Thickening of Frictional Hard-Sphere Suspensions
• Shear thickening in concentrated suspensions: phenomenology, mechanisms, and relations to jamming
• Self-diffusion in dense granular shear flows
• Critical scaling near jamming transition for frictional granular particles
• Macroscopic Discontinuous Shear Thickening vs Local Shear Jamming in Cornstarch
• Bidisperse and polydisperse suspension rheology at large solid fraction
• Inherent Rheology of a Granular Fluid in Uniform Shear Flow
• Segregation in a fluidized binary granular mixture: Competition between buoyancy and geometric forces
• Granular Brownian motion
• Shear and normal stress measurements in non-Brownian monodisperse and bidisperse suspensions
• Tracer diffusion in granular shear flows
• Segregation in granular binary mixtures: Thermal diffusion
• Brazil-nut effect versus reverse Brazil-nut effect in a moderately dense granular fluid
• The rheology of dense, polydisperse granular fluids under shear
• Rheological properties in a low-density granular mixture
• A unified description of gravity- and kinematics-induced segregation forces in dense granular flows
• Kinetic theory of shear thickening for a moderately dense gas-solid suspension: from discontinuous thickening to continuous thickening
• Grad's moment method for a granular fluid at moderate densities. Navier-Stokes transport coefficients
• Nanoparticle diffusion in sheared cellular blood flow
• Revisiting ignited-quenched transition and the non-Newtonian rheology of a sheared dilute gas-solid suspension
• Event Driven Langevin simulations of Hard Spheres
• Shear jamming, discontinuous shear thickening, and fragile states in dry granular materials under oscillatory shear
• Enskog kinetic theory for multicomponent granular suspensions
• Non-Newtonian hydrodynamics for a dilute granular suspension under uniform shear flow
• Transport coefficients for driven granular mixtures at low-density
• Self-Diffusion Scalings in Dense Granular Flows
• Enskog kinetic theory of rheology for a moderately dense inertial suspension
• Granular mixtures modeled as elastic hard spheres subject to a drag force
• Non-equilibrium phase transition in a sheared granular mixture
• Mass transport of an impurity in a strongly sheared granular gas
• Impurity in a sheared inelastic Maxwell gas
• Segregation by thermal diffusion in granular shear flows
• Two-Step Discontinuous Shear Thickening of Dilute Inertial Suspensions Having Soft-Core Potential
• Heat flux of driven granular mixtures at low density. Stability analysis of the homogeneous steady state
• Kinetic theory of discontinuous shear thickening
• Assessment of kinetic theories for moderately dense granular binary mixtures: Shear viscosity coefficient
• Enskog kinetic theory of binary granular suspensions: heat flux and stability analysis of the homogeneous steady state

Cited by in corpus (3)

• Rheology of granular particles immersed in a molecular gas under uniform shear flow
• Kinetic theory of dilute weakly charged granular gases with hard-core and inverse power-law interactions under uniform shear flow
• Kinetic theory of discontinuous shear thickening of a moderately dense inertial suspension of frictionless soft particles