Tracer diffusion coefficients in a moderately dense granular suspension. Stability analysis and thermal diffusion segregation

Abstract

The diffusion transport coefficients of a binary granular suspension where one of the components is present in tracer concentration are determined from the (inelastic) Enskog kinetic equation. The effect of the interstitial gas on the solid particles is accounted for in the kinetic equation through two different terms: (i) a viscous drag force proportional to the particle velocity and (ii) stochastic Langevin-like term defined in terms of the background temperature. The transport coefficients are obtained as the solutions of a set of coupled linear integral equations recently derived for binary granular suspensions with arbitrary concentration [Gómez González \emph{et al.}, Phys. Rev. E \textbf{101}, 012904 (2020)]. To achieve analytical expressions for the diffusion coefficients, the above integral equations are approximately solved by considering the so-called second Sonine approximation. The theoretical results for the tracer diffusion coefficient $D_0$ (coefficient connecting the mass flux with the gradient of density of tracer particles) are compared with those obtained by numerically solving the Enskog equation by means of the direct simulation Monte Carlo method. Although the first-Sonine approximation to $D_0$ yields in general a good agreement with simulation results, we show that the second-Sonine approximation leads to an improvement over the first-Sonine correction, especially when the tracer particles are much lighter than the granular gas. The expressions derived here for the diffusion coefficients are also used for two different applications. First, the stability of the homogeneous steady state is discussed. Second, segregation induced by a thermal gradient is studied. As expected, the results show that the corresponding phase diagrams for segregation clearly differ from those found in previous works when the effect of gas phase on grains is neglected.

arXiv comment27 pages, 15 figures, published in Physics of Fluids

References in corpus (33)

• A constitutive law for dense granular flows
• The Reverse Brazil Nut Problem: Competition between Percolation and Condensation
• Enskog Theory for Polydisperse Granular Mixtures. I. Navier-Stokes order Transport
• Shear thickening in granular suspensions: inter-particle friction and dynamically correlated clusters
• Kinetic Temperatures for a Granular Mixture
• Enskog Theory for Polydisperse Granular Mixtures II. Sonine Polynomial Approximation
• Energy partition and segregation for an intruder in a vibrated granular system under gravity
• Segregation in a fluidized binary granular mixture: Competition between buoyancy and geometric forces
• Segregation induced by inelasticity in a vibrofluidized granular mixture
• Diffusion in a Granular Fluid - Simulation
• Diffusion of impurities in a granular gas
• Brazil-nut effect versus reverse Brazil-nut effect in a moderately dense granular fluid
• Segregation in granular binary mixtures: Thermal diffusion
• Competition of Brazil nut effect, buoyancy, and inelasticity induced segregation in a granular mixture
• Thermal diffusion segregation in granular binary mixtures described by the Enskog equation
• Navier-Stokes transport coefficients of $d$-dimensional granular binary mixtures at low density
• Mass transport of impurities in a moderately dense granular gas
• Segregation by thermal diffusion of an intruder in a moderately dense granular fluid
• Active Microrheology of Driven Granular Particles
• Revisiting ignited-quenched transition and the non-Newtonian rheology of a sheared dilute gas-solid suspension
• Hydrodynamic profiles for an impurity in a open vibrated granular gas
• Enskog kinetic theory for multicomponent granular suspensions
• Instabilities in moderately dense granular binary mixtures
• Transport coefficients for driven granular mixtures at low-density
• Homogeneous states in driven granular mixtures: Enskog kinetic theory versus molecular dynamics simulations
• Segregation of an intruder in a heated granular dense gas
• Kinetic theory of granular particles immersed in a molecular gas
• Time-dependent homogeneous states of binary granular suspensions
• Transport coefficients for granular suspensions at moderate densities
• Diffusion of intruders in granular suspensions: Enskog theory and random walk interpretation
• Comment on "Kinetic theory models for granular mixtures with unequal granular temperature: Hydrodynamic velocity" [Phys. Fluids 33, 043321 (2021)]
• Generalized transport coefficients for inelastic Maxwell mixtures under shear flow
• Assessment of kinetic theories for moderately dense granular binary mixtures: Shear viscosity coefficient

Cited by in corpus (5)

• Diffusion of impurities in a moderately dense confined granular gas
• Rheology of granular particles immersed in a molecular gas under uniform shear flow
• Mean square displacement of intruders in freely cooling multicomponent granular mixtures
• Mobility and diffusion of intruders in granular suspensions. Einstein relation
• Diffusion of intruders in a granular gas thermostatted by a bath of elastic hard spheres