Kinetic theory of shear thickening for a moderately dense gas-solid suspension: from discontinuous thickening to continuous thickening

Abstract

The Enskog kinetic theory for moderately dense gas-solid suspensions under simple shear flow is considered as a model to analyze the rheological properties of the system. The influence of the environmental fluid on solid particles is modeled via a viscous drag force plus a stochastic Langevin-like term. The Enskog equation is solved by means of two independent but complementary routes: (i) Grad's moment method and (ii) event-driven Langevin simulation of hard spheres. Both approaches clearly show that the flow curve (stress-strain rate relation) depends significantly on the volume fraction of the solid particles. In particular, as the density increases, there is a transition from the discontinuous shear thickening (observed in dilute gases) to the continuous shear thickening for denser systems. The comparison between theory and simulations indicate that while the theoretical predictions for the kinetic temperature agree well with simulations for densities $\phi \lesssim 0.5$, the agreement for the other rheological quantities (the viscosity, the stress ratio and the normal stress differences) is limited to more moderate densities ($\phi \lesssim 0.3$) if the inelasticity during collisions between particles is not large. [This paper has been published in Phys. Rev. E {\bf 96}, 42903 (2017) but we have realized that there are some typos and mistakes after its publication. So we add the Erratum which will be published in PRE in the top of this paper.]

30 pages, 15 figures +Erratum 2 pages, 2 figures

References in corpus (7)

• Inherent Rheology of a Granular Fluid in Uniform Shear Flow
• Transport properties of dense dissipitive hard-sphere fluids for arbitrary energy loss models
• Thinning or thickening? Multiple rheological regimes in dense suspensions of soft particles
• Non-Newtonian hydrodynamics for a dilute granular suspension under uniform shear flow
• Divergence of Viscosity in Jammed Granular Materials: A Theoretical Approach
• Kinetic theory of discontinuous shear thickening
• A microscopic theory for discontinuous shear thickening of frictional granular materials

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• Rheology of dilute cohesive granular gases
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• 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
• Two-Step Discontinuous Shear Thickening of Dilute Inertial Suspensions Having Soft-Core Potential
• Simple shear flow in granular suspensions: Inelastic Maxwell models and BGK-type kinetic model
• Rheology of a dilute binary mixture of inertial suspension under simple shear flow
• Rheology of granular particles immersed in a molecular gas under uniform shear flow
• Non-monotonic Mpemba effect in binary molecular suspensions
• Rheology of dilute granular gas mixtures where the grains interact via a square shoulder and well potential
• Kinetic theory of discontinuous shear thickening of a moderately dense inertial suspension of frictionless soft particles
• Diffusion of intruders in a granular gas thermostatted by a bath of elastic hard spheres
• Discontinuous change of viscosity in a sheared granular gas with velocity-dependent restitution
• Impact of Softness of Particles on Rheology of Dilute Granular Gases
• Kinetic theory of discontinuous shear thickening for a dilute gas-solid suspension
• Exact Rheology of Uniform Shear Flow in a Gas of Inelastic and Rough Maxwell Particles