Kinetic theory of discontinuous shear thickening for a dilute gas-solid suspension

Abstract

A kinetic theory for a dilute gas-solid suspension under a simple shear is developed. With the aid of the corresponding Boltzmann equation, it is found that the flow curve (stress-strain rate relation) has a S-shape as a crossover from the Newtonian to the Bagnoldian for a granular suspension or from the Newtonian to a fluid having a viscosity proportional to the square of the shear rate for a suspension consisting of elastic particles. The existence of the S-shape in the flow curve directly leads to a discontinuous shear thickening (DST). This DST corresponds to the discontinuous transition of the kinetic temperature between a quenched state and an ignited state. The results of the event-driven Langevin simulation of hard spheres perfectly agree with the theoretical results without any fitting parameter. The simulation confirms that the DST takes place in the linearly unstable region of the uniformly sheared state.

21 pages, 6 figures (to be published in Progress of Theoretical and Experimental Physics)

References in corpus (11)

• Wet Granular Materials
• Inherent Rheology of a Granular Fluid in Uniform Shear Flow
• Granular Brownian motion
• Kinetic theory of shear thickening for a moderately dense gas-solid suspension: from discontinuous thickening to continuous thickening
• Rheological Chaos of Frictional Grains
• Non-Newtonian hydrodynamics for a dilute granular suspension under uniform shear flow
• Divergence of Viscosity in Jammed Granular Materials: A Theoretical Approach
• Kinetic theory for dilute cohesive granular gases with a square well potential
• Rheology of dilute cohesive granular gases
• Hydrodynamic instabilities in shear flows of cohesive granular particles
• A microscopic theory for discontinuous shear thickening of frictional granular materials