A Mean Field Model of Layering Instability in Shearing Suspensions

Abstract

Concentrated suspensions may shear-thin when the suspended particles form planar sheets that slide over one another with less friction than if the particles are randomly distributed. In a naïve model the suspension is described by a mean effective viscosity, and particles that collide with each other redistribute the mean density in the shearing direction. This leads to a diffusion equation for the particle density. If the viscosity in the unthinned state is a steeply increasing function of particle density the effective diffusion coefficient is negative and the diffusion equation, meaningful only on scales larger than the particle separation, is ill-posed. This singularity corresponds to the formation of planar sheets of particles and defines a critical particle density for the onset of shear thinning.

7 pp, 1 fig As published; revised in response to referees' comments

References in corpus (4)

• Shear thickening of cornstarch suspensions as a re-entrant jamming transition
• Density profiles of a colloidal liquid at a wall under shear flow
• Layering instability in a confined suspension flow
• Controlling colloidal sedimentation using time dependent shear

Cited by in corpus (1)

• Rheology of confined non-Brownian suspensions