Conjectures on the transition from Poiseuille to plug flow in suspensions

Abstract

A system of hard spheres (with negligible Brownian motion) is suspended in a viscous fluid, and a macroscopic shear rate s is imposed. In the resulting steady state, the probability p for one sphere to be exactly in contact with another sphere is finite (p > 0) and independent of s. When the concentration ϕ of spheres increases, they progressively become associated in clusters. We postulate that, when ϕ exceeds a certain critical value ϕc , an infinite cluster appears, in analogy with percolation problems. The hydrodynamics must then include two macroscopic velocity fields, and leads naturally to plug flows, in qualitative agreement with experimental observations ; however, the model predicts an anomaly in the plot of apparent viscosity versus concentration, which has not yet been observed