CONJECTURES ON THE TRANSITION FROM POISEUILLE TO PLUG FLOW IN SUSPENSIONS

A system is 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 greater than 0) and independent of s. When the concentration PHI of spheres increases, they progressively become associated in clusters. The author postulates that, when PHI exceeds a certain critical value PHI //c, 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.