Roll wave appearance in bentonite suspensions flowing down inclined planes

Abstract

As in Newtonian fluids, unconfined yield stress fluid slender flows are prone to become unstable and host travelling waves. We propose a non-local dimensionless number ψ, obtained from a physical order-of-magnitude analysis, to predict, for the first time, the transition that marks the onset of roll waves in unconfined discharges of bentonite, whose rheology was assumed as a Bingham plastic. Involved variables include the discharge volume flow, Bingham viscosity, mixture density, gravity acceleration, plane inclination and yield stress. Experimental verification considering various discharge flow-plane inclinations and concentrations of the mixture indicate that for values of ψ exceeding the unity, single or multiple roll waves appear.