Author(s): Aldo Tamburrino; Christian F. Ihle
Keywords: Bentonite; Bingham plastic; instability; roll waves; unconfined flow
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.