Experimental investigation of the spreading of viscoplastic fluids on inclined planes

We report experimental results related to the dam-break problem for viscoplastic fluids. Using image processing techniques, we were able to accurately reconstruct the free-surface evolution of fixed Volumes Of fluid suddenly released a plane. We used Carbopol Ultrez 10 as a viscoplastic material; its rheological behavior was closely approximated by a Herschel-Bulkley model for a fairly wide range of shear-rates. Varying the Carbopol concentration allowed LIS to change the yield stress and bulk viscosity. The yield stress ranged from 78 to 109 Pa, producing Bingham numbers in the 0.07-0.35 range. We investigated the behavior of a 43-kg mass released on a plane, whose inclination ranged from 0 degrees to 18 degrees. For each run, we observed that the behavior was nearly the same: at short times, the mass accelerated vigorously on gate opening and very quickly reached a nearly constant velocity. At time t=1 s, independently of plane inclination and yield stress, the mass reached a near-equilibrium regime, where the front position varied as a power function of time over several decades. We did not observe any run-out phase, during which the mass would have gradually come to a halt. The similarity in the flow behavior made it possible to derive an empirical scaling for the front position in the form, X-f = t(0.275)(sin alpha)(1/3) (sin alpha)(5/4), where alpha and t denote plane inclination and time, respectively, and which holds for sloping beds (alpha > 0). (C) 2008 Elsevier B.V. All rights reserved.