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 us 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 to 18° . 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\left{ (sin\, \alpha\right)}}^{\frac{1}{3}}\left (sin\, \alpha \right)}^{\frac{5}{4}}, where α and t denote plane inclination and time, respectively, and which holds for sloping beds $\left(\alpha \, >\, 0\right)$.