Experimental investigation of the spreading of viscoplastic fluids on inclined planes

Abstract

a b s t r a c tWe 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(sin˛) 1/3 (sin˛) 5/4 , where˛and t denote plane inclination and time, respectively, and which holds for sloping beds (˛> 0).

The dam-break problem for Herschel–Bulkley viscoplastic fluids down steep flumes

“…At the same time, a pulse originating from the flow rear overtook the front and gave new impetus to the head. This produced the kink that can be seen in all x f (t) curves for unconfined flows [52] and to lesser extent for confined flows (in particular runs (b), (d), (f), and (h) in Fig. 12).…”

“…We first determined the yield stress using a creep test [52]. We then determined the flow curve, i.e., the shear-stress/shear-rate relation.…”

A Numerthod for the Simulation of Free Surface Flows of Viscoplastic Fluid in 3D

“…We run numerical experiments with the following set of dimensional parameters which correspond to the experimental setting in [12]: X = 0.51m, Y = 0.3m, V = 0.06m^, a e {12°, 18°}, and two sets of Herschel-Bulkley model parameters, K = 47.68Pas""", n = 0.415, r^ = 89Pa and K = 75.84Pas"", n = 0.579, r^ = 109Pa. The Herschel-Bulkley model with such parameters was found in [12] to approximate the rheology of Carbopol Ultrez 10 gel of 0.30% Regarding tfie flow structure, tfie existing sfiallow-layer tfieory distinguisfies tfie yielding region close to tfie bottom boundary and tfie pseudo-plug region, tfie region wfiere tfie fluid is weakly yielded and considered solid up to fiigfier order terms witfi respect to tfie layer tfiickness.…”

“…The Herschel-Bulkley model with such parameters was found in [12] to approximate the rheology of Carbopol Ultrez 10 gel of 0.30% Regarding tfie flow structure, tfie existing sfiallow-layer tfieory distinguisfies tfie yielding region close to tfie bottom boundary and tfie pseudo-plug region, tfie region wfiere tfie fluid is weakly yielded and considered solid up to fiigfier order terms witfi respect to tfie layer tfiickness. Pseudo-plugs are predicted to dominate tfie dynamics over substantial regions of sfiallow flows.…”

Fluid boundary of a viscoplastic Bingham flow for finite solid deformations

“…For finite deformations and general yield criteria, the same procedure is used to compute flows for various geometries and realistic applications ( [2,1,5,8,7,15]). Numerical simulations of such models then compute the surface for which the plastic function vanishes, which involves the removal of singularities of the mathematical problem ( [16,15]).…”