Gravity-driven surges of a viscoplastic fluid: An experimental study

We present a new experimental setup dedicated to understanding the dynamics of gravity-driven free-surface surges made of viscoplastic fluids. It consists of a 3-m-long and 0.4-m-wide inclined channel whose bottom is constituted by an upward-moving conveyor belt with controlled velocity. This setup allows to create gravity-driven surges that are stationary in the laboratory frame. Series of experiments have been conducted using a kaolin slurry characterized by a Herschel-Bulkley rheology with a yield stress of the order of 10 Pa. The shape of the free-surface was monitored by means of a laser sheet projected with a low incidence angle and ultrasonic height sensors. The obtained stationary surges systematically present steep fronts followed by a zone of uniform fluid height. We report on the evolution of surge characteristics (uniform height, front shape) as a function of belt velocity. These results are then compared to the predictions of a theoretical model based on thin-layer approximation. Searching for traveling wave solutions to the classical shallow-water equations, we obtain an ordinary differential equation for the shape of the waves which, in the case of a Herschel-Bulkley fluid, is integrated numerically. The agreement between free-surface shapes computed from the model and those extracted from the experiments is good, including in the vicinity of the surge fronts. Lastly, we discuss perspectives offered by our setup for the study of viscoplastic surges with reference, in particular, to natural debris flows.