Collapse of a neutrally buoyant suspension column: from Newtonian to apparent non-Newtonian flow regimes

Abstract

Experiments on the collapse of non-colloidal and neutrally buoyant particles suspended in a Newtonian fluid column are presented, in which the initial volume fraction of the suspension $\unicode[STIX]{x1D719}$, the viscosity of the interstitial fluid $\unicode[STIX]{x1D707}_{f}$, the diameter of the particles $d$ and the mixing protocol, i.e. the initial preparation of the suspension, are varied. The temporal evolution of the slumping current highlights two main regimes: (i) an inertial-dominated regime followed by (ii) a viscous-dominated regime. The inertial regime is characterized by a constant-speed slumping which is shown to scale as in the case of a classical inertial dam-break. The viscous-dominated regime is observed as a decreasing-speed phase of the front evolution. Lubrication models for Newtonian and power-law fluids describe most of situations encountered in this regime, which strongly depends on the suspension parameters. The temporal evolution of the propagating front is used to extract the rheological parameters of the fluid models. At the early stages of the viscous-dominated regime, a constant effective shear viscosity, referred to as an apparent Newtonian viscous regime, is found to depend only on $\unicode[STIX]{x1D719}$ and $\unicode[STIX]{x1D707}_{f}$ for each mixing protocol. The obtained values are shown to be well fitted by the Krieger–Dougherty model whose parameters involved, say a critical volume fraction $\unicode[STIX]{x1D719}_{m}$ and the exponent of divergence, depend on the mixing protocol, i.e. the microscale interaction between particles. On a longer time scale which depends on $\unicode[STIX]{x1D719}$, the front evolution is shown to slightly deviate from the apparent Newtonian model. In this apparent non-Newtonian viscous regime, the power-law model, indicating both shear-thinning and shear-thickening behaviours, is shown to be more appropriate to describe the front evolution. The present experiments indicate that the mixing protocol plays a crucial role in the selection of a shear-thinning or shear-thickening type of collapse, while the particle diameter $d$ and volume fraction $\unicode[STIX]{x1D719}$ play a significant role in the shear-thickening case. In all cases, the normalized effective consistency of the power-law fluid model is found to be a unique function of $\unicode[STIX]{x1D719}$. Finally, an apparent viscoplastic regime, characterized by a finite length spreading reached at finite time, is observed at high $\unicode[STIX]{x1D719}$. This regime is mostly observed for volume fractions larger than $\unicode[STIX]{x1D719}_{m}$ and up to a volume fraction $\unicode[STIX]{x1D719}_{M}$ close to the random close packing fraction at which the initial column remains undeformed on opening the gate.

Collapse of a liquid-saturated granular column on a horizontal plane

“…2(a)], the liquid-grain column remains static after the sluice gate is opened (even after several hours). This observation has already been reported in the case of a neutrally buoyant suspension, with a = 1, φ > 0.61, and d < 230 μm [23]. This configuration will FIG.…”

“…Other configurations share some similarities with the present liquid-saturated granular column, namely, the slumping of a neutrally buoyant suspension [19][20][21][22][23] and the fully immersed granular collapse [24][25][26][27][28][29][30]. In the first case, the density of the interstitial fluid and that of the grains is similar and hence the granular pressure is canceled.…”

“…Contrary to a dry granular case, the collapse of a neutrally buoyant suspension column does not stop in most of the cases. However, the presence of the interface is shown to play a major role on the dynamics of the suspension, at least, at large initial volume fractions φ [22,23]. In the case of a fully immersed granular collapse, the granular pressure exists as grains are denser than the surrounding fluid, and the jamming process is recovered.…”

Impact of Fluidized Granular Flows into Water: Implications for Tsunamis Generated by Pyroclastic Flows

“…Additionally, in the case of dam-break flows on a horizontal plane, it is well known that a value of = 2 is hardly reached due to bottom shear dissipation, which becomes significant in regions where the depth of the current becomes small, particularly close to the front (Dressler, 1952;Hogg & Woods, 2001;Hogg & Pritchard, 2004). In the literature, the parameter is usually found in the range = [1 ∶ 2] (Bonometti et al, 2008(Bonometti et al, , 2017Dressler, 1954;Jánosi et al, 2004;Leal et al, 2006;Roche et al, 2008), according to the value = 1.4 obtained here. Similar conclusions can be drawn from the inset of Figure 3a.…”

Experimental investigation of tsunami waves generated by granular collapse into water

“…For tall grain columns (a 3), Larrieu, Staron & Hinch (2006) have shown that the dynamics can be understood from depth-averaged shallow-water equations applied to a thin horizontally spreading layer (with basal Coulomb friction), which is fed with vertical 'raining' grains (with no horizontal momentum) from the initial column in free fall. The influence of an ambient fluid on the granular collapse has then been investigated experimentally by Meruane, Tamburrino & Roche (2010), Rondon, Pouliquen & Aussillous (2011), Bougouin, Lacaze & Bonometti (2017) and Bougouin & Lacaze (2018), and numerically by Topin et al (2012). For immersed cases, the Stokes number that measures the importance of grain inertia relative to viscous forces and the solid/fluid density ratio are important dimensionless numbers that control the avalanche regime (Courrech du Pont et al 2003a).…”