The dam-break problem for concentrated suspensions of neutrally buoyant particles

This paper addresses the dam-break problem for particle suspensions, that is, the flow of a finite volume of suspension released suddenly down an inclined flume. We were concerned with concentrated suspensions made up of neutrally-buoyant non-colloidal particles within a Newtonian fluid. Experiments were conducted over wide ranges of slope, concentration, and mass. The major contributions of our experimental study are the simultaneous measurement of local flow properties far from the sidewalls (velocity profile and, with lower accuracy, particle concentration) and macroscopic features (front position, flow depth profile). To that end, the refractive index of the fluid was adapted to closely match that of the particles, enabling data acquisition up to particle volume fractions of 60%. Particle migration resulted in the blunting of the velocity profile, in contrast to the parabolic profile observed in homogeneous Newtonian fluids. The experimental results were compared with predictions from lubrication theory and particle migration theory. For solids fractions as large as 45%, the flow behaviour did not differ much from that of a homogeneous Newtonian fluid. More specifically, we observed that the velocity profiles were closely approximated by a parabolic form and there was little evidence of particle migration throughout the depth. For particle concentrations in the 52%–56% range, the flow depth and front position were fairly well predicted by lubrication theory, but taking a closer look at the velocity profiles revealed that particle migration had noticeable effects on the shape of the velocity profile (blunting), but had little impact on its strength, which explained why lubrication theory performed well. Particle migration theories (such as the shear-induced diffusion model) successfully captured the slow evolution of the velocity profiles. For particle concentrations in excess of 56%, the macroscopic flow features were grossly predicted by lubrication theory (to within 20% for the flow depth, 50% for the front position). The flows seemed to reach a steady state, i.e., the shape of the velocity profile showed little time dependence.

Dam Break of Newtonian Fluids and Granular Suspensions

Nicolas Andreini

The objective of this thesis was to increase our understanding of two-phase geophysical flows (e.g. debris flows) by providing velocity profiles in idealized laboratory avalanches. To that end, we developed a new experimental platform made up of an inclined flume coupled to an imaging system to measure velocity in granular suspension. The inclined flume was 3.5 m long and 10 cm wide and could be inclined from 0 to 35°. A reservoir with the capacity for 10 l of fluid was located in the upper part of the flume and closed with a pneumatic controlled gate. Velocity profiles were obtained using Particle Image Velocimetry (PIV) and index-of-refraction matching of the solid and liquid phases. We used transparent PMMA beads with mean diameters of 200 µm and the interstitial fluid was composed of a mixture of three fluids. The interstitial fluid was adapted in order to match the refraction index and the density of the solid phase. Using pulsed laser and a high speed camera we were able to measure velocity profiles at frequencies up to 1000 Hz with very good precision. Two additional cameras tracked the front position along the flume with a frequency of 30 Hz and a spatial resolution of 1 mm. Prior to acquiring data on the granular suspension, we tested our system on Newtonian fluids. Eight flow configurations were selected with different fluids (glycerol and triton X100), different slopes and different released masses. Velocity profiles were found to be parabolic far from the front as well as very close to the contact line. However, near the front, quantitative theoretical predictions given by lubrication theory diverged from experimental results. Velocities were significantly overestimated (∼ 400%) by the theory at low Reynolds numbers (Re < 2) and slightly underestimated (∼ 10%) at high Reynolds numbers (Re > 8). Very good agreement with theory far from the front indicated that the accuracy of the setup was good (reliable calibration procedure and image processing methods). Experiments on granular suspensions revealed a variety of behaviors depending on the particle concentration, the slope and the mass released. At solid fractions up to 45%, suspensions behaved as homogeneous viscous fluids. For the duration of the experiment, it was not possible to detect any inhomogeneity due to migration or sedimentation. In the range of shear rate tested and with the precision allowed by the setup no shear thickening or shear thinning was observed since velocity profiles remained perfectly Newtonian. For slightly more concentrated suspensions (up to 55%), we found that the flow dynamics at the bulk scale could still be described using a viscous theory. However, at the local scale, migration gave rise to concentration inhomogeneities producing a blunted velocity profile. The shape of the blunted profile was well described by the Mills and Snabre migration model coupled to a Krieger-Dougherty effective viscosity. However, magnitudes of the velocities were largely overestimated, most probably because we fitted the effective viscosity at higher shear rates. Above 55%, small released masses with high solid fractions stopped after a finite time and separation between fluid and solid phases occurred. The solid frame stayed at rest while the fluid seeped through the granular media eroding the front. For larger released masses, we observed successions of different regimes: After an inertial regime and a pseudo-viscous regime, the flow slowed down, corresponding to a new regime in which the shearing was localized in a thin layer at bottom and there was no shearing of the front. At the same time, we observed that the free surface deformed and became wavy. Fractures developed on the top of the flow and, if they grew sufficiently, modified the local velocity field substantially. Finally, at longer time (≥ 4 min) an intermittent motion (stick-slip) was observed with phases during which the suspension was flowing in a quasi-steady regime and phases during which the suspension was at a halt.

EPFL2012

Granular suspension avalanches. I. Macro-viscous behavior

Christophe Ancey, Nicolas Andreini, Gaël Epely Chauvin

We experimentally studied the flow behavior of a fixed volume of granular suspension, initially contained in a reservoir and released down an inclined flume. Here “granular suspension” refers to a suspension of non-Brownian particles in a viscous fluid. Depending on the solids fraction, density mismatch, and particle size distribution, a wealth of behaviors can be observed. Here we report and interpret results obtained with granular suspensions, which consisted of neutrally buoyant particles with a solids fraction (ϕ = 0.575–0.595) close to the maximum random packing fraction (estimated at ϕm = 0.625). The particles had the same refractive index as the fluid, which made it possible to measure the velocity profiles inside the moving bulk and far from the sidewalls. Additional information such as the front position and the flow depth was also recorded. Three regimes were observed. At early times, the flow features were reminiscent of homogeneous Newtonian fluids (e.g., the same dependence of the front position on time). At later times, the free surface became more and more bumpy as fractures developed within the bulk. This fracture process ultimately gave rise to a stick-slip regime, in which the suspension moved intermittently. In this paper, we focus on the first regime referred to as the macro-viscous regime. Although the bulk flow properties looked like those of Newtonian fluids, the internal dynamics were much richer.

Amer Inst Physics2013

Granular suspension avalanches. II. Plastic regime

Christophe Ancey, Nicolas Andreini, Gaël Epely Chauvin

We present flume experiments showing plastic behavior for perfectly density-matched suspensions of non-Brownian particles within a Newtonian fluid. In contrast with most earlier experimental investigations (carried out using coaxial cylinder rheometers), we obtained our rheological information by studying thin films of suspension flowing down an inclined flume. Using particles with the same refractive index as the interstitial fluid made it possible to measure the velocity field far from the wall using a laser-optical system. At long times, a stick-slip regime occurred as soon as the fluid pressure dropped sufficiently for the particle pressure to become compressive. Our explanation was that the drop in fluid pressure combined with the surface tension caused the flow to come to rest by significantly increasing flow resistance. However, the reason why the fluid pressure diffused through the pores during the stick phases escaped our understanding of suspension rheology.

Amer Inst Physics2013

Dam Break of Newtonian Fluids and Granular Suspensions

Nicolas Andreini

EPFL2012