Granular-front formation in free-surface flow of concentrated suspensions

A granular front emerges whenever the free-surface flow of a concentrated suspension spontaneously alters its internal structure, exhibiting a higher concentration of particles close to its front. This is a common and yet unexplained phenomenon, which is usually believed to be the result of fluid convection in combination with particle size segregation. However, suspensions composed of uniformly sized particles also develop a granular front. Within a large rotating drum, a stationary recirculating avalanche is generated. The flowing material is a mixture of a viscoplastic fluid obtained from a kaolin-water dispersion with spherical ceramic particles denser than the fluid. The goal is to mimic the composition of many common granular-fluid materials, such as fresh concrete or debris flow. In these materials, granular and fluid phases have the natural tendency to separate due to particle settling. However, through the shearing caused by the rotation of the drum, a reorganization of the phases is induced, leading to the formation of a granular front. By tuning the particle concentration and the drum velocity, it is possible to control this phenomenon. The setting is reproduced in a numerical environment, where the fluid is solved by a lattice-Boltzmann method, and the particles are explicitly represented using the discrete element method. The simulations confirm the findings of the experiments, and provide insight into the internal mechanisms. Comparing the time scale of particle settling with the one of particle recirculation, a nondimensional number is defined, and is found to be effective in predicting the formation of a granular front.

Figure 1

Schematics of the particle fluid mechanisms occurring in a rotating drum test. The color scheme is blue for the fluid and red for the particles. (a) Rotating drum reference system and common particle-fluid distribution. (b) Granular-front formation process by increasing the rotational velocity of the drum $\omega$. (c) LBM and DEM discretization mesh employed in the numerical simulations (a two-dimensional view is presented for simplicity). (d) Fluid-particle and particle-particle interactions considered as a result of a granular flow through a viscous flowing fluid. (e) Motion pattern of the particles at the front.

Figure 2

Pictures of the flow inside the drum. The same material shows different features at low and high drum speed.

Figure 3

Rotating drum at BOKU. (a) Height point laser, (b) normal load cell, (c) fluid pressure transducer, (d) high-speed camera, and (e) inner roofs (drop protection). Adapted from Refs. [32, 33].

Figure 4

Rheological behavior of the kaolin-water dispersion. The flow curve is approximated as a Bingham fluid (solid line).

Figure 5

Front as a function of the angular velocity of the drum and particle concentration.

Figure 6

Image front detection analysis. (a) Raw image, (b) binary image conversion, and (c) Canny edge detector. The yellow line presents the location of the flow front and the vertical dashed line is the median flow front ${\theta }_{\text{front}}$.

Figure 7

Snapshots of the DEM-LBM simulations (particle content of $31\%$). (a) The formation of a granular front by an increase in the angular velocity of the drum. The tangential velocity $v_{\theta }$ along a longitudinal profile for fluid (b) and particles (c).

Figure 8

Experimental and numerical flow height (a) and bulk basal pressure profiles (b) at $0.3\text{rad}/\text{s}$ and particle concentration of 31%. The dashed line has the height of one particle diameter.

Figure 9

Experimental and numerical values for the position of fluid front ${\theta }_{\text{f}}$ (blue), particle front ${\theta }_{\text{p}}$ (red), and center of volume ${\theta }_{\text{c}}$ (white) vs drum speed $\omega$ for (a) 13%, (b) 23%, (c) 31%, (d) 38%, and (e) 43% particle content. Markers are obtained from experimental measurements at 4 different drum speeds $\omega$ (see Sec. 2), while numerical simulations are performed every $0.25\text{rad}/\text{s}$ (see Sec. 3). The gray-scale contour map describes the particle accumulation in the mixture as obtained from the simulations.

Figure 10

Analytical flow height of a free surface flow down an incline against the experimental and numerical height (average height between ${25}^{\circ }$ and ${30}^{\circ }$). The solid lines are fit to the data points and highlight the linear behavior.

Figure 11

Numerical location of the fluid front ${\theta }_{\text{f}}$ as a function of the angular velocity of the drum $\omega$. Markers represent different particle contents. For a fluid-only simulation the trend is linear (solid line).

Figure 12

Qualitative representation of the particle trajectories. The position of two representative particles is tracked through the whole simulation, showing how the recirculation pattern continuously draws particles to the front, where they settle. Once the particles reach the bottom, they are drawn back towards the tail.

Figure 13

Settling velocity of the front particles, calculated using the simulations by averaging the vertical velocity of the particles in the range ${\theta }_{\text{p}}\le \theta \le {\theta }_{\text{p}}+2.5^{\circ }$. The marker shape indicates the composition of the flow, while the shading shows whether the fronts are separate (dark shades) or merged (light shades). When the fronts are separate, the settling velocity is equal to the settling velocity in the fluid $u_{\text{s}}^{\text{fluid}}$. This increases as soon as the two fronts get closer, because some particles fall no more through the fluid, but rather through a mixture of air and fluid, therefore reaching a higher velocity $u_{\text{s}}^{\text{air}}$.

Figure 14

Travel velocity $u_{\text{t}}^{\text{down}}$, calculated using the simulations by averaging the horizontal velocity of the particles laying on the top layer in the range ${\theta }_{\text{p}}+2.5^{\circ }\le \theta \le {\theta }_{\text{p}}+5.0^{\circ }$. The markers represent the composition of the flow. For the case of $13\%$ particles, there is no recirculating flow if $\omega <0.6\text{rad}/\text{s}$, and this velocity is close to zero. Elsewhere, a recirculating flow develops, and the velocity is correlated to the drum speed. The relative positions of the fronts does not seem to influence the travel velocity.

Figure 15

Angle separating the particle front and the fluid front $\mathrm{\Delta }\theta$ as a function of the time-scale ratio $\xi$. If the two fronts are separate, the data collapse on a lineal trend (continuous line). The simulation data are presented with gray markers, and experimental data with black markers.