Experimental investigation into segregating granular flows down chutes

Abstract

We experimentally investigated how a binary granular mixture made up of spherical glass beads ͑size ratio of 2͒ behaved when flowing down a chute. Initially, the mixture was normally graded, with all the small particles on top of the coarse grains. Segregation led to a grading inversion, in which the smallest particles percolated to the bottom of the flow, while the largest rose toward the top. Because of diffusive remixing, there was no sharp separation between the small-particle and large-particle layers, but a continuous transition. Processing images taken at the sidewall, we were able to measure the evolution of the concentration and velocity profiles. These experimental profiles were used to test a recent theory developed by Gray and Chugunov ͓J. Fluid Mech. 569, 365 ͑2006͔͒, who derived a nonlinear advection diffusion equation that describes segregation and remixing in dense granular flows of binary mixtures. We found that this theory was able to provide a consistent description of the segregation/remixing process under steady uniform flow conditions. To obtain the correct depth-averaged concentration far downstream, it was very important to use an accurate approximation to the downstream velocity profile through the avalanche depth. The S-shaped concentration profile in the far field provided a useful way of determining what we refer to as the Péclet number for segregation, a dimensionless number that quantifies how large the segregation is compared to diffusive remixing. While the theory was able to closely match the final fully developed concentration profile far downstream, there were some discrepancies in the inversion region ͑i.e., the region in which the mixing occurs͒. The reasons for this are not clear. The difficulty to set up the experiment with both well controlled initial conditions and a steady uniform bulk flow field is one of the most plausible explanations. Another interesting lead is that the flux of segregating particles, which was assumed to be a quadratic function of the concentration in small beads, takes a more complicated form.

Debris flows: Experiments and modelling

“…Savage and Lun's [10] movable hopper and splitter plate experiment provides one of the best data sets, but it is relatively low resolution with only five data points through the avalanche depth. Another approach is that of Wiederseiner et al [92] who used a high speed camera to take pictures through a transparent sidewall. By averaging 2000 frames and stitching together the images at 10 downstream locations a complete picture (Fig.…”

“…2(e) with a Péclet number equal to 19. Wiederseiner et al [92] used a standard Galerkin finite element method programmed in the pdepe routine in Matlab to solve the two-dimensional steady-state segregation equation (26) and hence determine an appropriate segregation rate S ls to match the experimental data. This solution is shown in Fig.…”

A hierarchy of particle-size segregation models: From polydisperse mixtures to depth-averaged theories

“…The equation is closely related to Burgers' equation, which Gray and Chugunov [20] exploited, by means of the Cole-Hopf transformation, to construct exact solutions for time-dependent segregation with diffusion. Wiederseiner et al [36] have obtained excellent agreement between the diffuse theory and detailed experimental data collected at the side wall of a chute. They showed that typical Peclet numbers Pe = Sr/Dr are of the order to 10-20.…”

Shear dispersion in dense granular flows

“…Thus, an avenue of future work is to incorporate non-Fickian effects such as volume-fraction variation and segregation of bidisperse materials by generalizing Eq. (1) using mixture theory [36], which leads to the addition of, e.g., a term proportional to Sγφ (1 − φ ) in q, where Sγ is a percolation velocity (see, e.g., [19,34,35]). For the case of granular materials immersed in a viscous fluid (e.g., concentrated colloidal suspensions), shear-induced migration effects due to hydrodynamic interactions [26,27,28,37] could also be included along these lines by augmenting q with a term proportional to d 2 φ ∇(φγ).…”

“…For α < 1, the velocity profile is convex; such profiles have been measured experimentally [34,35] in bidisperse chute flows, in which significant size segregation occurs.…”