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.

Optical measurement techniques such as particle image velocimetry (PIV) and laser Doppler velocimetry (LDV) are now routinely used in experimental fluid mechanics to investigate pure fluids or dilute suspensions. For highly concentrated particle suspensions, material turbidity has long been a substantial impediment to these techniques, which explains why they have been scarcely used so far. A renewed interest has emerged with the development of specific methods combining the use of iso-index suspensions and imaging techniques. This review paper gives a broad overview of recent advances in visualization techniques suited to concentrated particle suspensions. In particular, we show how classic methods such as PIV, LDV, particle tracking velocimetry, and laser induced fluorescence can be adapted to deal with concentrated particle suspensions.

In this paper, the flow dynamics of gravity currents on a horizontal plane is investigated from a theoretical point of view by seeking similarity solutions. The current is generated by unleashing a varying volume of heavy fluid within an ambient fluid of much lower density. Unlike earlier investigators, we assume that the ambient fluid exerts no significant resisting action on the current, and therefore the flow depth is expected to drop to zero at the front in the absence of friction. In this context, the shallow-water equations are highly appropriate for computing the mean velocity and flow depth of the current. The boundary condition imposed at the front leads to technical mathematical difficulties. Indeed, unlike in the Boussinesq case, no regular solution to the shallow-water equations satisfies the downstream condition, but when the flow is supercritical at the channel inlet, it is possible to construct a piecewise solution by patching a regular solution to an exceptional solution, which represents the head behavior. To better understand this result and make sure that the result is physically relevant, we consider the Navier-Stokes equations within the high-Reynolds-number limit. Approximate similarity solutions can be worked out, which support our earlier analysis on the shallow-water equations. While the flow body is self-similar and weakly rotational, the head is not self-similar, but tends toward a self-similarity shape at long times. It is characterized by a strong vorticity, a straight free surface, and a nonuniform velocity profile, which becomes flatter and flatter with time.

[1] In this paper, we seek similarity solutions to the shallow water (Saint-Venant) equations for describing the motion of a non-Boussinesq, gravity-driven current in an inertial regime. The current is supplied in fluid by a source placed at the inlet of a horizontal plane. Gratton and Vigo (1994) found similarity solutions to the Saint-Venant equations when a Benjamin-like boundary condition was imposed at the front (i.e., nonzero flow depth); the Benjamin condition represents the resisting effect of the ambient fluid for a Boussinesq current (i.e., a small-density mismatch between the current and the surrounding fluid). In contrast, for non-Boussinesq currents the flow depth is expected to be zero at the front in absence of friction. In this paper, we show that the Saint-Venant equations also admit similarity solutions in the case of non-Boussinesq regimes provided that there is no shear in the vertical profile of the streamwise velocity field. In that case, the front takes the form of an acute wedge with a straight free boundary and is separated from the body by a bore.

No abstract

No abstract

No abstract

No abstract