Experiments were performed in a vertical channel to study the behaviour of a monodisperse bubble suspension for which the dual limit of large Reynolds number and small Weber number was satisfied. Measurements of the liquid-phase velocity fluctuations were obtained with a hot-wire anemometer. The gas volume fraction, bubble velocity, bubble velocity fluctuations and bubble collision rate were measured using a dual impedance probe. Digital image analysis was performed to quantify the small polydispersity of the bubbles as well as the bubble shape.A rapid decrease in bubble velocity with bubble concentration in very dilute suspensions is attributed to the effects of bubble-wall collisions. The more gradual subsequent hindering of bubble motion is in qualitative agreement with the predictions of Spelt & Sangani (1998) for the effects of potential-flow bubble-bubble interactions on the mean velocity. The ratio of the bubble velocity variance to the square of the mean is O(0.1). For these conditions Spelt & Sangani predict that the homogeneous suspension will be unstable and clustering into horizontal rafts will take place. Evidence for bubble clustering is obtained by analysis of video images. The fluid velocity variance is larger than would be expected for a homogeneous suspension and the fluid velocity frequency spectrum indicates the presence of velocity fluctuations that are slow compared with the time for the passage of an individual bubble. These observations provide further evidence for bubble clustering.

The flow around a fixed cylinder immersed in a uniform granular flow is studied experimentally. Experiments are performed in a tall vertical chute producing a quasi two-dimensional granular flow. A storage bin at the top of the chute feeds glass particles into the channel while the mean velocity of the flow is controlled by varying the exit width of a hopper located at the channel bottom. Measurements of the drag force acting on a fixed cylinder are made using a strain gauge force measurement system. The flow velocity field is measured through a transparent wall using a particle image velocimetry analysis of high speed video recordings of the flow. Experiments are performed for a range of upstream particle velocities, cylinder diameters, and two sizes of glass particles. For the range of velocities studied, the mean drag force acting on the cylinder is independent of the mean flow velocity, contrary to what is expected from any ordinary fluid. The drag force increases with cylinder diameter and decreases with particle diameter. The drag force scales with the asymptotic static stress state in a tall granular bed. The drag coefficient, defined in terms of a dynamic pressure and an effective cylinder diameter, scales with the flow Froude number based on the hydraulic diameter of the channel. This analysis indicates that the drag acting on the cylinder is strongly affected by the surrounding channel geometry. Although the drag force on the cylinder does not change with the upstream flow velocity, the flow streamlines do change with velocity. A large stagnation zone forms at the leading edge of the cylinder while at the trailing edge an empty wake is observed. The wake size increases with flow velocity. Measurements of the flow vorticity and granular temperature are also presented and discussed.

In this paper we investigate a two-dimensional dilute granular flow around an immersed cylinder using discrete element computer simulations. Simulation measurements of the drag force acting on the cylinder, Fd, are expressed in terms of a dimensionless drag coefficient, Cd=Fd/[12ρν∞U∞2(D+d)], where ρ is the upstream particle mass density, ν∞ is the upstream solid fraction, U∞ is the upstream velocity, and (D+d) is the sum of the cylinder diameter, D, and surrounding particle diameter, d. The drag coefficient increases rapidly with decreasing Mach number for subsonic Mach numbers, but remains insensitive to Mach number for supersonic values. The drag coefficient is also a strong function of the flow Knudsen number, with the drag coefficient increasing with increasing Knudsen number and approaching an asymptotic value for very large Knudsen numbers. The drag coefficient decreases with decreasing normal coefficient of restitution and is relatively insensitive to the friction coefficient. Bow shock structures and expansion fans are also observed in the simulations and are compared to similar structures observed in compressible gas flows.

The motion of a spherical particle along a rough bed in a simple shear viscous flow is studied experimentally for a wide range of parameters, varying the particle size and density, the fluid viscosity and the shear rate γ. The instantaneous particle velocity is calculated in the stream, transverse and vertical directions, using a high-speed video imaging system. It is found that the normalized streamwise mean particle velocity U/US, where US is the Stokes settling velocity, depends only on the dimensionless shear rate μ γ/(Δ ρ g d), this relationship being independent of the particle Reynolds number Rep. This result holds for small Rep, which was the case in our experiments (Rep < 10). The characteristic amplitude and frequency of the velocity fluctuations are also given and discussed. A model is then proposed for the mean streamwise velocity, based on ideas of Bagnold (Proc. R. Soc. Lond. A, vol. 332, 1973, p. 473) and calculations of Goldman et al. (Chem. Engng Sci., vol. 22, 1967b, p. 653) for the velocity of a particle close to a smooth plane. From this model an equivalent bed roughness and an effective friction coefficient are deduced.

The conditions for which the paths of freely rising bubbles become oscillatory are studied experimentally using silicone oils with viscosities ranging from 0.5 to 9.4 times that of water. Since these fluids are nonpolar, as opposed to water, the gas-liquid interfaces remain clean without the need of an ultrapure environment. We find the Reynolds number at incipient transition to vary from 70 to 470, for decreasing liquid viscosity. Correspondingly, the bubble aspect ratio remains almost constant, ranging only from 2.36 to 2.0 for the same set of conditions. Hence, we argue that the dominant parameter to trigger the instability is the bubble shape and not the Reynolds number. Since vorticity generated at the bubble surface is almost independent of the Reynolds number and mostly depends on the bubble aspect ratio in the parameter range covered by our experiments, present results strongly support the view that path instability is a direct consequence of the wake instability that occurs when this surface vorticity exceeds a certain threshold.