Roberto Zenit

Particle{wall collisions in a viscous fluid

This paper presents experimental measurements of the approach and rebound of a particle colliding with a wall in a viscous fluid. The particles trajectory was controlled by setting the initial inclination angle of a pendulum immersed in a fluid. The resulting collisions were monitored using a high-speed video camera. The diameters of the particles ranged from 3 to 12 mm, and the ratio of the particle density to fluid density varied from 1.2 to 7.8. The experiments were performed using a thick glass or Lucite wall with different mixtures of glycerol and water. With these parameters, the Reynolds number defined using the velocity just prior to impact ranged from 10 to approximately 3000. A coefficient of restitution was defined from the ratio of the velocity just prior to and after impact. The experiments clearly demonstrate that the rebound velocity depends on the impact Stokes number (defined from the Reynolds number and the density ratio) and weakly on the elastic properties of the material. Below a Stokes number of approximately 10, no rebound of the particle occurred. For impact Stokes number above 500 the coefficient of restitution appears to asymptote to the values for dry collisions. The coefficients of restitution were also compared with previous experimental studies. In addition, the approach of the particle to the wall indicated that the particle slowed prior to impacting the surface. The distance at which the particles trajectory varied due to the presence of the wall was dependent on the impact Stokes number. The particle surface roughness was found to affect the repeatability of some measurements, especially for low impact velocities.

Measurements of the Average Properties of a Suspension of Bubbles Rising in a Vertical Channel

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.

Dense granular flow around an immersed cylinder

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.

Computer simulations of the collapse of a granular column

Recently, two independent groups reported experimental results on the process of collapse of a cylindrical granular column. It was found that the shape of the final deposit depended mostly on column aspect ratio; surprisingly, the frictional properties of the material appeared not to influence the results significantly. In this investigation, making use of discrete element code, simulations of an equivalent two-dimensional system were carried out. The numerical results qualitatively reproduce the behavior observed in experiments. Performing an energy balance of the system, the different deposit regimes can be discerned.

Collisional particle pressure measurements in solid-liquid flows

Experiments were conducted to measure the collisional particle pressure in both cocurrent and countercurrent flows of liquid-solid mixtures. The collisional particle pressure, or granular pressure, is the additional pressure exerted on the containing walls of a particulate system due to the particle collisions. The present experiments involve both a liquid-fluidized bed using glass, plastic or steel spheres and a vertical gravity-driven flow using glass spheres. The particle pressure was measured using a high-frequency-response flush-mounted pressure transducer. Detailed recordings were made of many different particle collisions with the active face of this transducer. The solids fraction of the flowing mixtures was measured using an impedance volume fraction meter. Results show that the magnitude of the measured particle pressure increases from low concentrations (>10% solid volume fraction), reaches a maximum for intermediate values of solid fraction (30-40%), and decreases again for more concentrated mixtures (>40%). The measured collisional particle pressure appears to scale with the particle dynamic pressure based on the particle density and terminal velocity. Results were obtained and compared for a range of particle sizes, as well as for two different test section diameters. In addition, a detailed analysis of the collisions was performed that included the probability density functions for the collisoin duration and collision impulse. Two distinct contributions to the collisional particle pressure were identified: one contribution from direct contact of particles with the pressure transducer, and the second one resulting from particle collisions in the bulk that are transmitted through the liquid to the pressure transducer.

Path instability of rising spheroidal air bubbles: A shape-controlled process

Received 27 March 2008; accepted 16 May 2008The conditions for which the paths of freely rising bubbles become oscillatory are studiedexperimentally using silicone oils with viscosities ranging from 0.5 to 9.4 times that of water. Sincethese fluids are nonpolar, as opposed to water, the gas-liquid interfaces remain clean without theneed of an ultrapure environment. We find the Reynolds number at incipient transition to vary from70 to 470, for decreasing liquid viscosity. Correspondingly, the bubble aspect ratio remains almostconstant, ranging only from 2.36 to 2.0 for the same set of conditions. Hence, we argue that thedominant parameter to trigger the instability is the bubble shape and not the Reynolds number. Sincevorticity generated at the bubble surface is almost independent of the Reynolds number and mostlydepends on the bubble aspect ratio in the parameter range covered by our experiments, presentresults strongly support the view that path instability is a direct consequence of the wake instabilitythat occurs when this surface vorticity exceeds a certain threshold. ©

Measurement of pseudoturbulence intensity in monodispersed bubbly liquids for 10<Re<500

Experiments were performed to measure the velocities of both phases in a monodispersed bubbly flow in a vertical column. Using water and water-glycerin mixtures, measurements were obtained for a range of Reynolds numbers from 10 to 500. For all cases, the Weber number was below 2. To generate a uniform stream of bubbles, an array of identical capillaries was used. To avoid coalescence, a small amount of salt was added to the interstitial fluid, which did not affect the fluid properties significantly. Measurements of the bubble phase velocity were obtained using a dual impedance probe and through high-speed digital video processing. A measurement of the vertical component of the fluctuating liquid velocity was obtained using a flying hotwire technique, which resolved the deficiency of this technique for flows with zero-mean velocity. To the best of our knowledge, this technique has not been used to study bubbly liquids in the past. It was found that for all cases, the bubble velocity decreases as the mean ...

The flow of non-Newtonian fluids around bubbles and its connection to the jump discontinuity

Abstract The flow field around air bubbles rising in aqueous polyacrylamide (PAAm) solutions was studied using a particle image velocimetry (PIV) system. This flow was analyzed in the vicinity of the critical bubble volume where the discontinuity of the terminal bubble velocity occurs. It was found that the flow configuration changes drastically below and above the critical bubble volume. The flow just below the critical bubble volume shows an upward flow at the front and back of the bubble with a symmetrical vortex around the bubble. The flow field obtained for a volume just above the critical one shows the appearance of the so-called negative wake behind the bubble. Additionally, it was found that the container walls affect significantly the magnitude of the terminal velocity as well as the velocity jump. However, the critical volume at which the velocity jump appears does not change for different container sizes.

Increased mobility of bidisperse granular avalanches

The unexpected behaviour of long-runout landslides has been a controversial subject of discussion in the geophysics community. In order to provide new insight into this phenomenon, we investigate the apparent reduction of friction resulting from the presence of a second species of smaller particles in the bulk of the granular material that forms the avalanche. Results obtained by means of a two-dimensional soft particle discrete element numerical simulation are presented. The numerical experiments consider an avalanche of two-size particles, originally placed over an inclined plane. The friction coefficient for the particle–particle and wall–particle contacts is held fixed. The granular mass is allowed to evolve with time, until it comes back to rest on a horizontal plane. The position of the centre of mass is located, such that the runout length L cm / H cm could be measured, with L cm and H cm being the horizontal distance travelled and the height lost by the avalanche centre of mass, respectively. Many simulations were performed keeping the area of the avalanche constant, varying only the area fraction of small particles. The results show that the runout length increases with the area fraction of small particles, reaching a maximum for a given area fraction of small particles. A detailed analysis of the particle distribution in the granular mass indicates that the apparent friction coefficient is affected by the formation of a layer of small particles at the base of the avalanche. This layer is identified as the source of ‘lubrication’. Furthermore, since there is a dependence of the runout on the fall height and the volume in real avalanches, some simulations with different areas and different fall heights were performed. The results show a tendency of the runout to increase with area, and to decrease with the initial fall height, which is in agreement with what is observed for geological events.

Motion of a particle near a rough wall in a viscous shear flow

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 y. 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/U S , where U S is the Stokes settling velocity, depends only on the dimensionless shear rate μγ/(Δpgd), this relationship being independent of the particle Reynolds number Re p . This result holds for small Re P , which was the case in our experiments (Re p <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 and calculations of Goldman et al. 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