Melany L. Hunt

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.

Local measurements of velocity fluctuations and diffusion coefficients for a granular material flow

Measurements were made of two components of the average and fluctuating velocities, and of the local self-diffusion coefficients in a flow of granular material. The experiments were performed in a 1 m-high vertical channel with roughened sidewalls and with polished glass plates at the front and the back to create a two-dimensional flow. The particles used were glass spheres with a nominal diameter of 3 mm. The flows were high density and were characterized by the presence of long-duration frictional contacts between particles. The velocity measurements indicated that the flows consisted of a central uniform regime and a shear regime close to the walls. The fluctuating velocities in the transverse direction increased in magnitude from the centre towards the walls. A similar variation was not observed for the streamwise fluctuations. The self-diffusion coefficients showed a significant dependence on the fluctuating velocities and the shear rate. The velocity fluctuations were highly anistropic with the streamwise components being 2 to 2.5 times the transverse components. The self-diffusion coefficients for the streamwise direction were an order-of-magnitude higher than those for the transverse direction. The surface roughness of the particles led to a decrease in the self-diffusion coefficients.

Liquid–solid flows using smoothed particle hydrodynamics and the discrete element method

Abstract This study presents a computational method combining smoothed particle hydrodynamics (SPH) and the discrete element method (DEM) to model flows containing a viscous fluid and macroscopic solid particles. The two-dimensional numerical simulations are validated by comparing the wake size, drag coefficient and local heat transfer for flow past a circular cylinder at Reynolds numbers near 100. The central focus of the work, however, is in computing flows of liquid–solid mixtures, such as the classic shear-cell experiments of Bagnold. Hence, the simulations were performed for neutrally buoyant particles contained between two plates for different solid fractions, fluid viscosities and shear rates. The tangential force resulting from the presence of particles shows an increasing dependence on the shear rate as observed in the Bagnold experiments. The normal force shows large variations with time, whose source is presently unclear but independent of the direct collisions between particles and the walls.

Dynamics of particle-particle collisions in a viscous liquid

When two solid spheres collide in a liquid, the dynamic collision process is slowed by viscous dissipation and the increased pressure in the interparticle gap as compared with dry collisions. This paper investigates liquid-immersed head-on and oblique collisions, which complements previously investigated particle-on-wall immersed collisions. By defining the normal from the line of centers at contact, the experimental findings support the decomposition of an oblique collision into its normal and tangential components of motion. The normal relative particle motion is characterized by an effective coefficient of restitution and a binary Stokes number with a correlation that follows the particle-wall results. The tangential motion is described by a collision model using a normal coefficient of restitution and a friction coefficient that are modified for the liquid effects.

Vertical Vibration of a Deep Bed of Granular Material in a Container

A deep bed of granular material (more than six layers of particles) was subjected to sinusoidal, vertical vibrations. Several phenomena were observed depending on the amplitude of excitation. These included heaping, surface waves, and arching; the transitions from one state to another involved various dynamic instabilites and bifurcations. The paper includes a description of these phenomena and the characteristic properties associated with each in addition to measurements of the transitions from one phenomena to another.

Oblique particle-wall collisions in a liquid

This paper presents experimental measurements of the approach and rebound of a particle colliding obliquely with a wall in a viscous fluid. Steel and glass particles 12.7 mm in diameter were used. The experiments were performed using a thick Zerodur wall (a glass-like material) with various mixtures of glycerol and water. Normal and tangential coefficients of restitution were defined from the ratios of the respective velocity components at the point of contact just prior to and after impact. These coefficients account for losses due to lubrication effects and inelasticity. A third parameter, a coefficient of sliding friction, provides a measure of the tangential force acting on the particle as it slides during a collision. Oblique collisions in a fluid are qualitatively similar to oblique collisions in a dry system, with a lowered friction coefficient dependent on surface roughness. For smooth surfaces the friction coefficient is drastically reduced due to lubrication effects. A theoretical model that takes into account the dependence of viscosity on pressure is proposed to explain the observed tangential force acting on a smooth sphere during an oblique collision. The model relies on an inferred uniform temperature increase within the lubrication layer, a consequence of viscous heating during impact. The tangential force felt by the particle is expressed as a friction coefficient dependent on the viscosity within the lubrication layer. The viscosity increases owing to pressure effects and decreases owing to thermal effects. For rough surfaces the friction coefficient is comparable to that measured in dry systems, since the surface asperities may interact with each other through the lubrication layer.

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.

Kinetic Theory Analysis of Flow-Induced Particle Diffusion and Thermal Conduction in Granular Material Flows

The kinetic theory model assumes that the particles are smooth, identical, and nearly elastic spheres, and that the binary collisions between the particles are isotropically distributed throughout the flow. The particle diffusivity and effective thermal conductivity are found to increase with the square root of the granular temperature, a term that quantifies the kinetic energy of the flow. The theoretical particle diffusivity is used to predict diffusion in a granular-flow mixing layer, and to compare qualitatively with recent experimental measurements

Shear-induced particle diffusion and longitudinal velocity fluctuations in a granular-flow mixing layer

In flows of granular material, collisions between individual particles result in the movement of particles in directions transverse to the bulk motion. If the particles were distinguishable, a macroscopic overview of the transverse motions of the particles would resemble a self-diffusion of molecules as occurs in a gas. The present granular- flow study includes measurements of the self-diffusion process, and of the corresponding profiles of the average velocity and of the streamwise component of the fluctuating velocity. The experimental facility consists of a vertical channel fed by an entrance hopper that is divided by a splitter plate. Using differently-coloured but otherwise identical glass spheres to visualize the diffusion process, the flow resembles a classic mixing-layer experiment. Unlike molecular motions, the local particle movements result from shearing of the flow; hence, the diffusion experiments were performed for different shear rates by changing the sidewall conditions of the test section, and by varying the flow rate and the channel width. In addition, experiments were also conducted using different sizes of glass beads to examine the scaling of the diffusion process. A simple analysis based on the diffusion equation shows that the thickness of the mixing layer increases with the square-root of downstream distance and depends on the magnitude of the velocity fluctuations relative to the mean velocity. The results are also consistent with other studies that suggest that the diffusion coefficient is proportional to the particle diameter and the square-root of the granular temperature.

Wall stresses in granular Couette flows of mono-sized particles and binary mixtures

Granular shear flows are studied in a gravity-free Couette geometry using a two-dimensional discrete element computer simulation. Upper and lower bounding walls are flat and frictional and move in opposing directions, while the right and left boundaries are periodic. Mono-size flows are examined at various concentrations and three different gap widths. Flows of binary mixtures with diameter ratios of 2, 5, and 10 are investigated as well. Mixture solid fraction ratios of small to large particles range from 0.4 to 5, with a constant overall solid fraction of 0.75 in two dimensions. Normal and shear stresses on the bounding walls are measured for various flow conditions. Both normal and shear stresses increase with solid fraction in same-size flows, and show a dependence on the wall spacing at low concentrations. Same-size particle flows show the existence of a critical wall solid fraction at which the granular temperature, strain rate, and stresses increase suddenly. Stresses in mixture flows with low solid fraction ratios of small to large particles are higher than for the mono-size system. For a fixed overall solid fraction of 0.75, mixture flow stresses also increase with diameter ratio of large to small particles. The ratio of shear to normal stress decreases with solid fraction in same-size flows. For mixture flows with constant overall solid fraction, the ratio increases with solid fraction ratio for size ratios of 5 and 10; it remains relatively constant in flows with a size ratio of only 2.