Oblique particlewall collisions in a liquid

Abstract

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.

Enhanced upswing in immersed collisions of tethered spheres

“…3͒ trend downwards with successive collisions, from e = 0.97± 0.04 at the first collision to e = 0.84± 0.03 at the eighth impact. This agrees with previous experiments, [3][4][5] which found that the restitution coefficient diminishes with decreasing Stokes number St= 2 9 S DH ͉ ˙2 − ˙1 ͉ cos 1 / L . The enhanced upswing observed despite these collisional losses indicates that they are overshadowed by other effects, which we characterize using the following model.…”

“…3,5 To clarify the interplay between vortex motions and immersed collisions, we conducted experiments with both isolated and colliding spheres, in the pendulum configurations illustrated in Fig. 1.…”

“…1. Each pendulum has height H = 180 mm and features a spherical bob of diameter D = 40 mm immersed in liquid in a tank of dimensions 500ϫ 400ϫ 350 mm 3 . To provide lateral restraint, a bifilar suspension is adopted.…”

The morphology and evolution of channels on the Wax Lake Delta, Louisiana, USA

“…where w p is the particle velocity of grain size D. It has been found that particle impacts are completely damped for St <~30 [Schmeeckle et al, 2001;Joseph and Hunt, 2004]. When the Stokes number is calculated for sand in the Wax Lake Outlet (D = 176 μm), and w p is set to the effective particle impact velocity (w i,eff , Table 4), St = 11.…”

A contact model for normal immersed collisions between a particle and a wall

“…The dependence of the coefficient of restitution on the Stokes number was also presented in the work by Gondret, Lance & Petit (2002); in this study, the authors measured the normal trajectory of the particle over multiple bounces. Joseph & Hunt (2004) examined oblique collisions between a particle and a wall. Later work by Yang & Hunt (2006) measured the coefficient of restitution for particle-particle collisions in a liquid and found a similar dependence on particle Stokes number.…”