Bouncing motion of spherical particles in fluids

Abstract

We investigate experimentally the bouncing motion of solid spheres onto a solid plate in an ambient fluid which is either a gas or a liquid. In particular, we measure the coefficient of restitution e as a function of the Stokes number, St, ratio of the particle inertia to the viscous forces. The coefficient e is zero at small St, increases monotonically with St above the critical value Stc and reaches an asymptotic value at high St corresponding to the classical “dry” value emax measured in air or vacuum. This behavior is observed for a large range of materials and a master curve e/emax=f(St) is obtained. If gravity is sufficient to describe the rebound trajectory (after the collision) in a gas, this is not the case in a liquid where drag and added-mass effect are important but not sufficient: History forces are shown to be non-negligible even at large Reynolds number.

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

“…Their model neglects the elastic deformation of the particles, which occurs over lengths comparable with the roughness height according to the elastohydrodynamics analysis in Davis et al (1986). The authors do not compare their results with the trajectory of a bouncing particle; however, they do compare with experimental measurements of the speeds of the particle before and after collision through the effective coefficient of restitution data from Gondret et al (2002). The recent work by Feng, Michaelides & Mao (2010) presents a collision model using a spring and dashpot, similar to softsphere collision models for dry granular flows.…”

“…Based on the measured temperature and apparent specific gravity, the concentration, density and viscosity of the mixture can be found from Dow Chemical Synthetic Glycerin Products. A typical value of the apparent specific gravity is 1.205 at 20 • C corresponding to a density of 1203 kg m −3 and a viscosity of 50.2 × 10 −3 Pa s. Gondret et al (2002) showed that the impact speed was not changing within this time interval in their experiments. Because of the small values of h(t = 0)/D, the particle does not achieve its terminal velocity before it contacts the wall.…”

“…When the particle Stokes number increases, the particle rebounds after collision. The experiments by Gondret et al (2002) include particle rebound but do not include the initial trajectory of the particle after it is released. To provide data with which to compare the simulations, new experiments are conducted where the particle is released from rest in a quiescent tank; the particle collides with the lower wall and rebounds several times.…”

“…Within this lower range of Stokes number, the simulation results are sensitive to the non-dimensional parameter δ ss . When using δ ss = 0.017 + 5 % the simulations predict a coefficient of restitution that follows the trend represented by the curve fit by Ruiz-Angulo & Hunt (2010) of the experimental data by Joseph et al (2001) and Gondret et al (2002).…”

“…The study by Joseph et al (2001) measured e d of around 0.90 for glass, steel and Nylon particles colliding against a Lucite wall with impact speeds from 40 to 360 mm s −1 ; e d was higher (approximately 0.97) when these particles impacted a harder glass or Zerodur surface. 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.…”