A numerical study on the coefficient of restitution of wet collisions

Abstract

Using smoothed particle hydrodynamics (SPH) simulations, we investigate the coefficient of restitution (COR) in wet collisions and identify a scaling law governing its behavior. The simulations employ an updated-Lagrangian, mesh-free framework that is validated against experimental measurements. We neglect surface tension effects since the impact conditions correspond to a moderate-to-high Weber number regime. The COR is found to depend on the Stokes number and a dimensionless film thickness defined as the ratio of the liquid film thickness to the diameter of the impacting solid bead. Two distinct regimes are observed, each characterized by different power-law exponents.

Figures (9)

• Figure 1: The physical scenario and the computational domain
• Figure 2: (a)Validation and particle-resolution analysis for the impact of a 5.5 mm glass bead onto a 0.45 mm thick M5 silicone-oil film. The rebound velocity obtained from ISPH simulations is compared with experimental measurements of Gollwitzer et al. Gollwitzer for increasing liquid particle resolution. (b) Relative $L_2$ error in rebound velocity as a function of liquid particle number for the impact of a 5.5 mm glass bead onto a 0.45 mm M5 silicone-oil film. The error decreases monotonically with increasing resolution and approaches convergence beyond approximately 178,000 particles.
• Figure 3: Parity plot comparing simulated and experimental Gollwitzer rebound velocities for the 178,220-particle resolution. The dashed line represents perfect agreement. The data cluster tightly around the identity line ($R^2 = 0.99937$, $\mathrm{RMSE} = 0.00524$), indicating excellent agreement with experiments.
• Figure 4: Coefficient of restitution (COR) as a function of Stokes number (St) for different liquid thicknesses of Water, compared with the experimental results of Gollwitzer et. al. Gollwitzer. Evidently, the Stokes number doesn't fully characterize wet-impact rebound.
• Figure 5: Position of center of gravity (COG) of the sphere vs. its normal velocity (absolute value) during impact onto a thin liquid film at an impact velocity of 0.30 m/s. The labeled points P1–P4 denote key stages of the interaction: initial contact with the liquid film (P1), collision with the solid substrate (P2 & P3) and separation from the liquid film defining the rebound velocity (P4).