The effect of surface roughness on the viscoelastic energy dissipation in a particle–wall collision

The particle collision on a wall with roughness is common in nature and industries, but not well understood yet. The presence of surface roughness greatly increases the complexity of local contact and makes it difficult to predict the energy dissipation by analytical models. In this work, we investigate the energy dissipation in a dynamic particle–wall collision with regular hemisphere roughness. The finite element method (FEM) with the standard linear solid model is used to solve the problem of non-ideal geometry, and extract the law of energy dissipation due to viscoelasticity. The results show that with the existence of surface roughness, the total viscoelastic dissipation is lower than that for a smooth surface, showing a higher restitution coefficient compared to the smooth surface. Based on the maximum number of asperities that particle contacts, the dynamic collisions can be categorized as the single-contact mode and multiple-contact mode. The variation of the total energy dissipation shows opposite trends with the roughness height in the two different modes. The collision time is recognized as the key to predict the total energy dissipation. Based on FEM simulation results, a piecewise correlation is established to estimate the Hertzian collision time with regular roughness. Finally, a correlation is proposed for the total energy dissipation in a viscoelastic particle–wall collision with regular roughness, which only takes the dimensionless relaxation time as the parameter. Covering different roughness heights, particle sizes, densities, relaxation times, and Young’s modulus, all the data are well correlated with the predicted curve.