New explicit correlations for the critical sticking velocity and restitution coefficient of small adhesive particles: A finite element study and validation

Abstract The collision between small adhesive particles and flat substrate is a fundamental phenomenon in both natural and industrial processes. Due to the complex coupling among the elastic deformation, surface adhesion and viscoelastic damping, a great gap still exists for directly obtaining a universal correlation for the restitution coefficient. In this work, we use the finite element method (FEM) to numerically investigate the wall collision of small adhesive particles. The surface adhesion is directly incorporated by the Hamaker theory and the viscoelastic dissipation is coupled to the local strain, stress and strain rate. The results show that the FEM model naturally captures the coupling between the surface adhesion and viscoelastic damping, and thus is capable to predict the proper restitution coefficient by directly using the surface energy of bulk materials, without any adjustment or fitting. By simulating a large number of wall collision cases in a wide range of impact parameters, we present new universal correlations for the restitution coefficient and critical sticking velocity, which agree well with the classic experimental data in a wide range of the incident velocity, particle size and particle/substrate material properties. Our explicit correlations can be easily incorporated into Eulerian-Lagrangian simulations for quantitatively describing the sticking/rebound behaviors of laden aerosol particles.