A finite element method (FEM) study on adhesive particle-wall normal collision

The adhesive collision between a micro-sized particle and wall is important for many natural phenomena and industrial processes. The critical adhesion velocity and restitution coefficient are mainly related to the loss of kinetic energy during the impact. Although several classical models have established the theoretical framework, the practical difficulty is the determination of coefficients. For example, the damping coefficient is often left as the fitting parameter. Sometimes, in order to obtain a good agreement with experimental results, complicated empirical correlations have to be introduced. One reason is that the damping coefficient is defined at the whole particle (usually corresponding to the overlap), not at the local region where damping actually occurs. In this work, we study the particle-wall collision process by finite element method which is able to resolve local stress and strain rate. The surface adhesion is incorporated in the simulation by manually adding and updating the force at the contact area. The results of FEM simulation agree well with reported experimental data for a wide range of particle/wall properties, particle size and impact velocity. The damping coefficient is then linearly correlated with the restitution coefficient for different properties, size and impact velocity, after being nondimensionalized by Hertz collision time and adhesion number. The simple relation has the potential to be extended to more complicated scenarios e.g. non-spherical particle collisions.