A Mathematical Model of the Impact and Adhesion of Microsphers

A model is presented for the low velocity planar impact of a micrometer-sized sphere (microsphere) having an arbitrary angle of approach to a surface in the presence of arbitrary contact and external forces. This model, based upon classical impact dynamics and Hertzian theories, analytically relates the velocity change of the microsphere to the physical parameters of the microsphere and the surface and to the microsphere-surface adhesion forces. The model is based upon two fundamental assumptions, namely, that the energy losses due to the process of material deformation and the process of adhesion are independent, and that the energy loss due to the adhesion process occurs only during the rebound phase of the impact. No assumptions are made about the nature of inelastic deformations in the formulation of the model, permitting it to apply equally well to viscoelastic, elastic-plastic, or other materials or combinations thereof. The utility and accuracy of the model is assessed by comparing its predictions to experimental results. The model and the experimental data are used further to explore the relationship between the work done by the adhesion fracture force during rebound and the theoretical energy associated with the van der Waals adhesion force. The ability of the model to predict critical velocities is illustrated and discussed also.