Three-Dimensional Modeling of Microsphere Contact/Impact with Smooth, Flat Surfaces

Abstract

A three-dimensional (3D) simulation model of a microsphere in contact with a nominally-smooth, flat surface is established. The model is based on Hertzian contact stresses, an idealized ring force distribution of adhesion, nonlinear damping, and friction. Although originally developed for the study of oblique impact, the model also is shown to describe the motion of a microsphere in sustained contact with a flat surface, including nonlinear normal oscillatory motion in the presence of sliding and rolling. Nonlinear, normal oscillatory motion is illustrated using conventional phaseplane techniques. Methods for the determination of damping coefficients associated with normal motion from impact experiments are discussed. The significance and modeling of rolling resistance and implications of asymmetric contact stress distributions are presented. Simulations show that energy exchange between translation and rotation can play an important role during oblique impact. The effects of complex initial conditions on the rebound and capture of a microsphere are significant as are the effects of contact friction. Results show that the inability to measure and the failure to account for rotational velocities in experimental measurements can limit the intepretation of the results.