Technical note Direct visualization and model validation of microsphere impact and surface capture

Digital high-speed photographic images of microsphere impact with a flat surface were made over a range of incident microsphere velocities. The incident and rebound velocities determined from successive images were used to validate a recently published model for low-speed impact. This model is shown to predict the experimental values of the normal coefficient of restitution and the surface-capture velocity to within 95% confidence. 2007 Elsevier Ltd. All rights reserved. In the experiments, 40-m diameter Ag-coated glass microspheres were dispersed from different heights above a flat silica surface 'target' under standard atmospheric conditions. A digital high-speed camera (Fastcam ultraAPX IMAGER, Fotron, ThorLABSinc) was used to record the microsphere incidence, rebound and surface capture at a frame rate of 6000 frames/s. Sequences of the obtained image were processed to obtain the exact microsphere coordinates in time, and, hence, the incident and rebound (if any) velocities of the microsphere normal to the target. An example case of experimental results and their comparison with the recently published impact model of Kim and Dunn (2007) are shown in Fig. 1. In this figure, the normal coefficient of restitution, en, defined as the ratio of rebound-to-incident normal velocities, is plotted versus the incident normal velocity. It is seen that en monotonically decreases to zero as the incident normal velocity of the microsphere decreases to the surface capture velocity, vc .F or this case, the capture velocity was 0.08 m/s. The maximum incident velocity was 0.44 m/s. These velocities are well below the yield velocity for the materials. The EA model, presented by Kim and Dunn (2007), considers an elastic impact with adhesion. The microspheres kinetic energy is related to the static elastic and adhesion forces and their dynamic dissipative forces. Because the range of velocities considered are well below the yield velocity of the materials, the dissipation forces due to plastic deformation can be neglected. The model expression for the normal coefficient of restitution is