Particle Bounce or Capture—Search for an Adequate Theory: I. Conservation-of-Energy Model for a Simple Collision Process

Abstract

Particle-surface collisions have been the object of a number of studies. In two of these studies, Dahneke (1971) and Wall et al (1990) derived simple models for predicting collision dynamics and particle bounce or capture. Neither model has yet provided full rationalization of measured bounce-or-capture data. In fact, the two models sometimes predict different results. Some confusion is evident, as is the need for a simple, reliable theory founded on basic physical laws to provide improved understanding of simple collisions and guide modeling of more complex ones. We rederive the Dahneke and Wall et al models considering the collision process in greater detail. We consider the simplest particle-surface-collision processes, namely, the idealized collision of a homogeneous, solid, non-rotating particle (a perfect sphere or right circular cylinder striking a surface end-on with its symmetry axis oriented normal to the surface) moving at normal incidence towards a flat, smooth surface of a solid body in vacuum. We find the models apply for complementary ranges of adhesion-energy increase during impact, ΔE = E_r — E_i where E_i and E_r are the interaction potential energies for the incident- and rebound-state particle-surface system. The Wall model applies for ΔE>0 and the Dahneke model for ΔE<0. On the basis that ΔE<0 is expected in particle-surface collisions, the Dahneke model is the physically reasonable one for the simplest collisions considered here, but in most cases the information provided by the two is essentially equivalent. A model is compared to measured collision-dynamics data for 1.27-μm-diameter polystyrene spheres in vacuum bouncing from thick, fused-silica and from thin (140 nm thick), gold-foil targets, under conditions approaching those of the simplest collision process. The basis for a new, dynamic model is described and discussed.