A simple conceptual model for the behaviour of an impacting rigid-plastic, spherical, nano-scale particle

The theory of low-velocity impact between nano-sized, spherical particles requires consideration of surface energy, which causes approach speeds to increase on first contact, and recoil speeds to reduce, just before geometrical separation. A conceptual model is developed in which six major regimes are identified: the pancake and/or thin-film regime results from extreme particle accelerations and particle flattening from surface energy; the disintegration and/or torus regime results from high kinetic energy causing the particle to disintegrate or to pass through itself (torus); the approach regime results when the particle ceases its approach without extreme geometrical changes (and this leads into the recoil regime); the escape regime results when the particle escapes from the surface; the capture regime occurs when the particle is trapped by the surface, about which it continues oscillating; and the stick regime where the recoil step does not proceed, and the particle remains at the position at the end of the approach regime. The approach regime is described by one non-dimensional parameter, and the recoil regime by another non-dimensional parameter. An upper bound for the duration of the approach regime is obtained which is independent of surface energy and initial approach speed. The recoil regime results in particle escape (capture) when the elastic energy exceeds (is less than or equal to) the surface energy at the beginning of recoil. Stick occurs when the surface energy at the beginning of recoil equals or exceeds twice the corresponding elastic energy.