The coefficient of restitution for the idealized impact of a spherical, nano-scale particle on a rigid plane

Abstract

The theory of low velocity impact between nano-sized, spherical particles and a rigid plane is developed by assuming fully plastic failure during approach and assuming the Johnson-Kandall-Roberts model of elasticity and adhesion applied during particle recoil. This model predicts initial particle acceleration on approach, followed by either deceleration and eventually instantaneous cessation of particle motion or extreme deformation and possible structural failure of the particle. If the approach motion ceases and the recoil begins, then either the particle is trapped on the surface or it separates. The typical frequency of oscillations of trapped particles is derived. Criteria for the occurrence of the various regimes are derived, together with conditions for when surface adhesion is important.

Characteristic Length and Time Scales Associated with the Impact of an Elasto-plastic Particle with a Large Hard Plane Surface

“…which follows from using (13), as well as (3.6) and (3.14) from Weir and McGavin [10]. For trapped particles, the coefficient of restitution in (1) is zero.…”

“…To understand this intrinsic approach speed, it is necessary to solve the dynamic problem of the approach of a nano-scale particle to a surface, with surface tension producing an attractive, and plastic deformation a repulsive force between the particle and the plane. In the limit of small initial approach velocity but a large surface tension, the maximum speed of approach is independent of the initial approach speed, and can be calculated as (as in Weir and McGavin [10] letting 6 7 in (2.10), differentiating with respect to time, and transforming back to dimensional quantities)…”

The effect of capillary force on airborne nanoparticle filtration

“…In this model, the yield stress is assumed to be constant for nanoscale materials. Based on this model, the critical velocity of the nanoparticles and pull-off force, respectively, are given as (Weir & McGavin, 2008) …”

Kontaktauflaung von Nanopartikeln bei Impaktion

“…Allerdings variiert die Ausprägung dieses Effekts mit dem Partikelmaterial und über den Verlauf bei sehr kleinen Partikeln bestehen weiterhin Unstimmigkeiten (inverse HallPetch-Beziehung [7]). Anders als bei Kollisionen von Partikeln im Mikrometerbereich beeinflussen bei Nanopartikeln Oberflächen-kräfte wie die Adhäsion die Dynamik des Stoßprozesses wesentlich [8].…”