Mechanics of nanoparticle adhesion — A continuum approach

38J. TomasFigure 9. Recalculated plastic contact deformation and sticking/bounce at central impact stressingusing data from Fig. 6. Two particles approach with velocities v 1 and v 2 , impact and the contact iselastic–plastically deformed (top panel). The inelastic deformation energy is dissipated into the contact.This is equivalent to the areas (gray tones) between the elastic–plastic boundary and adhesionboundary of the force–displacement lines which are obtained by integration (Eq. (91)). If the kineticenergy of these particles would be large enough, these particles can detach with rebound velocitiesv 1R and v 2R . The critical impact velocity for incipient yield of the contact is shown (Eq. (88)). Abovethis value, the two particles adhere or stick in practice, i.e., v 1R = 0. From this, the critical impact velocityv 1,H follows and is shown in the bottom panel versus particle center approach or displacementh K,U . The model of Hiller/Löffler predicts a constant velocity (Eq. (90)). However, practical experienceshows us that the faster the particles move and impact, the larger the contact displacement, andconsequently, the higher the tendency to stick. This is demonstrated by the curve of Eq. (93) in thebottom panel versus displacement h K,U .