Dynamic modeling of nano/microparticles displacement in multi-point contact based on the Rumpf model

In this paper, dynamic behavior of a nano particle on a rough surface in pushing based on the atomic force microscopy (AFM) was modeled and simulated by using the multipoint contact model. First, a multipoint contact model was extracted for two different roughness profiles of rough surfaces including the hexagonal and tetrahedral by combination of the Rumpf singular point contact model with JKR and Schwarz contact models, and the equations of the real contact area and adhesion force were proposed for multipoint contact of rough surfaces. Then, the dynamic behavior of particles in pushing on the rough substrate was modeled by using the new multipoint contact model. Additionally, simulation of the particles dynamics with radii of 50, 400 and 500 nm in moving on the different rough substrates was performed and analyzed, by assuming multipoint, singular point contacts, and flat surface contacts. Results showed that the multipoint contact model, especially in small radiuses of roughness has an essential impact on determining of the critical force. Moreover, assumptions of the flatness or the singular point contact leads to a considerable error to estimate the critical force. Results showed profiles of rough surface and roughness distribution are very important factors in determination the numbers of the contact points, and change the estimated amount of the critical force. In general, the obtained critical force based on the new multipoint contact model in comparison with the ones based on the flat surface and the singular point contact models, was decreased and increased, respectively.