Spherical volume elements scheme for calculating van der Waals force between irregular particles and rough surfaces

Various models were proposed to calculate the van der Waals (vdW) forces, but they have generally been complicated and time-consuming. In this paper, a spherical volume elements scheme to calculating the vdW force distributions is proposed, on the basis of the infinitesimal dividing modeling scheme. We apply this scheme to calculate the vdW force distributions between sphere and three types of surfaces with different roughness and also to irregular particles (cylinders, circular cone) orientated differently with respect to the surface. The simulation results reveal that the surface with low roughness has the narrowest force distributions. The average force for the circular cone bottom case is 1, 2, 37 times higher than the case of horizontal, vertical cylinder and circular cone top, respectively. The calculated force distributions are good agreement with exist experimental data. By defining the effective zones of both particles and surface, the computational time of the scheme is an order of magnitude faster than the case of considering the whole surface. The proposed model established the effective zone of the particles in contact from a completely new perspective and significantly simplifies the process of force evaluation.