Analytical dispersion force calculations for nontraditional geometries

Presented in this paper are first-principle-based approximate macroscopic models of the van der Waals adhesion force for a variety of particle shapes interacting with an infinite cylinder. In particular, expressions for the van der Waals adhesion force and interaction energy are developed for a (1) spherical particle/infinite cylinder, (2) disk-like particle/infinite cylinder, (3) disk-like particle oriented edgewise to an infinite cylinder, and (4) a deformed slice/infinite cylinder. The models presented depict expected trends in the behavior of both the force of adhesion and the interaction energy between different geometric configurations. These results are also used to demonstrate the impact of contact time on the adhesion force for cylindrical fibers in contact with a disk-shaped particle. After long time intervals where the disk-like particles have remained in contact with the cylinder, the adhesion force may lead to significant deformation of the attached particle. Hence, the adhesion force for a fourth geometric set which represents the most likely scenario for attached particles with long contact times is developed. As will be shown, this scenario results in the highest values of adhesion force and interaction energy.