On analytical integration of interaction potentials between cylindrical and rectangular bodies with a focus on van der Waals attraction

TL;DR

This paper derives exact and approximate analytical formulas for interaction potentials between cylindrical and rectangular bodies, focusing on van der Waals forces, to improve computational efficiency in modeling such interactions.

Contribution

It introduces new exact interaction laws for various geometries and exponents, including van der Waals forces, enhancing analytical tools for physical modeling.

Findings

Exact interaction laws for disk-plate and rectangle-rectangle geometries.

Approximate laws for disk-disk, point-cylinder, and disk-cylinder interactions.

Numerical example demonstrating application to elastic fiber interactions.

Abstract

The paper deals with the analytical integration of interaction potentials between specific geometries such as disks, cylinders, rectangles, and rectangular prisms. Interaction potentials are modeled as inverse-power laws with respect to the point-pair distance, and the complete body-body potential is obtained by pairwise summation (integration). Several exact new interaction laws are obtained, such as disk-plate and (in-plane) rectangle-rectangle for an arbitrary exponent, and disk-disk and rectangle-rectangle for van der Waals attraction. To balance efficiency and accuracy, additional approximate laws are proposed for disk-disk, point-cylinder, and disk-cylinder interactions. A brief numerical example illustrates the application of the pre-integrated Lennard-Jones disk-disk interaction potential for the interaction between elastic fibers.