A General Geometric Representation of Sphere-Sphere Interactions

Abstract

A general geometric representation of sphere-sphere interactions is derived using the bispherical coordinate system. It presents a dimensionless, scaled surface-to-surface separation parameter $s^{*}$, which is valid for all possible combinations of sphere size and separation distance. The proposed geometric description is not limited to sphere-sphere interactions, but also describes interactions that involve a point particle or a plane. The surface-to-surface separation parameter approaches the limit of $s^{*} = 1$ if the radii of both spheres are much smaller than the actual surface-to-surface separation distance s, i.e. in the limit of two point particles. On the other hand, the geometric limit of $s^{*} = 0$ corresponds to two planes, namely when the radii of both spheres are much larger than s.