Shapes of Non-symmetric Capillary Bridges

TL;DR

This paper investigates the shapes of non-symmetric capillary bridges between chemically distinct plates, providing a mathematical framework to characterize their shapes and the influence of physical parameters on their form.

Contribution

It introduces a quadrature formula for non-symmetric bridge shapes and analyzes waist points to understand shape variations under different physical conditions.

Findings

Waists are key points in bridge shapes, even in non-symmetric cases.

Shape formulas depend on the pressure difference sign.

Various bridge shapes are possible based on physical parameters.

Abstract

Here we study the shapes of droplets captured between chemically distinct parallel plates. This work is a preliminary step toward characterizing the influence of second-phase bridging between biomolecular surfaces on their solution contacts, i.e., capillary attraction or repulsion. We obtain a simple, variable-separated quadrature formula for the bridge shape. The technical complication of double-ended boundary conditions on the shapes of non-symmetric bridges is addressed by studying waists in the bridge shape, i.e., points where the bridge silhouette has zero derivative. Waists are always expected with symmetric bridges, but waist-points can serve to characterize shape segments in general cases. We study how waist possibilities depend on the physical input to these problems, noting that these formulae change with the sign of the inside-outside pressure difference of the bridge. These results permit a variety of different interesting shapes, and the development below is accompanied by several examples.