Equilibrium morphologies and effective spring constants of capillary bridges

TL;DR

This paper provides a theoretical analysis of liquid bridges between parallel plates, deriving equilibrium conditions, effective spring constants, and their dependence on contact angles, volume, and surface properties, with validation against simulations.

Contribution

It introduces a comprehensive theoretical framework for predicting equilibrium morphologies and spring constants of capillary bridges with complex surface properties.

Findings

Equilibrium exists when the sum of contact angles exceeds 180°.

Spring constant diverges at the 180° contact angle sum.

Spring constant decreases with increasing contact angle and volume.

Abstract

We theoretically study the behaviour of a liquid bridge formed between a pair of rigid and parallel plates. The plates are smooth, they may either be homogeneous or decorated by circular patches of more hydrophilic domains, and they are generally not identical. We calculate the mechanical equilibrium distance of the liquid bridge as a function of liquid volume, contact angle and radius of the chemical domain. We show that a liquid bridge can be an equilibrium configuration as long as the sum of the contact angles at the two walls is larger than $180^\circ$. When comparisons are possible, our results agree well with recent analytical and molecular dynamics simulation results. We also derive the effective spring constant of the liquid bridge as it is perturbed from its equilibrium distance. The spring constant diverges when the sum of the contact angles is $180^\circ$ and is finite otherwise. The value of the spring constant decreases with increasing contact angle and volume, and the rate, at which it decreases, depends strongly on the properties of the two plates.