Self-Similar Liquid Lens Coalescence

TL;DR

This paper investigates the dynamics of liquid lens coalescence on wet substrates, revealing self-similar growth patterns and deriving similarity solutions that match experiments across viscous and inertial regimes.

Contribution

It provides the first combined experimental and theoretical analysis of drop coalescence on pre-wetted surfaces, introducing similarity solutions for both viscous and inertial limits.

Findings

Excellent agreement between theory and experiments without adjustable parameters

Unified description of coalescence dynamics across viscosity regimes

Collapse of data onto a single curve for different viscosities

Abstract

A basic feature of liquid drops is that they can merge upon contact to form a larger drop. In spite of its importance to various applications, drop coalescence on pre-wetted substrates has received little attention. Here, we experimentally and theoretically reveal the dynamics of drop coalescence on a thick layer of a low-viscosity liquid. It is shown that these so-called "liquid lenses" merge by the self-similar vertical growth of a bridge connecting the two lenses. Using a slender analysis, we derive similarity solutions corresponding to the viscous and inertial limits. Excellent agreement is found with the experiments without any adjustable parameters, capturing both the spatial and temporal structure of the flow during coalescence. Finally, we consider the crossover between the two regimes and show that all data of different lens viscosities collapse on a single curve capturing the full range of the coalescence dynamics.