Dynamics of Connected Evaporating Droplets and Confined Dip Coating

Abstract

The dynamics of liquid–gas interfaces in contact with solid surfaces are central to a wide range of technological applications, from microfluidic devices to coating processes. Predicting interfacial behaviour in these systems is particularly challenging, as multiple physical mechanisms, including evaporation-driven flow, capillary transport, geometric confinement, and substrate motion, interact across different length and time scales. The interplay of these effects can give rise to complex phenomena, such as flow reversal, symmetry breaking, and dynamic instabilities. This thesis explores interfacial dynamics through two representative experimental systems. The first system focuses on the dynamics of two droplets connected by a microchannel and undergoing evaporation at a constant contact radius. Evaporation gradually changes their shape and disrupts the internal pressure balance, driving rapid capillary flow through the channel. This flow redistributes liquid between the droplets, counteracting the pressure differences and restoring equilibrium. Through this continuous feedback between evaporation and capillary transport, the droplets remain in quasi-steady state. Our experiments show that the channel flow between the droplets is strongly influenced by their geometry. When the droplets have equal contact radii but different volumes, the flow remains unidirectional throughout the evaporation process. However, if the contact radii differ, evaporation can induce droplet shape switching, which then leads to flow reversal. A linear stability analysis reveals that the quasi-steady states of the droplets are underpinned by a pitchfork bifurcation. As evaporation reduces droplet volume, the system progresses through a series of these quasi-steady states until the volume vanishes. When the droplets have equal contact radii, the bifurcation is supercritical. Breaking the symmetry of the contact radii unfolds this bifurcation, allowing droplet shape switching and the associated flow reversal to be interpreted as a dynamic jump from the disconnected branch to the connected branch. Consequently, this work establishes symmetry breaking as a fundamental mechanism for inducing evaporation-driven flow reversal in connected droplet systems. The second system investigates instabilities of the contact line and liquid meniscus in a confined dip-coating process. In this configuration, substrate motion and geometric confinement create a competition among viscous, capillary, and gravitational forces. When a solid wall is withdrawn from a liquid that partially wets it, the contact line undergoes a wetting transition at a critical capillary number. Below this threshold, only a static meniscus forms, whereas above it, a continuous liquid film is entrained onto the wall. Experiments measuring the time evolution of the contact lines and meniscus profile show that this critical transition is collectively determined by the gap spacing, which modifies the local force balance, and the liquid wettability, which controls the contact line’s ability to recede. Through further experiments on confined dip coating with a continuously moving solid wall, we show that after film deposition begins, further increases in the capillary number can trigger a second instability. When capillary number exceeds a second critical value, the liquid meniscus itself becomes unstable, developing three-dimensional waves. The influence of both the capillary number and the gap spacing on this meniscus instability is quantified by measuring the wavelength and growth rate of the emerging waves. Overall, this work establishes comprehensive experimental methodologies for characterizing microscale interfacial phenomena. By integrating theoretical modeling with experiments, the research provides a fundamental understanding of multiscale interfacial dynamics, where molecular-scale interactions govern macroscopic phenomena and short-time-scale processes influence long-time-scale behaviour. The findings offer critical insights with direct applications in microfluidics, precision coating processes, and droplet-based technologies.

Date of Award	5 Jan 2026
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Anne Juel (Main Supervisor), Andrew Hazel (Co Supervisor) & Finn Box (Co Supervisor)