# Bridging of liquid drops at chemically structured walls

## TL;DR

This study investigates how liquid drops bridge at chemically patterned walls with wet stripes, revealing the role of long-range forces and finite-size effects in phase transitions and droplet configurations.

## Contribution

It introduces a mesoscopic and microscopic theoretical analysis of bridging transitions at chemically structured surfaces, highlighting the scaling of free-energy contributions and phase diagram features.

## Key findings

- Bridging transitions driven by long-range forces scale with ln L.
- Surface phase diagram contains two triple points with coexisting droplet states.
- Symmetry considerations determine droplet configurations depending on stripe separation.

## Abstract

Using mesoscopic interfacial models and microscopic density functional theory we study fluid adsorption at a dry wall decorated with three completely wet stripes of width $L$ separated by distances $D_1$ and $D_2$. The stripes interact with the fluid with long-range forces inducing a large finite-size contribution to the surface free-energy. We show that this non-extensive free-energy contribution scales with $\ln L$ and drives different types of bridging transition corresponding to the merging of liquid drops adsorbed at neighbouring wetting stripes when the separation between them is molecularly small. We determine the surface phase diagram and show that this exhibits two triple points, where isolated drops, double drops and triple drops coexist. For the symmetric case, $D_1=D_2\equiv D$, our results also confirm that the equilbrium droplet configuration always has the symmetry of the substrate corresponding to either three isolated drops when $D$ is large or a single triple drop when $D$ is small; however, symmetry broken configurations do occur in a metastable part of the phase diagram which lies very close to the equilibrium bridging phase boundary. Implications for phase transitions on other types of patterned surface are considered.