# The collective behaviour of ensembles of condensing liquid drops on heterogeneous inclined substrates

## TL;DR

This study models the collective dynamics of condensing liquid drops on heterogeneous inclined surfaces, revealing how individual drop behaviour influences the formation of stable, balanced ensembles through bifurcation analysis and simulations.

## Contribution

It introduces a combined approach of bifurcation analysis and time simulations to understand ensemble behaviour of condensing drops on chemically heterogeneous substrates.

## Key findings

- Drops grow on hydrophilic spots and depin to slide along the surface.
- Ensembles reach a stationary state balancing condensation and outflow.
- Drop size distribution relates to single-drop bifurcation diagrams.

## Abstract

Employing a long-wave mesoscopic hydrodynamic model for the film height evolution we study ensembles of pinned and sliding drops of a volatile liquid that continuously condense onto a chemically heterogeneous inclined substrate. Our analysis combines, on the one hand, path continuation techniques to determine bifurcation diagrams for the depinning of single drops of nonvolatile liquid on single hydrophilic spots on a partially wettable substrate and, on the other hand, time simulations of growth and depinning of individual condensing drops as well as of the long-time behaviour of large ensembles of such drops. Pinned drops grow on the hydrophilic spots, depin and slide along the substrate while merging with other pinned drops and smaller drops that slide more slowly, and possibly undergo a pearling instability. As a result, the collective behaviour converges to a stationary state where condensation and outflow balance. The main features of the emerging drop size distribution can then be related to single-drop bifurcation diagrams.