Super lattice formation of an array of volatile wetting droplets

TL;DR

This paper investigates how ordered arrays of volatile wetting droplets form super lattices through Ostwald ripening, using diffusion models and analyzing growth patterns on square and triangular lattices.

Contribution

It introduces a general diffusion-based model for super lattice formation in volatile wetting droplets and explicitly analyzes square and triangular lattice configurations.

Findings

Dispersion relations for super-lattice growth are derived.

Super lattice formation depends on lattice geometry and diffusion dynamics.

The model provides insights into droplet array stability and pattern evolution.

Abstract

For an ordered array of critical volatile wetting droplets the formation of a super lattice by an Ostwald-ripening like competition process is considered. The underlying diffusion problem is treated within a quasistatic approximation and to first order in the inverse droplets distance. The approach is rather general but a square lattice and a triangular lattice are studied explicitly. Dispersion relations for the super-lattice growth of these arrays are calculated.