Control of droplet evaporation on smooth chemical patterns

TL;DR

This paper analyzes how chemical pattern variations on a surface influence droplet evaporation, revealing complex bifurcation behaviors and stability changes that affect droplet movement and equilibrium states.

Contribution

It provides a detailed bifurcation analysis of droplet equilibrium on chemically patterned surfaces, highlighting the impact of pattern symmetry and gradients on stability and dynamics.

Findings

Symmetric and periodic patterns induce bifurcations affecting droplet stability.

Chemical patterns with amplitude gradients create disconnected stable states.

Droplet position can change continuously during evaporation on gradient patterns.

Abstract

We investigate the evaporation of a two-dimensional droplet on a solid surface. The solid is flat but with smooth chemical variations that lead to a space-dependent local contact angle. We perform a detailed bifurcation analysis of the equilibrium properties of the droplet as its size is changed, observing the emergence of a hierarchy of bifurcations that strongly depends on the particular underlying chemical pattern. Symmetric and periodic patterns lead to a sequence of pitchfork and saddle-node bifurcations that make stable solutions to become saddle nodes. Under dynamic conditions, this change instability suggests that any perturbation in the system can make the droplet to shift laterally while relaxing to the nearest stable point, as is confirmed by numerical computations of the Cahn-Hilliard and Navier-Stokes system of equations. We also consider patterns with an amplitude gradient that creates a set of disconnected stable branches in the solution space, leading to a continuous change of the droplet's location upon evaporation.