Substrate Curvature Curbs the Coffee Ring Effect

TL;DR

This paper demonstrates that substrate curvature influences the evaporation flow in particle-laden droplets, with increased curvature promoting more uniform coatings by enhancing central evaporation and reducing ring formation.

Contribution

It introduces a geometric approach showing how substrate curvature suppresses the coffee ring effect, supported by a model of evaporation flow and local evaporation rate modifications.

Findings

Higher substrate curvature leads to more uniform particle deposits.

Curvature enhances central evaporation, reducing ring formation.

The proposed model explains the influence of curvature on evaporation dynamics.

Abstract

"When the liquid phase of a particle-laden droplet evaporates, a ring of solute is typically formed - what has become known as the "coffee ring effect". A key focus of recent work has been the suppression of the coffee-ring effect to leave behind more spatially-uniform particle coatings instead. Efforts to suppress the coffee ring effect often focus on physical effects such as Marangoni flows. Here we focus on a purely geometric effect - the effect of substrate curvature - by evaporating suspension droplets on spherical surfaces of different radius of curvature. We find that stains formed on more highly curved substrates are more uniform. To understand this, we propose a model of the evaporation-induced flow, combined with a detailed calculation of how curvature modifies the local evaporation rate. This model shows that evaporation in the centre of the droplet is enhanced, leading to increased concentration of solute there and a reduction in the propensity for ring-formation.