Contact-line deposits from multiple evaporating droplets

TL;DR

This paper develops a theoretical model to predict the non-uniform contact-line deposits, or 'coffee stains', left by multiple evaporating droplets, accounting for vapor field interactions and validating predictions with experimental data.

Contribution

It extends previous work by modeling the deposit patterns from multiple interacting droplets, revealing how proximity affects deposit size and distribution.

Findings

Deposit reduction is greatest where droplets are closest.

Model predictions align well with experimental results.

Shielding effects vary with droplet arrangements.

Abstract

Building on the recent theoretical work of Wray, Duffy and Wilson [J. Fluid Mech. 884, A45 (2020)] concerning the competitive diffusion-limited evaporation of multiple thin sessile droplets in proximity to each other, we obtain theoretical predictions for the spatially non-uniform densities of the contact-line deposits (often referred to as "coffee stains" or "ring stains") left on the substrate after such droplets containing suspended solid particles have completely evaporated. Neighbouring droplets interact via their vapour fields, which results in a spatially non-uniform "shielding" effect. We give predictions for the deposits from a pair of identical droplets, which show that the deposit is reduced the most where the droplets are closest together, and demonstrate excellent quantitative agreement with experimental results of Pradhan and Panigrahi [Coll. Surf. A 482, 562-567 (2015)]. We also give corresponding predictions for a triplet of identical droplets arranged in an equilateral triangle, which show that the effect of shielding on the deposit is more subtle in this case.