Contact-line deposits from multiple evaporating droplets

Alexander W. Wray, Patrick S. Wray, Brian R. Duffy, Stephen K. Wilson

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)
21 Downloads (Pure)


Building on the recent theoretical work of Wray et al. l [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 [Colloids. 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.
Original languageEnglish
Article number073604
Number of pages21
JournalPhysical Review Fluids
Issue number7
Publication statusPublished - 22 Jul 2021


  • droplets
  • evaporation
  • particles
  • contact-line deposits
  • coffee stains
  • ring stains
  • shielding effect


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