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Gravitational effects on coffee-ring formation during the evaporation of sessile droplets

Moore, Madeleine; Wray, Alexander

Authors

Madeleine Moore

Alexander Wray



Abstract

We consider the role of gravity in solute transport when a thin droplet evaporates. Under the physically relevant assumptions that the contact line is pinned and the solutal Péclet number, Pe , is large, we identify two asymptotic regimes that depend on the size of the Bond number, Bo . When Bo=O(1) as Pe→∞ , the asymptotic structure of solute transport follows directly from the surface-tension-dominated regime, whereby advection drives solute towards the contact line, only to be countered by local diffusive effects, leading to the formation of the famous ‘coffee ring.’ In the distinguished limit in which Bo=O(Pe4/3) as Pe→∞ , this interplay between advection and diffusion takes place alongside that between surface tension and gravity. In each regime, we perform a systematic asymptotic analysis of the solute transport and compare our predictions to numerical simulations. We identify the effect of gravity on the nascent coffee ring, providing quantitative predictions of the size, location and shape of the solute mass profile. In particular, for a fixed Péclet number, as the effect of gravity increases, the coffee ring is diminished in height and situated further from the contact line. Furthermore, for certain values of Bo , Pe and the evaporation time, a secondary peak may exist inside the classical coffee ring. The onset of this secondary peak is linked to the change in type of the critical point in the solute mass profile at the droplet centre. Both the onset and the peak characteristics are shown to be independent of Pe .

Citation

Moore, M., & Wray, A. (2023). Gravitational effects on coffee-ring formation during the evaporation of sessile droplets. Journal of Fluid Mechanics, 967, Article A26. https://doi.org/10.1017/jfm.2023.493

Journal Article Type Article
Acceptance Date Jun 9, 2023
Online Publication Date Jul 19, 2023
Publication Date Jul 25, 2023
Deposit Date Jul 20, 2023
Publicly Available Date Jul 21, 2023
Journal Journal of Fluid Mechanics
Print ISSN 0022-1120
Electronic ISSN 1469-7645
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Volume 967
Article Number A26
DOI https://doi.org/10.1017/jfm.2023.493
Keywords Mechanical Engineering; Mechanics of Materials; Condensed Matter Physics; Applied Mathematics
Public URL https://hull-repository.worktribe.com/output/4336932

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