The effect of the spatial variation of the evaporative flux on the deposition from a thin sessile droplet

A mathematical model for the effect of the spatial variation of the local evaporative flux on the evaporation of and deposition from a thin pinned particle-laden sessile droplet is formulated and solved. We then analyse the behaviour for a one-parameter family of local evaporative fluxes with the fr...

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Bibliographic Details
Published in:Journal of fluid mechanics 2023-08, Vol.970, Article A1
Main Authors: D'Ambrosio, Hannah-May, Wilson, Stephen K., Wray, Alexander W., Duffy, Brian R.
Format: Article
Language:English
Subjects:
Coffee
Deposition
Diffusion
Diffusion rate
Droplets
Evaporation
Fluctuations
Fluid mechanics
Free surfaces
Investigations
JFM Papers
Mathematical models
Parameters
Spatial variations
Substrates
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Summary:A mathematical model for the effect of the spatial variation of the local evaporative flux on the evaporation of and deposition from a thin pinned particle-laden sessile droplet is formulated and solved. We then analyse the behaviour for a one-parameter family of local evaporative fluxes with the free parameter $n \, (>-1)$ that exhibits qualitatively different behaviours mimicking those that can be obtained by, for example, surrounding the droplet with a bath of fluid or using a mask with one or more holes in it to achieve a desired pattern of evaporation enhancement and/or suppression. We show that when $-1< n1$ all of the particles are eventually advected to the centre of the droplet, and so the final deposit is at the centre of the droplet. In particular, the present work demonstrates that a singular (or even a non-zero) evaporative flux at the contact line is not an essential requirement for the formation of a ring deposit. In addition, we calculate the paths of the particles when diffusion is slower than both axial and radial advection, and show that in this regime all of the particles are captured by the descending free surface before eventually being deposited onto the substrate.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2023.503