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Coffee stain effect on a fibre from axisymmetric droplets

Published online by Cambridge University Press:  27 February 2023

Marie Corpart Open the ORCID record for Marie Corpart [Opens in a new window] ,
Frédéric Restagno Open the ORCID record for Frédéric Restagno [Opens in a new window]  and
François Boulogne Open the ORCID record for François Boulogne [Opens in a new window]
Marie Corpart
Affiliation:
CNRS, Laboratoire de Physique des Solides, Université Paris-Saclay, 91405 Orsay, France
Frédéric Restagno
Affiliation:
CNRS, Laboratoire de Physique des Solides, Université Paris-Saclay, 91405 Orsay, France
François Boulogne*
Affiliation:
CNRS, Laboratoire de Physique des Solides, Université Paris-Saclay, 91405 Orsay, France
*
†Email address for correspondence: francois.boulogne@cnrs.fr
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Abstract

The so-called coffee stain effect has been intensively studied over the past decades, but most of the studies have focused on sessile droplets. In this paper, we analyse the origin of the difference between the deposition of suspended particles in a sessile drop and in an axisymmetric drop deposited on a fibre. First, we model the shape of a drop on a fibre and its evaporative flux with some approximations to derive analytical calculations. Then, for pinned contact lines, we solve the hydrodynamics equations in the liquid phase under the lubrication approximation to determine the flow velocity toward the contact lines. We comment on these results by comparison to a sessile drop of similar evaporating conditions, and we show that the substrate curvature plays a role on the contact line depinning, the local evaporative flux and the liquid flow field. The competition between the advection and the Brownian motion indicates that the transport of the particles toward the contact line occurs in a volume localised in the close vicinity of the contact lines for a drop on a fibre. Thus, the fibre geometry induces a weaker accumulation of particles at the contact line compared to a sessile drop, leading to the more homogeneous deposit observed experimentally.

JFM classification

Interfacial Flows (free surface): Capillary flows Phase change: Condensation/evaporation Drops and Bubbles: Drops
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 957 , 25 February 2023 , A24
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

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Corpart et al. Supplementary Movie 1

Movie of the evolution of a drop on a fibre of radius a = 125µm observed in side view. The initial concentration is $c_i = 1. 10^8$ particles/mL and the movie is accelerated 40 times.

Download Corpart et al. Supplementary Movie 1(Video)
Video 5.9 MB

Corpart et al. Supplementary Movie 2

Movie of the evolution of a sessile drop, observed from below, of initial wetted length $R \approx 0.8$ mm. The initial concentration is $c_i = 1. 10^8$ particles/mL and the movie is accelerated 10 times.

Download Corpart et al. Supplementary Movie 2(Video)
Video 8.2 MB