Droplets sliding on single and multiple vertical fibers

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Droplets sliding on single and multiple vertical fibers

M. Leonard, J. Van Hulle, F. Weyer, D. Terwagne, and N. Vandewalle

Phys. Rev. Fluids 8, 103601 – Published 19 October 2023

Abstract

From microfluidics to fog-harvesting applications, tiny droplets are transported along various solid substrates including hairs, threads, grooves, and other light structures. Driven by gravity, a droplet sliding along a vertical fiber is a complex problem since it is losing volume and speed as it goes down. With the help of an original setup, we solve this problem by tracking in real-time droplet characteristics and dynamics. Single fibers as well as multiple fiber systems are studied to consider the presence of grooves. On both fibers and grooved threads, droplet speed and volume are seen to decay rapidly because the liquid entity is leaving a thin film behind. This film exerts a capillary force able to stop the droplet motion before it is completely drained. A model is proposed to capture the droplet dynamics. We evidence also that multiple vertical fibers are enhancing the droplet speed while simultaneously promoting increased liquid loss on grooves.

Received 4 May 2023
Accepted 28 August 2023

DOI:https://doi.org/10.1103/PhysRevFluids.8.103601

Physics Subject Headings (PhySH)

Drops & bubbles Liquid-solid interfaces Microfluidics

Fluid Dynamics

Authors & Affiliations

M. Leonard ¹, J. Van Hulle¹, F. Weyer ¹, D. Terwagne ², and N. Vandewalle¹

¹GRASP, Physics Department, University de Liège, Belgium
²Frugal LAB, Physics Department, Université Libre de Bruxelles, Belgium

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Issue

Vol. 8, Iss. 10 — October 2023

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Images

Figure 1
(a) Experimental pictures of droplets of 3 $μ l$ sliding down one, two, and three fibers of $d = 140 μ m$ from left to right. A liquid film is seen behind the droplet. Droplet shape characteristics: the height $L$ and the width $ℓ$ are emphasized in red. (b) Sketch of three horizontal cuts of the system: dry fibers in front of the droplet (orange), the droplet cross section (light blue), and the liquid film of thickness $δ$ after the passage of the droplet (dark blue).
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Figure 2
(a) Sketch of the experimental setup where a camera records the droplet placed on a moving thread. Back illumination allows contrasted images. (b) Typical measurements of a droplet sliding on a single vertical fiber ( $d = 140 μ m$ ): both the volume $Ω$ and the speed $v$ are decreasing rapidly over time.
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Figure 3
(a) Height of the droplet $L$ as a function of the width $ℓ$ of the droplet. All data points are colored as a function of the viscosity $η$ and the fiber number $n$ . See the color legend given as an inset. (b) Lengths are rescaled by the effective diameter $d_{e}$ . The region colored in red corresponds to the $Ω_{c} < 1$ criterion, such that a droplet there is no longer in a barrel configuration.
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Figure 4
(a) Volume loss rate $\dot{Ω}$ as a function of the droplet speed $v$ . Lines are linear fits used to extract the slopes for determining $\bar{δ}$ from Eq. (2). (b) Average liquid film thickness $\bar{δ}$ as a function of $n$ . Lines are fitted on the data to emphasize $η$ and $n$ dependencies, but should be considered as guides for the eye. (c) Average film thickness normalized by $η^{2 / 3}$ , emphasizing that the effect of viscosity is captured by the Landau-Levich model only for $n = 1$ .
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Figure 5
(a) Droplet speed as a function of $Ω$ emphasizing the gravity-driven mechanism. Each color is associated witht the viscosity $η$ and the fiber number $n$ . Error bars are given. Data are fitted by a linear model of Eq. (7). (b) Rescaled speed $v$ and volume $Ω$ according to Eq. (7). (c) From the slopes extracted in panel (a), the inverse dissipation factor $1 / ξ$ is estimated. It is plotted as a function of $n$ with the same color code. One observes that the presence of grooves favors the droplet motion; i.e., $1 / ξ$ increases with $n$ .
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Figure 6
(a) Sketch of the additional experiment where a single fiber of diameter $d$ is compared with $n = 2$ fibers of diameter $d / 2$ . The equivalent diameter $d_{e}$ is therefore conserved but grooves are present in the second case. (b) Droplet speed as a function of droplet volume for two situations illustrated in panel (a). Extra speed is clearly obtained for $n = 2$ .
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