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Marangoni-driven film climbing on a draining pre-wetted film

Published online by Cambridge University Press:  15 January 2020

Nan Xue Open the ORCID record for Nan Xue [Opens in a new window] ,
Min Y. Pack Open the ORCID record for Min Y. Pack [Opens in a new window]  and
Howard A. Stone Open the ORCID record for Howard A. Stone [Opens in a new window]
Nan Xue
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA
Min Y. Pack
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA Department of Mechanical Engineering, Baylor University, Waco, TX76798, USA
Howard A. Stone*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA
*
†Email address for correspondence: hastone@princeton.edu
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Abstract

Marangoni flow is the motion induced by a surface tension gradient along a fluid–fluid interface. In this study, we report a Marangoni flow generated when a bath of surfactant contacts a pre-wetted film of deionized water on a vertical substrate. The thickness profile of the pre-wetted film is set by gravitational drainage and so varies with the drainage time. The surface tension is lower in the bath due to the surfactant, and thus a liquid film climbs upwards along the vertical substrate due to the surface tension difference. Particle tracking velocimetry is performed to measure the dynamics in the film, where the mean fluid velocity reverses direction as the draining film encounters the front of the climbing film. The effect of the surfactant concentration and the pre-wetted film thickness on the film climbing is then studied. High-speed interferometry is used to measure the front position of the climbing film and the film thickness profile. As a result, higher surfactant concentration induces a faster and thicker climbing film. Also, for high surfactant concentrations, where Marangoni driving dominates, increasing the film thickness increases the rise speed of the climbing front, since viscous resistance is less important. In contrast, for low surfactant concentrations, where Marangoni driving balances gravitational drainage, increasing the film thickness decreases the rise speed of the climbing front while enhancing gravitational drainage. We rationalize these observations by utilizing a dimensionless parameter that compares the magnitudes of the Marangoni stress and gravitational drainage. A model is established to analyse the climbing front, either in the Marangoni-driving-dominated region or in the Marangoni-balanced drainage region. Our work highlights the effects of the gravitational drainage on the Marangoni flow, both by setting the thickness of a pre-wetted film and by resisting the film climbing.

JFM classification

Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 886 , 10 March 2020 , A24
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Xue et al. supplementary movie 1

Film climbing as inserting a dyed pre-wetted film on a glass substrate into a bath of dyed 1 mM SDS solution. Real time.

Download Xue et al. supplementary movie 1(Video)
Video 732.4 KB

Xue et al. supplementary movie 2

Particle tracking velocimetry for the 1 mM SDS solution in the bath. Real time (from 10 s to 14 s).

Download Xue et al. supplementary movie 2(Video)
Video 6.9 MB

Xue et al. supplementary movie 3

Interferometric movie for the measurement of film front position, for 3 mM SDS solution in the bath. ×0.1 real time.

Download Xue et al. supplementary movie 3(Video)
Video 676.2 KB

Xue et al. supplementary movie 4

Interferometric movie for the measurement of film front position, for 0.3 mM SDS solution in the bath. ×2 real time.

Download Xue et al. supplementary movie 4(Video)
Video 1.4 MB

Xue et al. supplementary movie 5

Interferometric movie for the measurement of film thickness profile, for 10 mM SDS solution in the bath. ×5 real time.

Download Xue et al. supplementary movie 5(Video)
Video 4 MB

Xue et al. supplementary movie 6

Interferometric movie for the measurement of film thickness profile, for 3 mM SDS solution in the bath. ×5 real time.

Download Xue et al. supplementary movie 6(Video)
Video 4 MB

Xue et al. supplementary movie 7

Interferometric movie for the measurement of film thickness profile, for 1 mM SDS solution in the bath. ×5 real time.

Download Xue et al. supplementary movie 7(Video)
Video 4 MB

Xue et al. supplementary movie 8

Interferometric movie for the measurement of film thickness profile, for 0.3 mM SDS solution in the bath. ×5 real time.

Download Xue et al. supplementary movie 8(Video)
Video 4.1 MB

Xue et al. supplementary movie 9

Interferometric movie for the measurement of film front position with a large field of view, for 3 mM SDS solution in the bath. ×0.1 real time.

Download Xue et al. supplementary movie 9(Video)
Video 680.9 KB