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2025 | OriginalPaper | Chapter

3. Thin-Film Flows: Classical Examples, Marangoni Motions, and Viscous Membranes

Author : Howard A. Stone

Published in: Interfacial Flows—The Power and Beauty of Asymptotic Methods

Publisher: Springer Nature Switzerland

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Abstract

This chapter provides an in-depth exploration of thin-film flows, beginning with a historical overview of dimensional analysis and its applications to interfacial tension problems. It introduces classical examples, such as the bursting of soap films and the coalescence of drops, to illustrate the principles of dimensional reasoning. The text delves into the dynamics of thin-film flows, including the role of Marangoni motions and viscous membranes, and presents detailed analyses of specific phenomena, such as the drainage of films on vertical plates and the spreading of films due to surface tension variations. The chapter also discusses the governing equations for thin films with surfactants, highlighting the unique challenges and solutions associated with these complex systems. Through a combination of theoretical insights and practical examples, the chapter offers a comprehensive understanding of thin-film behaviors, making it an essential resource for advanced researchers and practitioners in the field.
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Footnotes
1
Recall that for steady, laminar flow in a circular tube of radius R and length \(\ell \), the pressure drop \(\Delta p\) versus flow rate Q relation is
$$\begin{aligned} Q=\frac{\pi }{8}\frac{R^4\Delta p}{\mu \ell }.\qquad (3.7) \end{aligned}$$
.
 
2
One common exception to this trend are strong electrolytes in water. For example, the surface tension of salt water increases with the concentration of salt as a consequence of the favorable interactions of the salt ions with the polar molecules of water.
 
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Metadata
Title
Thin-Film Flows: Classical Examples, Marangoni Motions, and Viscous Membranes
Author
Howard A. Stone
Copyright Year
2025
Book
Interfacial Flows—The Power and Beauty of Asymptotic Methods

Print ISBN: 978-3-031-78763-8

Electronic ISBN: 978-3-031-78764-5

Copyright Year: 2025

DOI
https://doi.org/10.1007/978-3-031-78764-5_3

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