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2025 | OriginalPaper | Chapter

6. Coating and Rimming Flow, Rivulet Flow, and the Evaporation of a Sessile Droplet

Author : Stephen K. Wilson

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

Publisher: Springer Nature Switzerland

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Abstract

This chapter presents a thorough examination of thin-film fluid dynamics and evaporation processes, with a particular focus on coating, rimming, and rivulet flows, as well as the evaporation of sessile droplets. The analysis employs advanced asymptotic methods to explore the behavior of fluids on both stationary and rotating cylinders, providing a deep understanding of the underlying mechanisms. The chapter begins with an in-depth look at coating and rimming flows, discussing the pioneering work of Moffatt (1977) and subsequent studies that have expanded on this foundational research. It delves into the critical parameters that govern these flows, such as the aspect ratio of the film and the non-dimensional weight per unit axial length, and explores the different flow regimes that can occur. The chapter also examines the fascinating phenomenon of load shedding in coating flows and the development of rapid variation regions in rimming flows. Moving on to rivulet flow, the chapter investigates the gravity-driven draining of a viscous fluid down an inclined substrate. It discusses the unidirectional flow of a uniform rivulet, the locally unidirectional flow of a slowly-varying rivulet, and the non-uniform flow of a slender rivulet, providing a comprehensive overview of the various aspects of rivulet dynamics. The chapter also explores the evaporation of sessile droplets, a fundamental problem with wide-ranging applications. It discusses the diffusion-limited model of evaporation, which assumes that the evaporation is controlled by the diffusion of vapor in the quiescent atmosphere. The chapter examines the shape of the droplet, the evaporative problem, and the hydrodynamic and thermal problems associated with droplet evaporation. It also discusses the evolution and lifetime of thin droplets evaporating in different modes, including the constant radius (CR) mode, the constant angle (CA) mode, the stick-slide (SS) mode, and the stick-jump (SJ) mode. The chapter concludes with a discussion of various extensions and generalizations of the diffusion-limited model, including temperature-dependent saturation concentration, droplets on non-planar substrates, and the competitive evaporation of multiple droplets. Throughout the chapter, the use of asymptotic methods provides unique insights into the complex dynamics of fluid flow and evaporation, making it an essential resource for those interested in these phenomena.
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previous chapter Viscoelastic Lubrication Using the Second-Order Fluid
Footnotes
1
Note that Moffatt (1977) gave the incorrect value of 0.866 instead of \(\sqrt{6}/4 \simeq 0.612\) for the coefficient of \(\vert \theta \vert \) in his corresponding expression for the film thickness.
 
2
Note that Moffatt (1977) gave the slightly inaccurate numerical value of 4.428 for the critical weight.
 
3
Note that the corresponding critical values given by Tirumkudulu & Acrivos (2001), namely 1.5862 and 2.2135, are slightly inaccurate and should be 1.5859 and 2.2046.
 
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Metadata
Title
Coating and Rimming Flow, Rivulet Flow, and the Evaporation of a Sessile Droplet
Author
Stephen K. Wilson
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_6

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