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Thin-film equations are utilised in many different areas of fluid dynamics when there exists a direction in which the aspect ratio can be considered small. We consider thin free films with Marangoni effects in the extensional flow regime, where velocity gradients occur predominantly along the film. In practice, because of the local deposition of surfactants or input of energy, asymmetric distributions of surfactants or surface tension more generally, are possible. Such examples include the surface of bubbles and the rupture of thin films. In this study, we consider the asymmetric thin-film equations for extensional flow with Marangoni effects. Concentrating on the case of small Reynolds number$$ Re $$, we study the deposition of insoluble surfactants on one side of a liquid sheet otherwise at rest and the resulting thinning and rupture of the sheet. The analogous problem with a uniformly thinning liquid sheet is also considered. In addition, the centreline deformation is discussed. In particular, we show analytically that if the surface tension isotherm$$\sigma = \sigma (\varGamma )$$is nonlinear (surface tension$$\sigma$$varies with surfactant concentration$$\varGamma$$), then accounting for top–bottom asymmetry leads to slower (faster) thinning and pinching if$$\sigma = \sigma (\varGamma )$$is convex (concave). The analytical progress reported in this paper allows us to discuss the production of satellite drops from rupture via Marangoni effects, which, if relevant to surface bubbles, would be an aerosol production mechanism that is distinct from jet drops and film drops.
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The effects of surfactants on plunging breakers
The effects of surfactants on a mechanically generated plunging breaker are studied experimentally in a laboratory wave tank. Waves are generated using a dispersively focused wave packet with a characteristic wavelength of$$\lambda _0 = 1.18$$m. Experiments are performed with two sets of surfactant solutions. In the first set, increasing amounts of the soluble surfactant Triton X-100 are mixed into the tank water, while in the second set filtered tap water is left undisturbed in the tank for wait times ranging from 15 min to 21 h. Increasing Triton X-100 concentrations and longer wait times lead to surfactant-induced changes in the dynamic properties of the free surface in the tank. It is found that low surface concentrations of surfactants can dramatically change the wave breaking process by changing the shape of the jet and breaking up the entrained air cavity at the time of jet impact. Direct numerical simulations (DNS) of plunging breakers with constant surface tension are used to show that there is significant compression of the free surface near the plunging jet tip and dilatation elsewhere. To explore the effect of this compression/dilatation, the surface tension isotherm is measured in all experimental cases. The effects of surfactants on the plunging jet are shown to be primarily controlled by the surface tension gradient ($$\Delta \mathcal {E}$$) while the ambient surface tension of the undisturbed wave tank ($$\sigma _0$$) plays a secondary role.
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- PAR ID:
- 10483881
- Publisher / Repository:
- Journal of Fluid Mechanics
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 972
- ISSN:
- 0022-1120
- Page Range / eLocation ID:
- R5
- Subject(s) / Keyword(s):
- wave breaking, surface gravity waves
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2023.721
