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Film spreading from a miscible drop on a deep liquid layer
Published in Cambridge University Press
2017
Volume: 829
   
Pages: 304 - 327
Abstract
We study the spreading of a film from ethanol-water droplets of radii 0:9 mm<rd < 1:1 mm on the surface of a deep water layer for various concentrations of ethanol in the drop. Since the drop is lighter (§ =p1/pd 1:03), it stays at the surface of the water layer during the spreading of the film from the drop; the film is more viscous than the underlying water layer since x= μ1/μd <0:38. Inertial forces are not dominant in the spreading since the Reynolds numbers based on the film thickness hf are in the range 0:02 < Ref < 1:4. The spreading is surface-tension-driven since the film capillary numbers are in the range 0:0005 < Caf < 0:0069 and the drop Bond numbers are in the range 0:19 < Bod < 0:56. We observe that, when the drop is brought in contact with the water surface, capillary waves propagate from the point of contact, followed by a radially expanding, thin circular film of ethanol-water mixture. The film develops instabilities at some radius to form outward-moving fingers at its periphery while it is still expanding, till the expansion stops at a larger radius. The film then retracts, during which time the remaining major part of the drop, which stays at the centre of the expanding film, thins and develops holes and eventually mixes completely with water. The radius of the expanding front of the film scales as rf 1=4 and shows a dependence on the concentration of ethanol in the drop as well as on rd, and is independent of the layer height hl. Using a balance of surface tension and viscous forces within the film, along with a model for the fraction of the drop that forms the thin film, we obtain an expression for the dimensionless film radius r∗f=rf/rd in the form frf =tr∗ud =1/41=4, where tr∗ud with the time scale tud=μdr/δo and f is a function of Bod. Similarly, we show that the dimensionless velocity of film spreading, Cad μfμd/δ, scales as 4f4Cadrr∗ f-3. ©2017 Cambridge University Press.
About the journal
JournalData powered by TypesetJournal of Fluid Mechanics
PublisherData powered by TypesetCambridge University Press
ISSN00221120
Open AccessNo
Concepts (18)
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    Computer aided design
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    Drops
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    Ethanol
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    Reynolds number
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    Surface tension
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    Capillary numbers
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    Capillary wave
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    DIMENSIONLESS VELOCITY
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    ETHANOL WATER MIXTURES
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    INERTIAL FORCES
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    INTERFACIAL FLOW (FREE SURFACE)
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    POINT OF CONTACT
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    VISCOUS FORCES
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    Thin films
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    DEEP WATER
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    Droplet
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    Film
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    Free surface flow