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    Film spreading from a miscible drop on a deep liquid layer

    Year: 2017

    Journal: J. Fluid Mech., Volume 829, OCT 25, page 304–327

    Authors: Dandekar, Raj; Pant, Anurag; Puthenveettil, Baburaj A.

    Organizations: DST, Government of India [SR/FST/ETII-017/2003]

    Keywords: drops; interfacial flows (free surface); thin films

    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 ( D l = d > 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 D l = d > 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 t1 = 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 D rf = rd, in the form fr f D t d 1 = 4, where t d D t = t d, with the time scale t d D drd = 1 and f is a function of Bod. Similarly, we show that the dimensionless velocity of film spreading, Cad D uf d = 1 , scales as 4f 4Cad D r 3.
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