年間 4 号発行
ISSN 印刷: 1065-3090
ISSN オンライン: 1940-4336
Indexed in
VORTEX RING BELOW A SPREADING ALCOHOL FILM ON WATER
要約
We study the expansion of a vortex ring generated due to the spreading of ethanol-water droplets, with ethanol concentration range of 20% ≤ Ce ≤ 100%, on the surface of a 50-mm-deep water layer. Once deposited on the water layer, the surface tension difference leads to some part of the lighter ethanol droplet spreading as a thin film over the water layer. We observe an expanding vortex ring below the radially spreading film front. We visualize the film spreading from top using aluminum particles, while the vortex is visualized from the side using polyamide particles with laser induced fluorescence (LIF) from the dyed drop used to distinguish the alcohol from the water. Particle image velocimetry (PIV) is used to obtain the velocity and the vorticity fields below the spreading film. Vortex regions and their centers, identified by the λ2 method from the velocity fields, are tracked to determine the vortex expansion. We show that the vortex ring expands with the same velocity of expansion as that of the spreading ethanol film at the free surface, possibly since the vortex ring is created due to the surface tension difference across the film front. Using dimensional arguments, we also propose a scaling for the upward velocity, uΓ, induced by this expanding vortex ring and show that uΓ ~ t-1/2.
-
Adrian, R. and Westerweel, J., Particle Image Velocimetry, Cambridge, UK: Cambridge University Press, 2011.
-
Agrawal, A. and Prasad, A., Properties of Vortices in the Self-Similar Turbulent Jet, Experiments Fluids, vol. 33, no. 4, pp. 565-577,2002.
-
Bacri, L., Debregeas, G., and Brochard-Wyart, F., Experimental Study of the Spreading of a Viscous Droplet on a Nonviscous Liquid, Langmuir, vol. 12, no. 26, pp. 6708-6711, 1996.
-
Batchelor, G.K., An Introduction to Fluid Dynamics, Cambridge, UK: Cambridge Mathematical Library, Cambridge University Press, 2000.
-
Chong, M.S., Perry, A.E., and Cantwell, B.J., A General Classification of Three-Dimensional Flow Fields, Phys. Fluids A: FluidDyn., vol. 2, no. 5, pp. 765-777,1990.
-
Dandekar, R., Pant, A., and Puthenveettil, B.A., Film Spreading from a Miscible Drop on a Deep Liquid Layer, J. Fluid Mech, vol. 829, pp. 304-327,2017.
-
Dussaud, A.D. and Troian, S.M., Dynamics of Spontaneous Spreading with Evaporation on a Deep Fluid Layer, Phys. Fluids, vol. 10, no. 1, pp. 23-38,1998.
-
Ernst, R.C., Watkins, C.H., and Ruwe, H.H., The Physical Properties of the Ternary System Ethyl Alcohol-Glycerin-Water, J. Phys. Chem., vol. 40, no. 5, pp. 627-635,1935.
-
Fay, J.A., The Spread of Oil Slicks on a Calm Sea, in Oil on the Sea, A.P. Hoult, Ed., New York, NY: Springer Science and Business Media, pp. 53-63,1969.
-
Hernandez-Sanchez, J.F., Eddi, A., and Snoeijer, J.H., Marangoni Spreading due to a Localized Alcohol Supply on a Thin Water Film, Phys. Fluids, vol. 27, no. 3, p. 032003,2015.
-
Huang, H., Dabiri, D., and Gharib, M., On Errors of Digital Particle Image Velocimetry, vol. 8, no. 12, pp. 1427-1440,1997.
-
Hunt, J.C.R., Wray, A.A., and Moin, P., Eddies, Streams, and Convergence Zones in Turbulent Flows, Proc. Summer Program 1988, Center for Turbulence Research CTR-S 88, pp. 193-208,1988.
-
Jensen, O.E. and Grotberg, J.B., Insoluble Surfactant Spreading on a Thin Viscous Film: Shock Evolution and Film Rupture, J. Fluid Mech, vol. 240, pp. 259-288,1992.
-
Jeong, J. and Hussain, F., On the Identification of a Vortex, J. Fluid Mech., vol. 285, pp. 69-94,1995.
-
Joos, P. and Van Hunsel, J., Spreading of Aqueous Surfactant Solutions on Organic Liquids, J. Colloid Interf. Sci., vol. 106, no. 1, pp. 161-167,1985.
-
Kim, H., Lee, J., Kim, T.H., and Kim, H.Y., Spontaneous Marangoni Mixing of Miscible Liquids at a Liquid-Air Contact Line, Langmuir, vol. 31, no. 31, pp. 8726-8731,2015.
-
Raffel, M., Willert, C.E., Scarano, F., Kahler, C., Wereley, S.T., and Kompenhans, J., Particle Image Velocimetry: A Practical Guide, Berlin-Heidelberg, Germany: Springer, 2007.
-
Nobach, H. and Bodenschatz, E., Limitations of Accuracy in PIV due to Individual Variations of Particle Image Intensities, Exp. Fluids, vol. 47, no. 1, pp. 27-38,2009.
-
Wieneke, B., PIV Uncertainty Quantification from Correlation Statistics, Measurement Sci. Technol., vol. 26, no. 7, p. 074002,2015.
-
Zhou, J., Adrian, R.J., Balachandar, S., and Kendall, T.M., Mechanisms for Generating Coherent Packets of Hairpin Vortices in Channel Flow, J. Fluid Mech, vol. 387, pp. 353-396,1999.