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Film shape of partially wetting liquid while flowing down wetted surface

Authors: Romanov A.S., Semikolenov A.V. Published: 15.10.2015
Published in issue: #5(62)/2015  
DOI: 10.18698/1812-3368-2015-5-88-99

 
Category: Mechanics | Chapter: Mechanics of Liquid, Gas, and Plasma  
Keywords: partially wetting liquid, thin film, surface tension, disjoining pressure, contact of three phases, contact angle

The paper presents a method for noncontradictory description of a dynamic contact angle ofpartially wetting liquid while it flows down the hard surface. An additional chemical potential (disjoining pressure) is taken into account, when considering fluid particles in the liquid thin layers near the three-phase contact line. The application of the developed theory is demonstrated by calculating the liquid surface shape at different speeds.

References

[1] Martinson L.K., Malov Yu.I. Ed. by Zarubin V.S., Krishchenko A.P. Differentsial’nye uravneniya matematicheskoy fiziki [Differential equations of mathematical physics]. Moscow, MGTU im. N.E. Baumana Publ., 2011. 367 p.

[2] Deryagin B.V., Churaev N.V. Smachivayushchie plenki [Wetting films]. Moscow, Nauka Publ., 1984. 160 p.

[3] Deryagin B.V., Churaev N.V., Muler V.M. Poverkhnostnye sily [Surface forces]. Moscow, Nauka Publ., 1985. 399 p.

[4] Romanov A.S. The way of hydro dynamic description of partially wetting liquid spreading over the flat hard surface. Kolloidn. Zh. [Colloid J.], 1990, vol. 52, no. 1, pp. 93-99 (in Russ.).

[5] Zhen P.Zh. Wetting: statics and dynamics. Usp. Fiz. Nauk [Physics-Uspekhi], 1987, vol. 151, no. 4, pp. 619-681 (in Russ.).

[6] Pukhnachev V.V., Solonnikov V.A. Revisiting the dynamic wetting angle. Prikl. mat. i mekh. (J. Appl. Math. Mech.), 1982, vol. 46, no. 6, pp. 961-971.

[7] Radoev B., Steckelhuber Kl.W., Tsekov R., Letocart Ph. Wetting Film Dynamics and Stability. Col. Interface Sci. Ser. 3, 2007, pp. 151-172.

[8] Bing Dai, Gary Leal L., Redondo A. Disjoining Pressure for Nonuniform Thin Films. Phys. Rev. E, 2008, vol. 78, p. 061602.

[9] Aliev I.N., Yurchenko S.O. Nonlinear waves spreading over the nonviscous conductive liquid surface in the electric field. Izv. Akad. Nauk, Mekh. Zhidk. Gaza [Fluid Dyn.], 2009, no. 5, pp. 137-148 (in Russ.).

[10] Aliev I.N., Yurchenko S.O. Perturbation transition of the charged interface of non-miscible nonviscous liquids in the clearance between two electrodes. Izv. Akad. Nauk, Mekh. Zhidk. Gaza [Fluid Dyn.], 2010, no. 5, pp. 156-166 (in Russ.).

[11] Saramago B. Thin liquid wetting films. Current Opinion in Colloid & Interface Science, 2010, vol. 15, no. 5, pp. 330-340.

[12] Ren W., Hu D.E.W. Continuum Models for the Contact Line Problem. Physics of Fluids. 2010, vol. 22, no. 10, p. 102103-19.

[13] Patra Ajoy, Bandyopadhyay Dipankar Tomar, Gaurav, Sharma Ashutosh, Biswas Gautam. Instability and Dewetting of Ultrathin Solid Viscoelastic Films on Homogeneous and Heterogeneous Substrates. Journal of Chemical Physics, 2011, vol. 134, no. 6, p. 064705-11.

[14] Boinovich L., Emelyanko A. Wetting and Surface Forces. Adv. Colloid Interface Sci., 2011, vol. 165, pp. 60-69.

[15] Tsekov R., Toshev B.V. Capillary Pressure of Van der Waals Liquid Nanodrops. Kolloidn. Zh. [Colloid J.], 2012, vol. 74, no. 2, p. 286.

[16] Colosqui C.E., Kavousanakis M.E., Papathanasiou A.G., Kevrekidis I.G. Mesoscopic Model for Microscale Hydrodynamics and Interfacial Phenomena: Slip, Films, and Contact-Angle Hysteresis. Phys. Rev. E. Statistical, Nonlinear, and Soft Matter Physics, 2013, vol. 87, no. 1, p. 013302.

[17] Nikolov A., Wasan D. Wetting-Dewetting Films: The Role of Structural Forces. Advances in Colloid and Interface Science, 2014, vol. 206, pp. 207-221.

[18] Boinovich L., Emelyanko A. The Prediction of Wettability of Curved Surfaces on the Basis of the Isotherms of the Disjoining Pressure. Col. Surf. A: Physicochem. Eng. Aspects, 2011, vol. 383, pp. 10-16.

[19] Popescu M.N., Oshanin G., Dietrich S., Cazabat A.-M. Precursor Films in Wetting Phenomena. J. Phys.: Condens. Matter., 2012, vol. 24, p. 243102.

[20] Moulton D.E., Lega J. Effect of Disjoining Pressure in a Thin Film Equation with Nonuniform Forcing. European J. of Applied Math., 2013, vol. 24, pp. 887-920.

[21] Snoeijer Jacco H., Andreotti Br. Moving Contact Lines: Scales, Regimes, and Dynamical Transitions. Annu. Rev. Fluid Mech., 2013, vol. 45, pp. 269-292.

[22] Sibley D.N., Nold A., Savva N., Kalliadasis S. A Comparison of Slip, Disjoining Pressure, and Interface Formation Models for Contact Line Motion Through Asymptotic Analysis of Thin Two-Dimensional Droplet Spreading. J. of Engineering Math., 2014.

[23] Chaudhury K., Acharya V.P., Chakraborty S. Influence of Disjoining Pressure on the Dynamics of Steadily Moving Long Bubbles Inside Narrow Cylindrical Capillaries. Phys. Rev. E. 2014, vol. 89, p. 053002.

[24] Romanov A.S., Semikolenov A.V. Form of a free liquid surface, which is in equilibrium with its alfa-film. Jelektr. Nauchno-Tehn. Izd. "Inzhenernyy zhurnal: nauka i innovacii" [El. Sc.-Techn. Publ. "Eng. J.: Science and Innovation"], 2013, iss. 8. URL: http://engjournal.ru/catalog/fundamentals/physics/872.html (accessed 12.01.2015).

[25] Romanov A.S., Semikolenov A.V. Depressurized capillary filling in the asymptotic theory of wetting. Jelektr. Nauchno-Tehn. Izd. "Inzhenernyy zhurnal: nauka i innovacii" [El. Sc.-Techn. Publ. "Eng. J.: Science and Innovation"], 2013, iss. 4. URL: http://engjournal.ru/catalog/machin/rocket/699.html (accessed 12.01.2015).

[26] Samarskiy A.A., Sobol’ I.M. Numeral computation examples of temperature waves. Zh. Vychisl. Mat. Mat. Fiz. [Comput. Math. Math. Phys.], 1963, vol. 3, no. 4, pp. 702719 (in Russ).

[27] Pavlov K.B., Romanov A.S., Shakhorin A.P. The way of phenomenological description of partially wetting liquid spreading. Chislennye metody mekhaniki sploshnoy sredy [Numerical procedures of continuum mechanics]. Novosibirsk, 1986, vol. 17, no. 3, pp. 132-138 (in Russ.).

[28] Hocking L.M., River A.D. The spreading of a drop by capillary action. J. Fluid Mech., 1982, vol. 121, no. 1, pp. 37-55.

[29] Deryagin B.V., Churaev N.V., Ovcharenko F.D. Voda v dispersnykh sistemakh [Water in disperse systems]. Moscow, Khimiya Publ., 1989. 288 p.