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Phase transitions on partially contaminated surface under the influence of thermocapillary flow

Published online by Cambridge University Press:  27 August 2019

A. V. Shmyrov
Affiliation:
Institute of Continuous Media Mechanics, Russian Academy of Science, Perm 614013, Russia
A. I. Mizev*
Affiliation:
Institute of Continuous Media Mechanics, Russian Academy of Science, Perm 614013, Russia
V. A. Demin
Affiliation:
Department of Theoretical Physics, Perm State National Research University, Perm 614990, Russia
M. I. Petukhov
Affiliation:
Department of Theoretical Physics, Perm State National Research University, Perm 614990, Russia
D. A. Bratsun
Affiliation:
Department of Applied Physics, Perm National Research Polytechnic University, Perm 614990, Russia
*
Email address for correspondence: alex_mizev@icmm.ru

Abstract

We study, both experimentally and theoretically, the fluid flow driven by a thermocapillary effect applied to a partially contaminated interface in a two-dimensional slot of finite extent. The contamination is due to the presence of an insoluble surfactant which is convected by the flow forming a stagnant zone by the colder edge of the interface. The thermocapillary surface stress is produced by a special optocapillary system, which makes it possible, first, to get an almost linear temperature profile along the interface and, second, to apply a surface pressure large enough to force the surfactant to experience a phase transition to a more condensed state. This enabled us for the first time since the release of the paper by Carpenter & Homsy (J. Fluid Mech., vol. 155, 1985, pp. 429–439) to test experimentally their theoretical predictions and obtain new results for the case when the contamination exists simultaneously in two phase states within the interface. We show that one part of the surface is free of surfactant and subject to vigorous thermocapillary flow, while another part is stagnant and subject to creeping flow with a surface velocity which is approximately two orders of magnitude smaller. We found that the extent of the stagnant zone theoretically predicted earlier does not coincide with the newly obtained experimental data. In this paper, we suggest analytical and numerical solutions for the position of the edge of the stagnation zone, which are in perfect agreement with the experimental data.

Type
JFM Papers
Copyright
© 2019 Cambridge University Press 

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References

Abramzon, A. A. & Gaevoy, G. M. 1979 Surface-Active Substances (reference book) (in Russian). Leningrad.Google Scholar
Adam, N. K. 1952 The Physics and Chemistry of Surfaces. Oxford University Press.Google Scholar
Adamson, A. W. & Gast, A. P. 1967 Physical Chemistry of Surfaces, vol. 15. Interscience.Google Scholar
Bach, C. & Schwabe, D. 2015 Surface waves in thermocapillary flow – revisited. Eur. Phys. J. Spec. Top. 224 (2), 319340.10.1140/epjst/e2015-02363-5Google Scholar
Benz, S. & Schwabe, D. 2001 The three-dimensional stationary instability in dynamic thermocapillary shallow cavities. Exp. Fluids 31 (4), 409416.10.1007/s003480100316Google Scholar
Birikh, R. V. 1966 Thermocapillary convection in a horizontal layer of liquid. J. Appl. Mech. Tech. Phys. 7 (3), 4344.10.1007/BF00914697Google Scholar
Birikh, R., Briskman, V., Velarde, M. & Legros, J.-C. 2003 Liquid Interfacial Systems: Oscillations and Instability. CRC Press.Google Scholar
Bratsun, D., Kostarev, K., Mizev, A., Aland, S., Mokbel, M., Schwarzenberger, K. & Eckert, K. 2018 Adaptive micromixer based on the solutocapillary Marangoni effect in a continuous-flow microreactor. Micromachines 9 (11), 600.10.3390/mi9110600Google Scholar
Burguete, J., Mukolobwiez, N., Daviaud, F., Garnier, N. & Chiffaudel, A. 2001 Buoyant-thermocapillary instabilities in extended liquid layers subjected to a horizontal temperature gradient. Phys. Fluids 13 (10), 27732787.10.1063/1.1398536Google Scholar
Carpenter, B. & Homsy, G. M. 1985 The effect of surface contamination on thermocapillary flow in a two-dimensional slot. Part 2. Partially contaminated interfaces. J. Fluid Mech. 155, 429439.10.1017/S0022112085001884Google Scholar
Carpenters, B. M. & Homsy, G. M. 1990 High Marangoni number convection in a square cavity. Part ii. Phys. Fluids A 2, 137149.10.1063/1.857763Google Scholar
Chen, J.-C. & Shih-Fan, K. 1992 Thermocapillary convection in a rectangular cavity under the influence of surface contamination. Intl J. Heat Mass Transfer 35 (11), 29052910.10.1016/0017-9310(92)90310-OGoogle Scholar
Cuenot, B., Magnaudet, J. & Spennato, B. 1997 The effects of slightly soluble surfactants on the flow around a spherical bubble. J. Fluid Mech. 339, 2553.10.1017/S0022112097005053Google Scholar
Davis, R. E. & Acrivos, A. 1966 The influence of surfactants on the creeping motion of bubbles. Chem. Engng Sci. 21 (8), 681685.10.1016/0009-2509(66)80017-9Google Scholar
De Vahl Davis, G. 1983 Natural convection of air in a square cavity. A bench mark solution. Intl J. Numer. Meth. Fluids 3, 249264.10.1002/fld.1650030305Google Scholar
Downing, H. D. & Williams, D. 1975 Optical constants of water in the infrared. J. Geophys. Res. 80 (12), 16561661.10.1029/JC080i012p01656Google Scholar
Frumkin, A. 1947 On surfactants and interfacial motion. Zh. Fiz. Khim. 21, 11831204.Google Scholar
Gershuni, G. & Zhukhovitskii, E. 1976 Convective stability of incompressible fluids. Keter Publishing House.Google Scholar
Griffith, R. M. 1962 The effect of surfactants on the terminal velocity of drops and bubbles. Chem. Engng Sci. 17 (12), 10571070.10.1016/0009-2509(62)80084-0Google Scholar
Guenther, C. & Mueller, U.1987 Rayleigh–Bénard convection in a Hele-Shaw cell: a numerical study. NASA Tech. Rep. N88.Google Scholar
Hanumanthu, R. & Stebe, K. J. 2007 Transient enhancement of thermocapillary flow in a two-dimensional cavity by a surfactant. Phys. Fluids 19 (4), 042103.10.1063/1.2714778Google Scholar
Harper, J. F. 1974 On spherical bubbles rising steadily in dilute surfactant solutions. Q. J. Mech. Appl. Maths 27 (1), 87100.10.1093/qjmam/27.1.87Google Scholar
Homsy, G. M. & Meiburg, E. 1984 The effect of surface contamination on thermocapillary flow in a two-dimensional slot. J. Fluid Mech. 139, 443459.10.1017/S0022112084000446Google Scholar
Hosokawa, S., Hayashi, K. & Tomiyama, A. 2018 Evaluation of adsorption of surfactant at a moving interface of a single spherical drop. Exp. Therm. Fluid Sci. 96, 397405.10.1016/j.expthermflusci.2018.03.026Google Scholar
Ju, J. & Warrick, J. 2013 Passive micromixer using by convection and surface tension effects with air–liquid interface. BioChip J. 7, 361366.10.1007/s13206-013-7407-1Google Scholar
Kawamura, H., Tagaya, E. & Hoshino, Y. 2007 A consideration on the relation between the oscillatory thermocapillary flow in a liquid bridge and the hydrothermal wave in a thin liquid layer. Intl J. Heat Mass Transfer 50 (7–8), 12631268.10.1016/j.ijheatmasstransfer.2006.09.035Google Scholar
Keller, J. R. & Bergman, T. L. 1990 Thermosolutal inducement of no-slip free surfaces in combined Marangoni-buoyancy driven cavity flows. J. Heat Transfer 112 (2), 363369.10.1115/1.2910386Google Scholar
Kirdyashkin, A. G. 1984 Thermogravitational and thermocapillary flows in a horizontal liquid layer under the conditions of a horizontal temperature gradient. Intl J. Heat Mass Transfer 27 (8), 12051218.10.1016/0017-9310(84)90048-6Google Scholar
Koschmieder, E. L. 1993 Bénard Cells and Taylor Vortices. Cambridge University Press.Google Scholar
Krzan, M. & Malysa, K. 2002 Profiles of local velocities of bubbles in n-butanol, n-hexanol and n-nonanol solutions. Colloids Surf A 207 (1), 279291.10.1016/S0927-7757(02)00163-2Google Scholar
Lappa, M. 2009 Thermal Convection: Patterns, Evolution and Stability. John Wiley.10.1002/9780470749982Google Scholar
Linde, H. & Friese, P. 1971 Experimenteller Nachweis einer neuen hydrodynamischen Oberflächenstabilität. Z. Phys. Chem. 247 (2), 225232.Google Scholar
Loglio, G., Innocenti, N. D., Tesei, U., Cini, R. & Qi-Shan, W. 1989 Rising of gas bubbles in an aqueous medium in presence of surfactants. Il Nuovo Cimento C 12 (3), 289.10.1007/BF02507201Google Scholar
Maceiras, R., Santana, R. & Alves, S. S. 2007 Rise velocities and gas–liquid mass transfer of bubbles in organic solutions. Chem. Engng Sci. 62 (23), 67476753.10.1016/j.ces.2007.06.029Google Scholar
Masud, J., Kamotani, Y. & Ostrach, S. 1997 Oscillatory thermocapillary flow in cylindrical columns of high Prandtl number fluids. J. Thermophys. Heat Transfer 11 (1), 105111.10.2514/2.6207Google Scholar
Merson, R. L. & Quinn, J. A. 1965 Stagnation in a fluid interface: properties of the stagnant film. AIChE J. 11 (3), 391395.10.1002/aic.690110306Google Scholar
Miller, R. & Liggieri, L. 2009 Interfacial Rheology. CRC Press.Google Scholar
Mizev, A. 2005 Influence of an adsorption layer on the structure and stability of surface tension driven flows. Phys. Fluids 17 (12), 122107.10.1063/1.2150794Google Scholar
Mizev, A. I. & Schwabe, D. 2009 Convective instabilities in liquid layers with free upper surface under the action of an inclined temperature gradient. Phys. Fluids 21 (11), 112102.10.1063/1.3251755Google Scholar
Mizev, A., Trofimenko, A., Schwabe, D. & Viviani, A. 2013 Instability of Marangoni flow in the presence of an insoluble surfactant. Experiments. Eur. Phys. J. Spec. Top. 219 (1), 8998.10.1140/epjst/e2013-01784-4Google Scholar
Nepomnyashchy, A., Simanovskii, I. & Legros, J. C. 2006 Interfacial Convection in Multilayer Systems. Springer.Google Scholar
Nieves-Remacha, M. J., Kulkarni, A. A. & Jensen, K. F. 2012 Hydrodynamics of liquid–liquid dispersion in an advanced-flow reactor. Indust. Engng Chem. Res. 51, 1625116262.10.1021/ie301821kGoogle Scholar
Palaparthi, R., Papageorgiou, D. T. & Maldarelli, C. 2006 Theory and experiments on the stagnant cap regime in the motion of spherical surfactant-laden bubbles. J. Fluid Mech. 559, 144.10.1017/S0022112005007019Google Scholar
Palmer, K. F. & Williams, D. 1974 Optical properties of water in the near infrared. J. Opt. Soc. Am. 64 (8), 11071110.10.1364/JOSA.64.001107Google Scholar
Pearson, J. R. A. 1958 On convection cells induced by surface tension. J. Fluid Mech. 4 (5), 489500.10.1017/S0022112058000616Google Scholar
Riley, R. J. & Neitzel, G. P. 1998 Instability of thermocapillary–buoyancy convection in shallow layers. Part 1. Characterization of steady and oscillatory instabilities. J. Fluid Mech. 359, 143164.10.1017/S0022112097008343Google Scholar
Roché, M., Li, Z., Griffiths, I. M., Le Roux, S., Cantat, I., Saint-Jalmes, A. & Stone, H. A. 2014 Marangoni flow of soluble amphiphiles. Phys. Rev. Lett. 112 (20), 208302.10.1103/PhysRevLett.112.208302Google Scholar
Savic, P.1953 Circulation and distortion of liquid drops falling through a viscous medium report, Natl. Res. Council, Canada. Tech. Rep. NRC-MT-22.Google Scholar
Schwabe, D. 2005 Hydrothermal waves in a liquid bridge with aspect ratio near the Rayleigh limit under microgravity. Phys. Fluids 17 (11), 112104.10.1063/1.2135805Google Scholar
Schwabe, D. 2006 Marangoni instabilities in small circular containers under microgravity. Exp. Fluids 40 (6), 942950.10.1007/s00348-006-0130-0Google Scholar
Schwabe, D., Möller, U., Schneider, J. & Scharmann, A. 1992 Instabilities of shallow dynamic thermocapillary liquid layers. Phys. Fluids A 4 (11), 23682381.10.1063/1.858478Google Scholar
Seemann, R., Brinkmann, M., Pfohl, T. & Herminghaus, S. 2012 Droplet based microfluidics. Rep. Prog. Phys. 75 (1), 016601.10.1088/0034-4885/75/1/016601Google Scholar
Sen, A. K. & Davis, S. H. 1982 Steady thermocapillary flows in two-dimensional slots. J. Fluid Mech. 121, 163186.10.1017/S0022112082001840Google Scholar
Shmyrov, A., Mizev, A., Demin, V., Petukhov, M. & Bratsun, D. 2018 On the extent of surface stagnation produced jointly by insoluble surfactant and thermocapillary flow. Adv. Colloid Interface Sci. 255, 1017.10.1016/j.cis.2017.08.010Google Scholar
Sim, B.-C. & Zebib, A. 2002 Thermocapillary convection in liquid bridges with undeformable curved surfaces. J. Thermophys. Heat Transfer 16 (4), 553561.10.2514/2.6715Google Scholar
Sinz, D. K., Hanyak, M. & Darhuber, A. A. 2013 Self-induced surfactant transport along discontinuous liquid–liquid interfaces. J. Phys. Chem. Lett. 4, 10391043.10.1021/jz400287xGoogle Scholar
Smith, M. K. & Davis, S. H. 1983 Instabilities of dynamic thermocapillary liquid layers. Part 1. Convective instabilities. J. Fluid Mech. 132, 119144.10.1017/S0022112083001512Google Scholar
Song, H., Tice, J. D. & Ismagilov, R. F. 2003 A microfluidic system for controlling reaction networks in time. Angew. Chem. 42 (7), 768772.10.1002/anie.200390203Google Scholar
Suciu, D. G., Smigelschi, O. & Ruckenstein, E. 1967 Some experiments on the Marangoni effect. AIChE J. 13 (6), 11201124.10.1002/aic.690130616Google Scholar
Takagi, S. & Matsumoto, Y. 2011 Surfactant effects on bubble motion and bubbly flows. Annu. Rev. Fluid Mech. 43 (1), 615636.10.1146/annurev-fluid-122109-160756Google Scholar
Takagi, S., Ogasawara, T. & Matsumoto, Y. 2008 The effects of surfactant on the multiscale structure of bubbly flows. Phil. Trans. R. Soc. Lond A 366 (1873), 21172129.10.1098/rsta.2008.0023Google Scholar
Vinnichenko, N. A., Pushtaev, A. V., Plaksina, Y. Y., Rudenko, Y. K. & Uvarov, A. V. 2018 Horizontal convection driven by nonuniform radiative heating in liquids with different surface behavior. Intl J. Heat Mass Transfer 126, 400410.10.1016/j.ijheatmasstransfer.2018.06.036Google Scholar
Vogel, M. J. & Hirsa, A. H. 2002 Concentration measurements downstream of an insoluble monolayer front. J. Fluid Mech. 472, 283305.10.1017/S0022112002002197Google Scholar
Wanschura, M., Shevtsova, V. M., Kuhlmann, H. C. & Rath, H. J. 1995 Convective instability mechanisms in thermocapillary liquid bridges. Phys. Fluids 7 (5), 912925.10.1063/1.868567Google Scholar
Xu, J. & Zebib, A. 1998 Oscillatory two- and three-dimensional thermocapillary convection. J. Fluid Mech. 364, 187209.10.1017/S0022112098001232Google Scholar
Yamada, T. & Ono, N. 2015 A study on micromixing utilizing Marangoni effect induced on gas–liquid free interfaces. J. Micro Nano-Manufacturing 3, 021003.Google Scholar