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Liquid plug formation from heated binary mixtures in capillary tubes

Published online by Cambridge University Press:  24 February 2020

Cunjing Lv Open the ORCID record for Cunjing Lv [Opens in a new window] ,
Subramanyan N. Varanakkottu  and
Steffen Hardt Open the ORCID record for Steffen Hardt [Opens in a new window]
Cunjing Lv
Affiliation:
Institute for Nano- and Microfluidics, Technische Universität Darmstadt, 64287Darmstadt, Germany Department of Engineering Mechanics, Tsinghua University, 100084Beijing, China
Subramanyan N. Varanakkottu
Affiliation:
Department of Physics, National Institute of Technology Calicut, 673601Kozhikode, Kerala, India
Steffen Hardt*
Affiliation:
Institute for Nano- and Microfluidics, Technische Universität Darmstadt, 64287Darmstadt, Germany
*
†Email address for correspondence: [email protected]
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Abstract

We study the formation of liquid plugs in a vertical heated tube in contact with a reservoir filled with a binary liquid mixture. Various morphologies, such as liquid films, rings and plugs, are observed. A key phenomenon is the transition between a liquid ring and a plug, which is described using the concept of a quasi-static minimal energy surface that becomes unstable when the liquid volume exceeds a specific value. The critical diameter of the liquid ring and the volume and the position of the formed plug are obtained from an analytical model. The inner diameter of the liquid ring obeys a $d_{l}\sim (t_{0}-t)^{0.57\pm 0.02}$ scaling law shortly before forming a plug at time $t_{0}$. The height of the liquid column created develops according to $X\sim (t-t_{0})^{0.5\pm 0.01}$ in the first moments. The subsequent time evolution is described by a damped harmonic oscillator based on a scaling analysis. The discoveries presented in this work could be of great importance for our understanding of thermally induced interfacial phenomena in confined space.

JFM classification

Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Thin films Phase change: Condensation/evaporation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 889 , 25 April 2020 , A15
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

Basu, A. S. & Gianchandani, Y. B. 2007 Shaping high-speed Marangoni flow in liquid films by microscale perturbations in surface temperature. Appl. Phys. Lett. 90, 034102.CrossRefGoogle Scholar
Bekki, S., Vignes-Adler, M., Nakache, E. & Adler, P. M. 1990 Solutal Marangoni effect. J. Colloid Surface Sci. 140, 492–506.CrossRefGoogle Scholar
Bénard, H. 1900 Étude expérimentale des courants de convection dans une nappe liquide. Régime permanent: tourbillons cellulaires. J. Phys. Theor. Appl. 9, 513–524.CrossRefGoogle Scholar
Bennett, D. E., Gallardo, B. S. & Abbott, N. L. 1996 Dispensing surfactants from electrodes: Marangoni phenomenon at the surface of aqueous solutions of (11-Ferrocenylundecyl)trimethylammonium bromide. J. Am. Chem. Soc. 118, 6499–6505.CrossRefGoogle Scholar
Berger, R. E. & Corrsin, S. 1974 A surface tension gradient mechanism for driving the pre-corneal tear film after a blink. J. Biomech. 7, 225–238.CrossRefGoogle ScholarPubMed
Bird, J. C., Ristenpart, W. D., Belmonte, A. & Stone, H. A. 2009 Critical angle for electrically driven coalescence of two conical droplets. Phys. Rev. Lett. 103, 164502.CrossRefGoogle ScholarPubMed
Bohm, J., Lüdge, A. & Schröder, W. 1994 Crystal growth by floating zone melting. In Handbook of Crystal Growth (ed. Hurle, D. T. J.), Basic Techniques, vol. 2a, p. 213. North Holland.Google Scholar
Bonn, D., Eggers, J., Indekeu, J., Meunier, J. & Rolley, E. 2009 Wetting and spreading. Rev. Mod. Phys. 81, 739–805.CrossRefGoogle Scholar
Bostwick, J. B. & Steen, P. H. 2015 Stability of constrained capillary surfaces. Annu. Rev. Fluid Mech. 47, 539–568.CrossRefGoogle Scholar
Buffone, C., Sefiane, K. & Christy, J. R. E. 2005 Experimental investigation of self-induced thermocapillary convection for an evaporating meniscus in capillary tubes using micro-particle image velocimetry. Phys. Fluids 17, 052104.CrossRefGoogle Scholar
Burton, J. C., Waldrep, R. & Taborek, P. 2005 Scaling and instabilities in bubble pinch-off. Phys. Rev. Lett. 94, 184502.CrossRefGoogle ScholarPubMed
Bush, J. W. M. & Hu, D. L. 2006 Walking on water: biolocomotion at the interface. Annu. Rev. Fluid Mech. 38, 339–369.CrossRefGoogle Scholar
Carroll, B. J. 1976 The accurate measurement of contact angle, phase contact areas, drop volume, and Laplace excess pressure in drop-in-fiber systems. J. Colloid Interface Sci. 57, 488–495.CrossRefGoogle Scholar
Cazabat, A. M., Heslot, F., Troian, S. M. & Carles, P. 1990 Fingering instability of thin spreading films driven by temperature gradients. Nature 346, 824–826.CrossRefGoogle Scholar
Cecere, A., Buffone, C. & Savino, R. 2014 Self-induced Marangoni flow in evaporating alcoholic solutions. Intl J. Heat Mass Transfer 78, 852–859.CrossRefGoogle Scholar
Chraïbi, H. & Delville, J.-P. 2012 Thermocapillary flows and interface deformations produced by localized laser heating in confined environment. Phys. Fluid 24, 032102.CrossRefGoogle Scholar
Clements, J. A., Hustead, R. F., Johnson, R. P. & Gribetz, I. 1961 Pulmonary surface tension and alveolar stability. J. Appl. Phys. 16, 444–450.CrossRefGoogle ScholarPubMed
Collicott, S. H., Lindsley, W. G. & Frazer, D. G. 2006 Zero-gravity liquid–vapor interfaces in circular cylinders. Phys. Fluids 18, 087109.CrossRefGoogle Scholar
Craster, R. V. & Matar, O. K. 2009 Dynamics and stability of thin liquid films. Rev. Mod. Phys. 81, 1131–1198.CrossRefGoogle Scholar
Darhuber, A. A. & Troian, S. M. 2005 Principles of microfluidic actuation by modulation of surface stresses. Annu. Rev. Fluid Mech. 37, 425–455.CrossRefGoogle Scholar
Diguet, A., Guillermic, R.-M., Magome, N., Saint-Jalmes, A., Chen, Y., Yoshikawa, K. & Baigl, D. 2009 Photomanipulation of a droplet by the chromocapillary effect. Angew. Chem. Intl Ed. Engl. 48, 9281–9284.CrossRefGoogle ScholarPubMed
Duclaux, V., Clanet, C. & Quéré, D. 2006 The effects of gravity on the capillary instability in tubes. J. Fluid Mech. 556, 217–226.CrossRefGoogle Scholar
Eddi, A., Winkels, K. G. & Snoeijer, J. H. 2013 Influence of droplet geometry on the coalescence of low viscosity drops. Phys. Rev. Lett. 111, 144502.CrossRefGoogle ScholarPubMed
Eggers, J., Fontelos, M. A., Leppinen, D. & Snoeijer, J. H. 2007 Theory of the collapsing axisymmetric cavity. Phys. Rev. Lett. 98, 094502.CrossRefGoogle ScholarPubMed
Eggers, J., Lister, J. R. & Stone, H. A. 1999 Coalescence of liquid drops. J. Fluid Mech. 401, 293–310.CrossRefGoogle Scholar
Everett, D. H. & Haynes, J. M. 1972 Model studies of capillary condensation. I. Cylindrical pore with zero contact angle. J. Colloid Interface Sci. 38, 125–137.CrossRefGoogle Scholar
Farahi, R. H., Passian, A., Ferrell, T. L. & Thundat, T. 2004 Microfluidic manipulation via Marangoni forces. Appl. Phys. Lett. 85, 4237–4239.CrossRefGoogle Scholar
Gallardo, B. S., Gupta, V. K., Eagerton, F. D., Jong, L. I., Craig, V. S., Shah, R. R. & Abbott, N. L. 1999 Electrochemical principles for active control of liquids on submillimeter scales. Science 283, 57–60.CrossRefGoogle ScholarPubMed
Gauglitz, P. A. & Radke, C. J. 1988 An extended evolution equation for liquid film breakup in cylindrical capillaries. Chem. Engng Sci. 43, 1457–1465.CrossRefGoogle Scholar
Gekle, S., Snoeijer, J. H., Lohse, D. & Meer, D. 2009 Approach to universality in axisymmetric bubble pinch-off. Phys. Rev. E 80, 036305.Google ScholarPubMed
de Gennes, P.-G., Brochard-Wyart, F. & Quéré, D. 2004 Capillarity and Wetting Phenomena. Springer.CrossRefGoogle Scholar
Gibbs, J. W. 1878 On the equilibrium of heterogeneous substances. Trans. Conn. Acad. 3, 343–524.Google Scholar
Gordillo, J. M., Sevilla, A., Rodríguez-Rodríguez, J. & Martinez-Bazan, C. 2005 Axisymmetric bubble pinch-off at high Reynolds numbers. Phys. Rev. Lett. 95, 194501.CrossRefGoogle ScholarPubMed
Gotkis, Y., Ivanov, I., Murisic, N. & Kondic, L. 2006 Dynamic structure formation at the fronts of volatile liquid drops. Phys. Rev. Lett. 97, 186101.CrossRefGoogle ScholarPubMed
Grotberg, J. B. 1994 Pulmonary flow and transport phenomena. Annu. Rev. Fluid Mech. 26, 529–571.CrossRefGoogle Scholar
Halpern, D., Jensen, O. E. & Grotbert, J. B. 1998 A theoretical study of surfactant and liquid delivery into the lung. J. Appl. Phys. 85, 333–352.CrossRefGoogle ScholarPubMed
Hosoi, A. E. & Bush, J. W. M. 2001 Evaporative instabilities in climbing films. J. Fluid Mech. 442, 217–239.CrossRefGoogle Scholar
Hu, D. L. & Bush, J. W. M. 2010 The hydrodynamics of water-walking arthropods. J. Fluid Mech. 644, 5–33.CrossRefGoogle Scholar
Jensen, O. E. 2000 Draining collars and lenses in liquid-lined vertical tubes. J. Colloid Interface Sci. 221, 38–49.CrossRefGoogle ScholarPubMed
Keiser, L., Bense, H., Colinet, P., Bico, J. & Reyssat, E. 2017 Marangoni bursting: evaporation-induced emulsification of binary mixtures on a liquid layer. Phys. Rev. Lett. 118, 074504.CrossRefGoogle ScholarPubMed
Khattab, I. S., Bandarkar, F., Fakhree, M. & Jouyban, A. 2012 Density, viscosity, and surface tension of water + ethanol mixtures from 293 to 323 K. Korean J. Chem. Engng 29, 812–817.CrossRefGoogle Scholar
Kundan, A., Plawsky, J. L. & Wayner, P. C. 2015 Effect of capillary and Marangoni forces on transport phenomena in microgravity. Langmuir 31, 5377–5386.CrossRefGoogle ScholarPubMed
Langbein, D. W. 2002 Capillary Surfaces: Shape-Stability-Dynamics, in Particular Under Weightlessness, 178 edn. Springer Science Business Media.CrossRefGoogle Scholar
Leppinen, D. & Lister, J. R.2005 Capillary pinch-off of inviscid fluids at varying density ratios: the bubble limit. American Physical Society, 58th Annual Meeting of the Division of Fluid Dynamics, November 20–22, 2005, abstract id. BD.006.Google Scholar
Lin, S. P. & Brenner, H. 1982 Tear film rupture. J. Colloid Interface Sci. 89, 226–231.CrossRefGoogle Scholar
Lin, S. P. & Liu, W. C. 1975 Instability of film coating of wires and tubes. AIChE J. 21, 775–782.CrossRefGoogle Scholar
Longuet-Higgins, M., Kerman, B. R. & Lunde, K. 1991 The release of air bubbles from an underwater nozzle. J. Fluid Mech. 230, 365–390.CrossRefGoogle Scholar
Lv, C. & Hardt, S.2019 Wetting of an annular liquid in a tube. Preprint, arXiv:1909.12008.Google Scholar
Lv, C., Varanakkottu, S. N., Baier, T. & Hardt, S. 2018 Controlling the trajectories of nano/micro particles using light-actuated Marangoni flow. Nano Lett. 18, 6924–6930.CrossRefGoogle ScholarPubMed
Magnus, W., Oberhettinger, F. & Soni, R. P. 1966 Formulas and Theorems for the Special Functions of Mathematical Physics, 3rd edn. Springer.CrossRefGoogle Scholar
de Maleprade, H., Clanet, C. & Quéré, D. 2016 Spreading of bubbles after contacting the lower side of an aerophilic slide immersed in water. Phys. Rev. Lett. 117, 094501.Google ScholarPubMed
Marangoni, C. 1871 Über die Ausbreitung der Tropfen einer Flüssigkeit auf der Oberfläche einer anderen. Ann. Phys. Chem. 143, 337–354.CrossRefGoogle Scholar
Markos, M. & Ajaev, V. S. 2006 Steady flow and evaporation of a volatile liquid in a wedge. Phys. Fluids 18, 092102.CrossRefGoogle Scholar
Maxwell, J. C. 1878 Encyclopædia Britannica, 9th edn. vol. 5, p. 56. Adam and Charles Black.Google Scholar
van der Mensbrugghe, G. L. 1869 Sur la tension superficielle des liquids considérée au point de vue de certains mouvements observés à leur surface, Mém. couronnés et Mém. Savants étrangers. Acad. R. Belgique (Brussels) 34, 3–67.Google Scholar
Nakata, S., Lguchi, Y., Ose, S., Kuboyama, M., Ishii, T. & Yoshikawa, K. 1997 Self-rotation of a camphor scraping on water: new insight into the old problem. Langmuir 13, 4454–4458.CrossRefGoogle Scholar
Oguz, H. N. & Prosperetti, A. 1993 Dynamics of bubble growth and detachment from a needle. J. Fluid Mech. 257, 111.CrossRefGoogle Scholar
Paulsen, J. D., Carmigniani, R., Kannan, A., Burton, J. C. & Nagel, S. R. 2014 Coalescence of bubbles and drops in an outer fluid. Nat. Commun. 5, 3182.CrossRefGoogle Scholar
Pearson, J. R. A. 1958 On convection cells induced by surface tension. J. Fluid Mech. 4, 489–500.CrossRefGoogle Scholar
Plateau, J. A. F. 1873 Statique expérimentale et théorique des liquides soumis aux seules force moléculaires, vol. 1, p. 265. Gauthier-Villars.Google Scholar
Rayleigh, L. 1890 Measurements of the amount of oil necessary in order to check the motions of camphor upon water. Proc. R. Soc. Lond. 47, 364–367.Google Scholar
Reddy, R. P. & Lienhard, J. H. 1989 The peak boiling heat flux in saturated ethanol–water mixtures. J. Heat Transfer 111, 480–487.CrossRefGoogle Scholar
Ristenpart, W. D., McCalla, P. M., Roy, R. V. & Stone, H. A. 2006 Coalescence of spreading droplets on a wettable substrate. Phys. Rev. Lett. 97, 064501.CrossRefGoogle ScholarPubMed
Sammarco, T. S. & Burns, M. A. 1999 Thermocapillary pumping of discrete drops in microfabricated analysis devices. Am. Inst. Chem. Engng J. 45, 350–366.CrossRefGoogle Scholar
Schatz, M. F. & Neitzel, G. P. 2001 Experiments on thermocapillary instabilities. Annu. Rev. Fluid Mech. 33, 93–127.CrossRefGoogle Scholar
Schwabe, D. & Scharmann, A. 1979 Some evidence for the existence and magnitude of a critical Marangoni number for the onset of oscillatory flow in crystal growth melts. J. Cryst. Growth 46, 125–131.CrossRefGoogle Scholar
Scriven, L. E. & Sternling, C. V. 1960 The Marangoni effects. Nature 187, 186–188.CrossRefGoogle Scholar
Squires, T. M. & Quake, S. R. 2005 Microfluidics: fluid physics at the nanoliter scale. Rev. Mod. Phys. 77, 977–1026.CrossRefGoogle Scholar
Struik, D. J. 1961 Lectures on Classical Differential Geometry. Addison-Wesley.Google Scholar
Teng, H., Cheng, P. & Zhao, T. S. 1999 Instability of condensate film and capillary blocking in small-diameter-thermosyphon condensers. Intl J. Heat Mass Transfer 42, 3071–3083.CrossRefGoogle Scholar
Thomson, J. 1855 On certain curious motions observable at the surfaces of wine and other alcoholic liquors. Phil. Mag. 10, 330–333.CrossRefGoogle Scholar
Thoroddsen, S. T., Etoh, T. G., Takehara, K. & Ootsuka, N. 2005 On the coalescence speed of bubbles. Phys. Fluids 17, 071703.CrossRefGoogle Scholar
Thoroddsen, S. T., Etoh, T. G. & Takehara, K. 2007 Experiments on bubble pinch-off. Phys. Fluids 19, 042101.CrossRefGoogle Scholar
Varanakkottu, S. N., George, S., Baier, T., Hardt, S., Ewald, M. & Biesalski, M. 2013 Particle manipulation based on optically controlled free surface hydrodynamics. Angew. Chem. Intl Ed. Engl. 52, 7291–7295.CrossRefGoogle ScholarPubMed
Venerus, D. C. & Simavilla, D. N. 2015 Tears of wine: new insights on an old phenomenon. Sci. Rep. 5, 16162.Google ScholarPubMed
Wodlei, F., Sebilleau, J., Magnaudet, J. & Pimienta, V. 2018 Marangoni-driven flower-like patterning of an evaporating drop spreading on a liquid substrate. Nat. Commun. 9, 820.CrossRefGoogle ScholarPubMed
Yamamoto, D., Nakajima, C., Shioi, A., Krafft, M. P. & Yoshikawa, K. 2015 The evolution of spatial ordering of oil drops fast spreading on a water surface. Nat. Commun. 6, 7189.CrossRefGoogle ScholarPubMed
Yang, L. & Homsy, G. M. 2006 Steady three-dimensional thermocapillary flows and dryout inside a V-shaped wedge. Phys. Fluids 18, 042107.CrossRefGoogle Scholar
Zhang, H., Nikolov, A., Feng, J. & Wasan, D. 2016 The dynamics of the annular liquid layer inside a cylindrical capillary. Phys. Fluids 28, 024107.CrossRefGoogle Scholar

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