Spreading and retraction dynamics of sessile evaporating droplets comprising volatile binary mixtures. (English) Zbl 1461.76449

Summary: The dynamics of thin volatile droplets comprising of binary mixtures deposited on a heated substrate are investigated. Using lubrication theory, we develop a novel one-sided model to predict the spreading and retraction of an evaporating sessile axisymmetric droplet formed of a volatile binary mixture on a substrate with high wettability. A thin droplet with a moving contact line is considered, taking into account the variation of liquid properties with concentration as well as the effects of inertia. The parameter space is explored and the resultant effects on wetting and evaporation are evaluated. Increasing solutal Marangoni stress enhances spreading rates in all cases, approaching those of superspreading liquids. To validate our model, experiments are conducted with binary ethanol-water droplets spreading on hydrophilic glass slides heated from below. The spreading rate is quantified, revealing that preferential evaporation of the more volatile component (ethanol) at the contact line drives superspreading, leading in some cases to a contact line instability. Good qualitative agreement is found between our model and experiments, with quantitative agreement being achieved in terms of spreading rate.


76T06 Liquid-liquid two component flows
76D45 Capillarity (surface tension) for incompressible viscous fluids
76R05 Forced convection


Full Text: DOI arXiv


[1] Abe, Y., Iwasaki, A. & Tanaka, K.2004Microgravity experiments on phase change of self-rewetting fluids. Ann. N.Y. Acad. Sci.1027, 269-285.
[2] Ajaev, V. S.2005Spreading of thin volatile liquid droplets on uniformly heated surfaces. J. Fluid Mech.528, 279-296. · Zbl 1165.76313
[3] Anderson, D. M. & Davis, S. H.1995The spreading of volatile liquid droplets on heated surfaces. Phys. Fluids7, 248-265. · Zbl 0843.76016
[4] Bar-Cohen, A., Arik, M. & Ohadi, M.2006Direct liquid cooling of high flux micro and nano electronic components. Proc. IEEE94 (8), 1549-1570.
[5] Bennacer, R. & Sefiane, K.2014Vortices, dissipation and flow transition in volatile binary drops. J. Fluid Mech.749, 649-665.
[6] Berthier, J.2013 Theory of wetting. In Micro-Drops and Digital Microfluidics, 2nd edn (ed. J. Berthier), Micro and Nano Technologies, chap. 2, pp. 7-73. William Andrew.
[7] Bonn, D., Eggers, J., Indekeu, J., Meunier, J. & Rolley, E.2009Wetting and spreading. Rev. Mod. Phys.81 (2), 739-805.
[8] Bourges-Monnier, C. & Shanahan, M. E. R.1995Influence of evaporation on contact angle. Langmuir11 (7), 2820-2829.
[9] Brutin, D., Sobac, B., Loquet, B. & Sampol, J.2011Pattern formation in drying drops of blood. J. Fluid Mech.667, 85-95. · Zbl 1225.76007
[10] Burelbach, J. P., Bankoff, S. G. & Davis, S. H.1988Nonlinear stability of evaporating condensing liquid-films. J. Fluid Mech.195, 463-494. · Zbl 0653.76035
[11] Cachile, M., Be, O. & Cazabat, A. M.2002aEvaporating droplets of completely wetting liquids. Langmuir18 (15), 7985-7990.
[12] Cachile, M., Benichou, O., Poulard, C. & Cazabat, A. M.2002bEvaporating droplets. Langmuir18 (21), 8070-8078.
[13] Calvert, P.2001Inkjet printing for materials and devices. Chem. Mater.13 (10), 3299-3305.
[14] Cazabat, A. M. & Cohen Stuart, M. A.1986Dynamics of wettlng: effects of surface roughness. J. Phys. Chem.90 (22), 5845-5849.
[15] Chen, J. D.1988Experiments on a spreading drop and its contact angle on a solid. J. Colloid Interface Sci.122 (1), 60-72.
[16] Chen, J. D. & Wada, N.1989Wetting dynamics of the edge of a spreading drop. Phys. Rev. Lett.62 (26), 3050-3054.
[17] Chen, R., Zhang, L., Zang, D. & Shen, W.2016Blood drop patterns: formation and applications. Adv. Colloid Interface Sci.231, 1-14.
[18] Chen, Y., He, B., Lee, J. & Patankar, N. A.2005Anisotropy in the wetting of rough surfaces. J. Colloid Interface Sci.281 (2), 458-464.
[19] Christy, J. R. E., Hamamoto, Y. & Sefiane, K.2011Flow transition within an evaporating binary mixture sessile drop. Phys. Rev. Lett.106 (20), 205701.
[20] Christy, J. R. E., Sefiane, K. & Munro, E.2010A study of the velocity field during evaporation of sessile water and water/ethanol drops. J. Bionic Engng7 (4), 321-328.
[21] Damak, M., Mahmoudi, S. R., Hyder, N. & Varanasi, K. K.2016Enhancing droplet deposition through in-situ precipitation. Nat. Commun.7, 12560.
[22] Deegan, R. D., Bakajin, O., Dupont, T. F., Huber, G., Nagel, S. R. & Witten, T. A.1997Capillary flow as the cause of ring stains from dried liquid drops. Nature389 (6653), 827-829.
[23] Deegan, R. D., Bakajin, O., Dupont, T. F., Huber, G., Nagel, S. R. & Witten, T. A.2000Contact line deposits in an evaporating drop. Phys. Rev. E62 (1), 756-765.
[24] Deng, W. & Gomez, A.2011Electrospray cooling for microelectronics. Intl J. Heat Mass Transfer54 (11-12), 2270-2275.
[25] Diddens, C.2017Detailed finite element method modeling of evaporating multi-component droplets. J. Comput. Phys.340, 670-687.
[26] Diddens, C., Kuerten, J. G. M., Van Der Geld, C. W. M. & Wijshoff, H. M. A.2017Modeling the evaporation of sessile multi-component droplets. J. Colloid Interface Sci.487, 426-436.
[27] Dunn, G. J., Wilson, S. K., Duffy, B. R., David, S. & Sefiane, K.2009The strong influence of substrate conductivity on droplet evaporation. J. Fluid Mech.623, 329-351. · Zbl 1157.76303
[28] Ehrhard, P.1993Experiments on isothermal and non-isothermal spreading. J. Fluid Mech.257, 463-483.
[29] Ehrhard, P. & Davis, S. H.1991Non-isothermal spreading of liquid drops on horizontal plates. J. Fluid Mech.229, 365-388. · Zbl 0850.76760
[30] Extrand, C. W. & Moon, S. I.2010When sessile drops are no longer small: transitions from spherical to fully flattened. Langmuir76 (23), 11815-11822.
[31] Fukatani, Y., Orejon, D., Kita, Y., Takata, Y., Kim, J. & Sefiane, K.2016Effect of ambient temperature and relative humidity on interfacial temperature during early stages of drop evaporation. Phys. Rev. E93 (4), 043103.
[32] De Gennes, P. G.1985Wetting: statics and dynamics. Rev. Mod. Phys.57 (3), 827-863.
[33] Girard, F. & Antoni, M.2008Influence of substrate heating on the evaporation dynamics of pinned water droplets. Langmuir24 (20), 11342-11345.
[34] Gotkis, Y., Ivanov, I., Murisic, N. & Kondic, L.2006Dynamic structure formation at the fronts of volatile liquid drops. Phys. Rev. Lett.97 (18), 1-4.
[35] Guéna, G., Poulard, C. & Cazabat, A. M.2007Evaporating drops of alkane mixtures. Colloids Surf. A298 (1-2), 2-11. · Zbl 1161.76464
[36] Hu, H. & Larson, R. G.2002Evaporation of a sessile droplet on a substrate. J. Phys. Chem. B106 (6), 1334-1344.
[37] Hu, H. & Larson, R. G.2006Marangoni effect reverses coffee-ring depositions. J. Phys. Chem. B110 (14), 7090-7094.
[38] Karapetsas, G., Craster, R. V. & Matar, O. K.2011On surfactant-enhanced spreading and superspreading of liquid drops on solid surfaces. J. Fluid Mech.670, 5-37. · Zbl 1225.76040
[39] Karapetsas, G., Matar, O. K., Valluri, P. & Sefiane, K.2012Convective rolls and hydrothermal waves in evaporating sessile drops. Langmuir28, 11433-11439.
[40] Karapetsas, G., Sáenz, P. J., Sefiane, K., Valluri, P. & Matar, O. K.2010 Numerical study of the evaporation of sessile drops: formation of hydrothermal waves. In 63nd Annu. Meet. APS Div. Fluid Dyn., p. 65. American Physical Society.
[41] Keiser, L., Bense, H., Colinet, P., Bico, J. & Reyssat, E.2017Marangoni bursting: evaporation-induced emulsification of binary mixtures on a liquid layer. Phys. Rev. Lett.118 (7), 1-5.
[42] Kim, J.2007Spray cooling heat transfer: the state of the art. Intl J. Heat Fluid Flow28 (4), 753-767.
[43] Knudsen, M.1950The Kinetic Theory of Gases: Some Modern Aspects. Methuen and Company. · JFM 60.1420.10
[44] Larson, R. G.2014Transport and deposition patterns in drying sessile droplets. AIChE J.60, 1538-1571.
[45] Li, Y., Lv, P., Diddens, C., Tan, H., Wijshoff, H., Versluis, M. & Lohse, D.2018Evaporation-triggered segregation of sessile binary droplets. Phys. Rev. Lett.120 (22), 224501.
[46] Liu, C., Bonaccurso, E. & Butt, H.-J.2008Evaporation of sessile water/ethanol drops in a controlled environment. Phys. Chem. Chem. Phys.10 (47), 7150-7157.
[47] Mamalis, D., Koutsos, V. & Sefiane, K.2018Nonisothermal spreading dynamics of self-rewetting droplets. Langmuir34, 1916-1931.
[48] Matar, O. K.2002Nonlinear evolution of thin free viscous films in the presence of soluble surfactant. Phys. Fluids14 (12), 4216-4234. · Zbl 1185.76245
[49] Moosman, S. & Homsy, G. M.1980Evaporating menisci of wetting fluids. J. Colloid Interface Sci.73 (1), 212-223.
[50] Mouat, A. P., Wood, C. E., Pye, J. E. & Burton, J. C.2020Tuning contact line dynamics and deposition patterns in volatile liquid mixtures. Phys. Rev. Lett.124, 064502.
[51] Murisic, N. & Kondic, L.2011On evaporation of sessile drops with moving contact lines. J. Fluid Mech.679, 219-246. · Zbl 1241.76383
[52] Nakae, H., Inui, R., Hirata, Y. & Saito, H.1998Effects of surface roughness on wettability. Acta Mater.46 (7), 2313-2318.
[53] Parsa, M., Harmand, S., Sefiane, K., Bigerelle, M. & Deltombe, R.2015Effect of substrate temperature on pattern formation of nanoparticles from volatile drops. Langmuir31 (11), 3354-3367.
[54] Persad, A. H. & Ward, C. A.2016Expressions for the evaporation and condensation coefficients in the Hertz-Knudsen relation. Chem. Rev.116 (14), 7727-7767.
[55] Picknett, R. G. & Bexton, R.1977The evaporation of sessile or pendant drops in still air. J. Colloid Interface Sci.61 (2), 336-350.
[56] Plesset, M. S. & Prosperetti, A.1976Flow of vapour in a liquid enclosure. J. Fluid Mech.78 (3), 433-444. · Zbl 0356.76019
[57] Poulard, C., Bénichou, O. & Cazabat, A. M.2003Freely receding evaporating droplets. Langmuir19 (21), 8828-8834.
[58] 2013 R: A language and environment for statistical computing.
[59] Rafaï, S, Sarker, D., Bergeron, V., Meunier, J. & Bonn, D.2002Superspreading: aqueous surfactant drops spreading on hydrophobic surfaces. Langmuir18 (26), 10486-10488.
[60] Ristenpart, W. D., Kim, P. G., Domingues, C., Wan, J. & Stone, H. A.2007Influence of substrate conductivity on circulation reversal in evaporating drops. Phys. Rev. Lett.99 (23), 234502.
[61] Sáenz, P. J., Sefiane, K., Kim, J., Matar, O. K. & Valluri, P.2015Evaporation of sessile drops: a three-dimensional approach. J. Fluid Mech.772, 705-739.
[62] Sáenz, P. J., Wray, A. W., Che, Z., Matar, O. K., Valluri, P., Kim, J. & Sefiane, K.2017Dynamics and universal scaling law in geometrically-controlled sessile drop evaporation. Nat. Commun.8, 14783.
[63] Scriven, L. E. & Sternling, C. V.1960The Marangoni effects. Nature187 (4733), 186-188.
[64] Sefiane, K.2010On the formation of regular patterns from drying droplets and their potential use for bio-medical applications. J. Bionic Engng7, S82-S93.
[65] Sefiane, K., David, S. & Shanahan, M. E. R.2008aWetting and evaporation of binary mixture drops. J. Phys. Chem. B112 (36), 11317-11323.
[66] Sefiane, K., Moffat, J. R., Matar, O. K. & Craster, R. V.2008bSelf-excited hydrothermal waves in evaporating sessile drops. Appl. Phys. Lett.93 (7), 074103.
[67] Sefiane, K., Steinchen, A. & Moffat, R.2010On hydrothermal waves observed during evaporation of sessile droplets. Colloids Surf. A365 (1-3), 95-108.
[68] Sefiane, K., Tadrist, L. & Douglas, M.2003Experimental study of evaporating water-ethanol mixture sessile drop: influence of concentration. Intl J. Heat Mass Transfer46 (23), 4527-4534.
[69] Sefiane, K., Wilson, S. K., David, S., Dunn, G. J. & Duffy, B. R.2009On the effect of the atmosphere on the evaporation of sessile droplets of water. Phys. Fluids21 (6), 062101. · Zbl 1183.76463
[70] Semenov, S., Trybala, A., Rubio, R. G., Kovalchuk, N., Starov, V. & Velarde, M. G.2014Simultaneous spreading and evaporation: recent developments. Adv. Colloid Interface Sci.206, 382-398.
[71] Shahidzadeh-Bonn, N., Rafaï, S., Azouni, A. & Bonn, D.2006Evaporating droplets. J. Fluid Mech.549, 307-313.
[72] Singh, M., Haverinen, H. M., Dhagat, P. & Jabbour, G. E.2010Inkjet printing – process and its applications. Adv. Mater.22 (6), 673-685.
[73] Siregar, D. P., Kuerten, J. G. M. & Van Der Geld, C. W. M.2013Numerical simulation of the drying of inkjet-printed droplets. J. Colloid Interface Sci.392, 388-395.
[74] Sobac, B. & Brutin, D.2012Thermal effects of the substrate on water droplet evaporation. Phys. Rev. E86, 021602. · Zbl 1275.76011
[75] Srinivasan, S., Mckinley, G. H. & Cohen, R. E.2011Assessing the accuracy of contact angle measurements for sessile drops on liquid-repellent surfaces. Langmuir27 (22), 13582-13589.
[76] Starov, V. & Sefiane, K.2009On evaporation rate and interfacial temperature of volatile sessile drops. Colloids Surf. A333 (1-3), 170-174.
[77] Sultan, E., Boudaoud, A. & Ben Amar, M.2005Evaporation of a thin film: diffusion of the vapour and Marangoni instabilities. J. Fluid Mech.543, 183-202. · Zbl 1088.76013
[78] Tan, H., Diddens, C., Lv, P., Kuerten, J. G. M., Zhang, X. & Lohse, D.2016Evaporation-triggered microdroplet nucleation and the four life phases of an evaporating Ouzo drop. Proc. Natl Acad. Sci. USA113 (31), 8642-8647. · Zbl 1423.76480
[79] Theodorakis, P. E., Müller, E. A., Craster, R. V. & Matar, O. K.2015Superspreading: mechanisms and molecular design. Langmuir31 (8), 2304-2309.
[80] Williams, A. G. L.2018 Evaporation of binary liquids: planar layers and sessile drops. PhD thesis, University of Edinburgh.
[81] Winkels, K. G., Weijs, J. H., Eddi, A. & Snoeijer, J. H.2012Initial spreading of low-viscosity drops on partially wetting surfaces. Phys. Rev. E85, 055301.
[82] Yu, Y., Zhu, H., Frantz, J. M., Reding, M. E., Chan, K. C. & Ozkan, H. E.2009Evaporation and coverage area of pesticide droplets on hairy and waxy leaves. Biosyst. Engng104 (3), 324-334.
[83] Zhong, X. & Duan, F.2016Flow regime and deposition pattern of evaporating binary mixture droplet suspended with particles. Eur. Phys. J. E39 (2), 18.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.