Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-26T20:12:22.792Z Has data issue: false hasContentIssue false
  • English
  • Français

Evaporation of sessile drops: a three-dimensional approach

Published online by Cambridge University Press:  08 May 2015

P. J. Sáenz Open the ORCID record for P. J. Sáenz [Opens in a new window] ,
K. Sefiane ,
J. Kim ,
O. K. Matar  and
P. Valluri
P. J. Sáenz
Affiliation:
Institute for Materials and Processes, The University of Edinburgh, Edinburgh EH9 3JL, UK
K. Sefiane
Affiliation:
Institute for Materials and Processes, The University of Edinburgh, Edinburgh EH9 3JL, UK International Institute for Carbon-Neutral Energy Research (I2CNER), Kyushu University, Fukuoka 819-0395, Japan
J. Kim
Affiliation:
Department of Mechanical Engineering, The University of Maryland, College Park, MD 20742, USA
O. K. Matar
Affiliation:
Department of Chemical Engineering, Imperial College London, London, SW7 2AZ, UK
P. Valluri*
Affiliation:
Institute for Materials and Processes, The University of Edinburgh, Edinburgh EH9 3JL, UK
*
†Email address for correspondence: prashant.valluri@ed.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

The evaporation of non-axisymmetric sessile drops is studied by means of experiments and three-dimensional direct numerical simulations (DNS). The emergence of azimuthal currents and pairs of counter-rotating vortices in the liquid bulk flow is reported in drops with non-circular contact area. These phenomena, especially the latter, which is also observed experimentally, are found to play a critical role in the transient flow dynamics and associated heat transfer. Non-circular drops exhibit variable wettability along the pinned contact line sensitive to the choice of system parameters, and inversely dependent on the local contact-line curvature, providing a simple criterion for estimating the approximate contact-angle distribution. The evaporation rate is found to vary in the same order of magnitude as the liquid–gas interfacial area. Furthermore, the more complex case of drops evaporating with a moving contact line (MCL) in the constant contact-angle mode is addressed. Interestingly, the numerical results demonstrate that the average interface temperature remains essentially constant as the drop evaporates in the constant-angle (CA) mode, while this increases in the constant-radius (CR) mode as the drops become thinner. It is therefore concluded that, for increasing substrate heating, the evaporation rate increases more rapidly in the CR mode than in the CA mode. In other words, the higher the temperature the larger the difference between the lifetimes of an evaporating drop in the CA mode with respect to that evaporating in the CR mode.

JFM classification

Phase change: Condensation/evaporation Drops and Bubbles: Drops and Bubbles Multiphase and Particle-laden Flows: Multiphase flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 772 , 10 June 2015 , pp. 705 - 739
Check for updates
Copyright
© 2015 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ajaev, V. S. 2005 Spreading of thin volatile liquid droplets on uniformly heated surfaces. J. Fluid Mech. 528, 279–296.CrossRefGoogle Scholar
Anderson, D. M. & Davis, S. H. 1995 The spreading of volatile liquid droplets on heated surfaces. Phys. Fluids 7 (2), 248–265.CrossRefGoogle Scholar
Anderson, D. M., McFadden, G. B. & Wheeler, A. A. 1998 Diffuse-interface methods in fluid mechanics. Annu. Rev. Fluid Mech. 30, 139–165.CrossRefGoogle Scholar
Ascher, U. M., Ruuth, S. J. & Wetton, B. T. R. 1995 Implicit explicit methods for time-dependent partial differential equations. SIAM J. Numer. Anal. 32 (3), 797–823.CrossRefGoogle Scholar
Badalassi, V. E., Ceniceros, H. D. & Banerjee, S. 2003 Computation of multiphase systems with phase field models. J. Comput. Phys. 190 (2), 371–397.CrossRefGoogle Scholar
Birdi, K. S., Vu, D. T. & Winter, A. 1989 A study of the evaporation rates of small water drops placed on a solid surface. J. Phys. Chem. 93 (9), 3702–3703.CrossRefGoogle Scholar
Bourgès-Monnier, C. & Shanahan, M. E. R. 1995 Influence of evaporation on contact angle. Langmuir 11 (7), 2820–2829.CrossRefGoogle Scholar
Burelbach, J. P., Bankoff, S. G. & Davis, S. H. 1988 Nonlinear stability of evaporating/condensing liquid films. J. Fluid Mech. 195, 463–494.CrossRefGoogle Scholar
Cahn, J. W. 1961 On spinodal decomposition. Acta Metall. 9 (9), 795–801.CrossRefGoogle Scholar
Cahn, J. W. & Hilliard, J. E. 1958 Free energy of a nonuniform system. Part 1. Interfacial free energy. J. Chem. Phys. 28 (2), 258–267.CrossRefGoogle Scholar
Cahn, J. W. & Hilliard, J. E. 1959 Free energy of a nonuniform system. Part 3. Nucleation in a two-component incompressible fluid. J. Chem. Phys. 31 (3), 688–699.CrossRefGoogle Scholar
Carlson, A., Do-Quang, M. & Amberg, G. 2009 Modeling of dynamic wetting far from equilibrium. Phys. Fluids 21 (12), 121701.CrossRefGoogle Scholar
Cazabat, A. M. & Guena, G. 2010 Evaporation of macroscopic sessile droplets. Soft Matt. 6 (12), 2591–2612.CrossRefGoogle Scholar
Crafton, E. F. & Black, W. Z. 2004 Heat transfer and evaporation rates of small liquid droplets on heated horizontal surfaces. Intl J. Heat Mass Transfer 47 (6–7), 1187–1200.CrossRefGoogle Scholar
David, S., Sefiane, K. & Tadrist, L. 2007 Experimental investigation of the effect of thermal properties of the substrate in the wetting and evaporation of sessile drops. Colloids Surf. A 298 (1–2), 108–114.CrossRefGoogle Scholar
Deegan, R. D., Bakajin, O., Dupont, T. F., Huber, G., Nagel, S. R. & Witten, T. A. 1997 Capillary flow as the cause of ring stains from dried liquid drops. Nature 389 (6653), 827–829.CrossRefGoogle Scholar
Deegan, R. D., Bakajin, O., Dupont, T. F., Huber, G., Nagel, S. R. & Witten, T. A. 2000 Contact line deposits in an evaporating drop. Phys. Rev. E 62 (1), 756–765.CrossRefGoogle Scholar
Ding, H., Gilani, M. N. H. & Spelt, P. D. M. 2010 Sliding, pinch-off and detachment of a droplet on a wall in shear flow. J. Fluid Mech. 644, 217–244.CrossRefGoogle Scholar
Ding, H. & Spelt, P. D. M. 2007a Inertial effects in droplet spreading: a comparison between diffuse-interface and level-set simulations. J. Fluid Mech. 576, 287–296.CrossRefGoogle Scholar
Ding, H. & Spelt, P. D. M. 2007b Wetting condition in diffuse interface simulations of contact line motion. Phys. Rev. E 75 (4), 046708.CrossRefGoogle ScholarPubMed
Ding, H. & Spelt, P. D. M. 2008 Onset of motion of a three-dimensional droplet on a wall in shear flow at moderate Reynolds numbers. J. Fluid Mech. 599, 341–362.CrossRefGoogle Scholar
Ding, H., Spelt, P. D. M. & Shu, C. 2007 Diffuse interface model for incompressible two-phase flows with large density ratios. J. Comput. Phys. 226 (2), 2078–2095.CrossRefGoogle Scholar
Dunn, G. J., Wilson, S. K., Duffy, B. R., David, S. & Sefiane, K. 2009 The strong influence of substrate conductivity on droplet evaporation. J. Fluid Mech. 623, 329–351.CrossRefGoogle Scholar
Erbil, H. Y. 2012 Evaporation of pure liquid sessile and spherical suspended drops: a review. Adv. Colloid Interface Sci. 170 (1–2), 67–86.CrossRefGoogle ScholarPubMed
Erbil, H. Y., McHale, G. & Newton, M. I. 2002 Drop evaporation on solid surfaces: constant contact angle mode. Langmuir 18 (7), 2636–2641.CrossRefGoogle Scholar
Fang, G. & Ward, C. 1999 Temperature measured close to the interface of an evaporating liquid. Phys. Rev. E 59 (1), 417–428.CrossRefGoogle Scholar
Gatapova, E. Y., Semenova, A. A., Zaitsev, D. V. & Kabov, O. A. 2014 Evaporation of a sessile water drop on a heated surface with controlled wettability. Colloids Surf. A 441, 776–785.CrossRefGoogle Scholar
Girard, F. & Antoni, M. 2008 Influence of substrate heating on the evaporation dynamics of pinned water droplets. Langmuir 24 (20), 11342–11345.CrossRefGoogle ScholarPubMed
Girard, F., Antoni, M., Faure, S. & Steinchen, A. 2006 Evaporation and Marangoni driven convection in small heated water droplets. Langmuir 22 (26), 11085–11091.CrossRefGoogle ScholarPubMed
Girard, F., Antoni, M., Faure, S. & Steinchen, A. 2008a Influence of heating temperature and relative humidity in the evaporation of pinned droplets. Colloids Surf. A 323 (1–3), 36–49.CrossRefGoogle Scholar
Girard, F., Antoni, M. & Sefiane, K. 2008b On the effect of Marangoni flow on evaporation rates of heated water drops. Langmuir 24 (17), 9207–9210.CrossRefGoogle ScholarPubMed
Hu, H. & Larson, R. G. 2002 Evaporation of a sessile droplet on a substrate. J. Phys. Chem. B 106 (6), 1334–1344.CrossRefGoogle Scholar
Hu, H. & Larson, R. G. 2005a Analysis of the effects of Marangoni stresses on the microflow in an evaporating sessile droplet. Langmuir 21 (9), 3972–3980.CrossRefGoogle Scholar
Hu, H. & Larson, R. G. 2005b Analysis of the microfluid flow in an evaporating sessile droplet. Langmuir 21 (9), 3963–3971.CrossRefGoogle Scholar
Hu, H. & Larson, R. G. 2006 Marangoni effect reverses coffee-ring depositions. J. Phys. Chem. B 110 (14), 7090–7094.CrossRefGoogle ScholarPubMed
Jacqmin, D. 1999 Calculation of two-phase Navier–Stokes flows using phase-field modeling. J. Comput. Phys. 155 (1), 96–127.CrossRefGoogle Scholar
Jacqmin, D. 2000 Contact-line dynamics of a diffuse fluid interface. J. Fluid Mech. 402, 57–88.CrossRefGoogle Scholar
Jansen, H. P., Zandvliet, H. J. W. & Kooij, E. S. 2015 Evaporation of elongated droplets on chemically stripe-patterned surfaces. Intl J. Heat Mass Transfer 82, 537–544.CrossRefGoogle Scholar
Karapetsas, G., Matar, O. K., Valluri, P. & Sefiane, K. 2012 Convective rolls and hydrothermal waves in evaporating sessile drops. Langmuir 28 (31), 11433–11439.CrossRefGoogle ScholarPubMed
Kim, T. H., Kommer, E., Dessiatoun, S. & Kim, J. 2012 Measurement of two-phase flow and heat transfer parameters using infrared thermometry. Intl J. Multiphase Flow 40, 56–67.CrossRefGoogle Scholar
Liu, X. D., Osher, S. & Chan, T. 1994 Weighted essentially nonoscillatory schemes. J. Comput. Phys. 115 (1), 200–212.CrossRefGoogle Scholar
Moffat, J. R., Sefiane, K. & Shanahan, M. E. R. 2009 Effect of $\text{TiO}_{2}$ nanoparticles on contact line stick–slip behavior of volatile drops. J. Phys. Chem. B 113 (26), 8860–8866.CrossRefGoogle Scholar
Mollaret, R., Sefiane, K., Christy, J. R. E. & Veyret, D. 2004 Experimental and numerical investigation of the evaporation into air of a drop on a heated surface. Chem. Engng Res. Des. 82 (A4), 471–480.CrossRefGoogle Scholar
Murisic, N. & Kondic, L. 2011 On evaporation of sessile drops with moving contact lines. J. Fluid Mech. 679, 219–246.CrossRefGoogle Scholar
Nguyen, T. A. H. & Nguyen, A. V. 2012 Increased evaporation kinetics of sessile droplets by using nanoparticles. Langmuir 28 (49), 16725–16728.CrossRefGoogle ScholarPubMed
Nguyen, T. A. H., Nguyen, A. V., Hampton, M. A., Xu, Z. P., Huang, L. B. & Rudolph, V. 2012 Theoretical and experimental analysis of droplet evaporation on solid surfaces. Chem. Engng Sci. 69 (1), 522–529.CrossRefGoogle Scholar
Orejon, D., Sefiane, K. & Shanahan, M. E. R. 2011 Stick–slip of evaporating droplets: substrate hydrophobicity and nanoparticle concentration. Langmuir 27 (21), 12834–12843.CrossRefGoogle ScholarPubMed
Picknett, R. G. & Bexon, R. 1977 Evaporation of sessile or pendant drops in still air. J. Colloid Interface Sci. 61 (2), 336–350.CrossRefGoogle Scholar
Poulard, C., Benichou, O. & Cazabat, A. M. 2003 Freely receding evaporating droplets. Langmuir 19 (21), 8828–8834.CrossRefGoogle Scholar
Qian, T. Z., Wang, X. P. & Sheng, P. 2006 A variational approach to moving contact line hydrodynamics. J. Fluid Mech. 564, 333–360.CrossRefGoogle Scholar
Ristenpart, W. D., Kim, P. G., Domingues, C., Wan, J. & Stone, H. A. 2007 Influence of substrate conductivity on circulation reversal in evaporating drops. Phys. Rev. Lett. 99 (23), 234502.CrossRefGoogle ScholarPubMed
Rowan, S. M., Newton, M. I. & McHale, G. 1995 Evaporation of microdroplets and the wetting of solid surfaces. J. Phys. Chem. 99 (35), 13268–13271.CrossRefGoogle Scholar
Ruiz, O. E. & Black, W. Z. 2002 Evaporation of water droplets placed on a heated horizontal surface. Trans. ASME J. Heat Transfer 124 (5), 854–863.CrossRefGoogle Scholar
Sáenz, P. J., Valluri, P., Sefiane, K., Karapetsas, G. & Matar, O. K. 2014 On phase change in Marangoni-driven flows and its effects on the hydrothermal-wave instabilities. Phys. Fluids 26 (2), 024114.CrossRefGoogle Scholar
Sefiane, K. & Bennacer, R. 2011 An expression for droplet evaporation incorporating thermal effects. J. Fluid Mech. 667, 260–271.CrossRefGoogle Scholar
Sefiane, K., Moffat, J. R., Matar, O. K. & Craster, R. V. 2008 Self-excited hydrothermal waves in evaporating sessile drops. Appl. Phys. Lett. 93 (7), 074103.CrossRefGoogle Scholar
Sefiane, K. & Tadrist, L. 2006 Experimental investigation of the de-pinning phenomenon on rough surfaces of volatile drops. Intl Commun. Heat Mass Transfer 33 (4), 482–490.CrossRefGoogle Scholar
Sefiane, K., Wilson, S. K., David, S., Dunn, G. J. & Duffy, B. R. 2009 On the effect of the atmosphere on the evaporation of sessile droplets of water. Phys. Fluids 21 (6), 062101.CrossRefGoogle Scholar
Seppecher, P. 1996 Moving contact lines in the Cahn–Hilliard theory. Intl J. Engng Sci. 34 (9), 977–992.CrossRefGoogle Scholar
Shanahan, M. E. R. 1995 Simple theory of stick–slip wetting hysteresis. Langmuir 11 (3), 1041–1043.CrossRefGoogle Scholar
Shanahan, M. E. R., Sefiane, K. & Moffat, J. R. 2011 Dependence of volatile droplet lifetime on the hydrophobicity of the substrate. Langmuir 27 (8), 4572–4577.CrossRefGoogle ScholarPubMed
Sobac, B. & Brutin, D. 2012 Thermal effects of the substrate on water droplet evaporation. Phys. Rev. E 86 (2), 021602.CrossRefGoogle ScholarPubMed
Stauber, J. M., Wilson, S. K., Duffy, B. R. & Sefiane, K. 2014 On the lifetimes of evaporating droplets. J. Fluid Mech. 744, R2.CrossRefGoogle Scholar
Sui, Y., Ding, H. & Spelt, P. D. M. 2014 Numerical simulations of flows with moving contact lines. Annu. Rev. Fluid Mech. 46 (1), 97–119.CrossRefGoogle Scholar
Valluri, P., Naraigh, L. O., Ding, H. & Spelt, P. D. M. 2010 Linear and nonlinear spatio-temporal instability in laminar two-layer flows. J. Fluid Mech. 656, 458–480.CrossRefGoogle Scholar
van der Waals, J. D. 1979 The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density. J. Stat. Phys. 20 (2), 197–200.CrossRefGoogle Scholar
Ward, C. & Fang, G. 1999 Expression for predicting liquid evaporation flux: statistical rate theory approach. Phys. Rev. E 59 (1), 429–440.CrossRefGoogle Scholar
Xu, X. F. & Luo, J. B. 2007 Marangoni flow in an evaporating water droplet. Appl. Phys. Lett. 91 (12), 124102.CrossRefGoogle Scholar
Yang, K., Hong, F. & Cheng, P. 2014 A fully coupled numerical simulation of sessile droplet evaporation using arbitrary Lagrangian–Eulerian formulation. Intl J. Heat Mass Transfer 70, 409–420.CrossRefGoogle Scholar
Yue, P. T., Zhou, C. F. & Feng, J. J. 2010 Sharp-interface limit of the Cahn–Hilliard model for moving contact lines. J. Fluid Mech. 645, 279–294.CrossRefGoogle Scholar