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A Mesoscale Modeling of Wetting: Theory and Numerical Simulations

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The Surface Wettability Effect on Phase Change

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Abstract

This chapter illustrates a mesoscale, Diffuse Interface (DI), modeling of liquid-vapor systems close to solid surfaces. The model is built upon the Square Gradient Approximation (SGA) of the more general Density Functional Theory (DFT), to take into account the wetting properties of the solid surfaces and dynamic conditions. The formal derivation of the fluid-solid interaction potential is here reviewed, showing the connection with the Young-Laplace laws [40, 76] for sufficiently large bubbles/drops. The final section shows how the model can be numerically exploited to address the heterogeneous bubble nucleation process, including the description of thermal fluctuations into the model. Bubbles spontaneously appear during the simulation thanks to the fluid fluctuations, instead of being ad-hoc patched in the initial condition, allowing the statistical analysis of the nucleation process in terms of nucleation rate and spatial distribution. This opens the route for a multiscale simulation strategy, providing a continuum framework bridging the gap between the Molecular Dynamics (MD) simulations and the macroscopic Computational Fluid Dynamics (CFD).

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References

  1. Anderson, D., McFadden, G., & Wheeler, A. (1998). Diffuse-interface methods in fluid mechanics. Annual Review of Fluid Mechanics, 30, 139–165.

    Article  MathSciNet  MATH  Google Scholar 

  2. Balboa, F., Bell, J. B., Delgado-Buscalioni, R., Donev, A., Fai, T. G., Griffith, B. E., & Peskin, C. S. (2012). Staggered schemes for fluctuating hydrodynamics. Multiscale Modeling & Simulation, 10, 1369–1408.

    Article  MathSciNet  MATH  Google Scholar 

  3. Belardinelli, D., Sbragaglia, M., Gross, M., & Andreotti, B. (2016). Thermal fluctuations of an interface near a contact line. Physical Review E, 94, 052803.

    Google Scholar 

  4. Bergeron, V., Bonn, D., Martin, J. Y., & Vovelle, L. (2000). Controlling droplet deposition with polymer additives. Nature, 405, 772–775.

    Article  Google Scholar 

  5. Bourdon, B., Rioboo, R., Marengo, M., Gosselin, E., & De Coninck, J. (2012). Influence of the wettability on the boiling onset. Langmuir, 28, 1618–1624.

    Article  Google Scholar 

  6. Box, G., Muller, M. E. et al. (1958). A note on the generation of random normal deviates. The Annals of Mathematical Statistics, 29, 610–611.

    Article  MATH  Google Scholar 

  7. Braga, C., Smith, E. R., Nold, A., Sibley, D. N., & Kalliadasis, S. (2018). The pressure tensor across a liquid-vapour interface. The Journal of chemical physics, 149, 044705.

    Google Scholar 

  8. Buff, F., Lovett, R., & Stillinger Jr, F. (1965). Interfacial density profile for fluids in the critical region. Physical Review Letters, 15, 621.

    Article  Google Scholar 

  9. Cahn, J. W. (1977). Critical point wetting. The Journal of Chemical Physics, 66, 3667–3672.

    Article  Google Scholar 

  10. Carey, V., & Wemhoff, A. (2005). Thermodynamic analysis of near-wall effects on phase stability and homogeneous nucleation during rapid surface heating. International journal of heat and mass transfer, 48, 5431–5445.

    Article  MATH  Google Scholar 

  11. Chaudhri, A., Bell, J. B., Garcia, A. L., & Donev, A. (2014). Modeling multiphase flow using fluctuating hydrodynamics. Physical Review E, 90, 033014.

    Google Scholar 

  12. Cox, R. (1986). The dynamics of the spreading of liquids on a solid surface. part 1. viscous flow. Journal of Fluid Mechanics, 168, 169–194.

    Article  MATH  Google Scholar 

  13. Davis, S. H. et al. (1974). On the motion of a fluid-fluid interface along a solid surface. Journal of Fluid Mechanics, 65, 71–95.

    Article  MATH  Google Scholar 

  14. De Gennes, P.-G., Brochard-Wyart, F., & Quéré, D. (2013). Capillarity and wetting phenomena: drops, bubbles, pearls, waves. Springer Science & Business Media.

    Google Scholar 

  15. De Groot, S. R., & Mazur, P. (2013). Non-equilibrium thermodynamics. Courier Dover Publications.

    Google Scholar 

  16. Dell’Isola, F., Gouin, H., & Rotoli, G. (1996). Nucleation of spherical shell-like interfaces by second gradient theory: Numerical simulations. European Journal of Mechanics, B/Fluids, 15, 545–568.

    MATH  Google Scholar 

  17. Delong, S., Griffith, B. E., Vanden-Eijnden, E., & Donev, A. (2013). Temporal integrators for fluctuating hydrodynamics. Physical Review E, 87, 033302.

    Google Scholar 

  18. Dussan, E. (1979). On the spreading of liquids on solid surfaces: static and dynamic contact lines. Annual Review of Fluid Mechanics, 11, 371–400.

    Article  Google Scholar 

  19. Español, P. (1998). Stochastic differential equations for non-linear hydrodynamics. Physica A: Statistical Mechanics and its Applications, 248, 77–96.

    Article  Google Scholar 

  20. Evans, R., Stewart, M. C., & Wilding, N. B. (2017). Drying and wetting transitions of a lennard-jones fluid: Simulations and density functional theory. The Journal of Chemical Physics, 147, 044701.

    Article  Google Scholar 

  21. Fernandez-Toledano, J.-C., Blake, T., Lambert, P., & De Coninck, J. (2017). On the cohesion of fluids and their adhesion to solids: Young’s equation at the atomic scale. Advances in colloid and interface science, 245, 102–107.

    Article  Google Scholar 

  22. Fox, R. F., & Uhlenbeck, G. E. (1970). Contributions to non-equilibrium thermodynamics. i. theory of hydrodynamical fluctuations. Physics of Fluids (1958-1988), 13, 1893–1902.

    Google Scholar 

  23. Frumkin, A. (1938). Phenomena of wetting and adhesion of bubbles. i. Zh. Fiz. Khim, 12, 337–45.

    Google Scholar 

  24. Fürstner, R., Barthlott, W., Neinhuis, C., & Walzel, P. (2005). Wetting and self-cleaning properties of artificial superhydrophobic surfaces. Langmuir, 21, 956–961.

    Article  Google Scholar 

  25. Gallo, M., Magaletti, F., & Casciola, C. M. (). Heterogeneous bubble nucleation dynamics. Journal of Fluid Mechanics, 906.

    Google Scholar 

  26. Gallo, M., Magaletti, F., & Casciola, C. M. (2018a). Fluctuating hydrodynamics as a tool to investigate nucleation of cavitation bubbles. Multiphase Flow: Theory and Applications, (p. 347).

    MATH  Google Scholar 

  27. Gallo, M., Magaletti, F., & Casciola, C. M. (2018b). Thermally activated vapor bubble nucleation: The landau-lifshitz–van der waals approach. Phys. Rev. Fluids, 3, 053604. https://link.aps.org/doi/10.1103/PhysRevFluids.3.053604. https://doi.org/10.1103/PhysRevFluids.3.053604.

  28. Gallo, M., Magaletti, F., Cocco, D., & Casciola, C. M. (2020). Nucleation and growth dynamics of vapour bubbles. Journal of Fluid Mechanics, 883.

    Google Scholar 

  29. Gibbs, J. W. (1906). The scientific papers of J. Willard Gibbs volume 1. Longmans, Green and Company.

    Google Scholar 

  30. Gránásy, L. (1998). Semiempirical van der waals/cahn–hilliard theory: size dependence of the tolman length. The Journal of chemical physics, 109, 9660–9663.

    Google Scholar 

  31. Hardy, W. B. (1919). Iii. the spreading of fluids on glass. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 38, 49–55.

    Article  Google Scholar 

  32. Hirt, C. W., & Nichols, B. D. (1981). Volume of fluid (vof) method for the dynamics of free boundaries. Journal of computational physics, 39, 201–225.

    Article  MATH  Google Scholar 

  33. Hocking, L. (1976). A moving fluid interface on a rough surface. Journal of Fluid Mechanics, 76, 801–817.

    Article  MATH  Google Scholar 

  34. Huh, C., & Scriven, L. (1971). Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. Journal of colloid and interface science, 35, 85–101.

    Article  Google Scholar 

  35. Huisman, W. J., Peters, J. F., Zwanenburg, M. J., de Vries, S. A., Derry, T. E., Abernathy, D., & van der Veen, J. F. (1997). Layering of a liquid metal in contact with a hard wall. Nature, 390, 379–381.

    Article  Google Scholar 

  36. Jamet, D., Lebaigue, O., Coutris, N., & Delhaye, J. (2001). The second gradient method for the direct numerical simulation of liquid–vapor flows with phase change. Journal of Computational Physics, 169, 624–651.

    Article  MathSciNet  MATH  Google Scholar 

  37. Johnson, J. K., Zollweg, J. A., & Gubbins, K. E. (1993). The lennard-jones equation of state revisited. Molecular Physics, 78, 591–618.

    Google Scholar 

  38. Koumoutsakos, P. (2005). Multiscale flow simulations using particles. Annu. Rev. Fluid Mech., 37, 457–487.

    Article  MathSciNet  MATH  Google Scholar 

  39. Landau, L. D., & Lifshits, E. M. (1959). Fluid mechanics, by LD Landau and EM Lifshitz volume 11. Pergamon Press Oxford, UK.

    Google Scholar 

  40. Laplace, P.-S. (1807). Theory of capillary attraction. Supplements to the 10th book of Celestial Mechanics.

    Google Scholar 

  41. Laurila, T., Carlson, A., Do-Quang, M., Ala-Nissila, T., & Amberg, G. (2012). Thermohydrodynamics of boiling in a van der waals fluid. Physical Review E, 85, 026320.

    Google Scholar 

  42. Liu, J., Landis, C. M., Gomez, H., & Hughes, T. J. (2015). Liquid–vapor phase transition: Thermomechanical theory, entropy stable numerical formulation, and boiling simulations. Computer Methods in Applied Mechanics and Engineering, 297, 476–553.

    Google Scholar 

  43. Lutsko, J. F. (2011). Density functional theory of inhomogeneous liquids. iv. squared-gradient approximation and classical nucleation theory. The Journal of chemical physics, 134, 164501.

    Google Scholar 

  44. Magaletti, F., Gallo, M., Marino, L., & Casciola, C. M. (2015a). Dynamics of a vapor nanobubble collapsing near a solid boundary. In Journal of Physics: Conference Series (p. 012012). IOP Publishing volume 656.

    Google Scholar 

  45. Magaletti, F., Gallo, M., Marino, L., & Casciola, C. M. (2016). Shock-induced collapse of a vapor nanobubble near solid boundaries. International Journal of Multiphase Flow, 84, 34–45.

    Article  MathSciNet  Google Scholar 

  46. Magaletti, F., Georgoulas, A., & Marengo, M. (2020). Unraveling low nucleation temperatures in pool boiling through fluctuating hydrodynamics simulations. International Journal of Multiphase Flow, (p. 103356).

    Google Scholar 

  47. Magaletti, F., Marino, L., & Casciola, C. (2015b). Shock wave formation in the collapse of a vapor nanobubble. Physical Review Letters, 114, 064501.

    Google Scholar 

  48. Magaletti, F., Marino, L., & Casciola, C. M. (2015c). Diffuse interface modeling of a radial vapor bubble collapse. In Journal of Physics: Conference Series (p. 012028). IOP Publishing volume 656.

    Google Scholar 

  49. Matsumoto, M., & Nishimura, T. (1998). Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Transactions on Modeling and Computer Simulation (TOMACS), 8, 3–30.

    Article  MATH  Google Scholar 

  50. Menzl, G., Gonzalez, M. A., Geiger, P., Caupin, F., Abascal, J. L., Valeriani, C., & Dellago, C. (2016). Molecular mechanism for cavitation in water under tension. Proceedings of the National Academy of Sciences, 113, 13582–13587.

    Google Scholar 

  51. Nijmeijer, M., Bakker, A., Bruin, C., & Sikkenk, J. (1988). A molecular dynamics simulation of the lennard-jones liquid–vapor interface. The Journal of chemical physics, 89, 3789–3792.

    Article  Google Scholar 

  52. Pourali, M., Meloni, S., Magaletti, F., Maghari, A., Casciola, C. M., & Ciccotti, G. (2014). Relaxation of a steep density gradient in a simple fluid: Comparison between atomistic and continuum modeling. The Journal of Chemical Physics, 141, 154107.

    Google Scholar 

  53. Qian, T., Wang, X.-P., & Sheng, P. (2003). Molecular scale contact line hydrodynamics of immiscible flows. Physical Review E, 68, 016306.

    Article  Google Scholar 

  54. Ren, W., & E, W. (2007). Boundary conditions for the moving contact line problem. Physics of fluids, 19, 022101.

    Google Scholar 

  55. Rubı, J., & Mazur, P. (2000). Nonequilibrium thermodynamics and hydrodynamic fluctuations. Physica A: Statistical Mechanics and its Applications, 276, 477–488.

    Article  MathSciNet  Google Scholar 

  56. Sanyal, M., Sinha, S., Huang, K., & Ocko, B. (1991). X-ray-scattering study of capillary-wave fluctuations at a liquid surface. Physical review letters, 66, 628.

    Article  Google Scholar 

  57. Scognamiglio, C., Magaletti, F., Izmaylov, Y., Gallo, M., Casciola, C. M., & Noblin, X. (2018). The detailed acoustic signature of a micro-confined cavitation bubble. Soft matter.

    Google Scholar 

  58. Sengers, J. V., & de Zárate, J. M. O. (2007). Thermal fluctuations in non-equilibrium thermodynamics. Journal of Non-Equilibrium Thermodynamics, 32, 319–329.

    Article  MATH  Google Scholar 

  59. Seppecher, P. (1996). Moving contact lines in the cahn-hilliard theory. International journal of engineering science, 34, 977–992.

    Article  MATH  Google Scholar 

  60. Shahidzadeh-Bonn, N., Tournié, A., Bichon, S., Vié, P., Rodts, S., Faure, P., Bertrand, F., & Azouni, A. (2004). Effect of wetting on the dynamics of drainage in porous media. Transport in porous media, 56, 209–224.

    Article  Google Scholar 

  61. Shang, B. Z., Voulgarakis, N. K., & Chu, J.-W. (2011). Fluctuating hydrodynamics for multiscale simulation of inhomogeneous fluids: Mapping all-atom molecular dynamics to capillary waves. The Journal of chemical physics, 135, 044111.

    Article  Google Scholar 

  62. Shen, B., Yamada, M., Hidaka, S., Liu, J., Shiomi, J., Amberg, G., Do-Quang, M., Kohno, M., Takahashi, K., & Takata, Y. (2017). Early onset of nucleate boiling on gas-covered biphilic surfaces. Scientific reports, 7, 2036.

    Article  Google Scholar 

  63. Sides, S. W., Grest, G. S., & Lacasse, M.-D. (1999). Capillary waves at liquid-vapor interfaces: A molecular dynamics simulation. Physical Review E, 60, 6708.

    Article  Google Scholar 

  64. Sikkenk, J., Indekeu, J., Van Leeuwen, J., & Vossnack, E. (1987). Molecular-dynamics simulation of wetting and drying at solid-fluid interfaces. Physical review letters, 59, 98.

    Article  Google Scholar 

  65. Soltman, D., Smith, B., Kang, H., Morris, S., & Subramanian, V. (2010). Methodology for inkjet printing of partially wetting films. Langmuir, 26, 15686–15693.

    Article  Google Scholar 

  66. Tarazona, P., & Evans, R. (1984). A simple density functional theory for inhomogeneous liquids: Wetting by gas at a solid-liquid interface. Molecular Physics, 52, 847–857.

    Article  Google Scholar 

  67. Tarazona, P., Marconi, U. M. B., & Evans, R. (1987). Phase equilibria of fluid interfaces and confined fluids: non-local versus local density functionals. Molecular Physics, 60, 573–595.

    Article  Google Scholar 

  68. Thompson, P. A., & Robbins, M. O. (1989). Simulations of contact-line motion: slip and the dynamic contact angle. Physical review letters, 63, 766.

    Article  Google Scholar 

  69. Tolman, R. C. (1949). The effect of droplet size on surface tension. The journal of chemical physics, 17, 333–337.

    Article  Google Scholar 

  70. Tremblay, A.-M., Arai, M., & Siggia, E. (1981). Fluctuations about simple nonequilibrium steady states. Physical Review A, 23, 1451.

    Article  Google Scholar 

  71. Triezenberg, D., & Zwanzig, R. (1972). Fluctuation theory of surface tension. Physical Review Letters, 28, 1183–1185.

    Article  Google Scholar 

  72. Tryggvason, G., Dabiri, S., Aboulhasanzadeh, B., & Lu, J. (2013). Multiscale considerations in direct numerical simulations of multiphase flows. Physics of Fluids, 25, 031302.

    Google Scholar 

  73. Uline, M. J., & Corti, D. S. (2007). Activated instability of homogeneous bubble nucleation and growth. Physical review letters, 99, 076102.

    Google Scholar 

  74. Van der Waals, J. (1979). The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density. Journal of Statistical Physics, 20, 200–244.

    Article  Google Scholar 

  75. Welch, S. W., & Wilson, J. (2000). A volume of fluid based method for fluid flows with phase change. Journal of computational physics, 160, 662–682.

    Article  MATH  Google Scholar 

  76. Young, T. (1805). Iii. an essay on the cohesion of fluids. Philosophical transactions of the royal society of London, (pp. 65–87).

    Google Scholar 

  77. Yu, C.-J., Richter, A., Datta, A., Durbin, M., & Dutta, P. (2000). Molecular layering in a liquid on a solid substrate: an x-ray reflectivity study. Physica B: Condensed Matter, 283, 27–31.

    Article  Google Scholar 

  78. Zhang, J., Borg, M. K., & Reese, J. M. (2017). Multiscale simulation of dynamic wetting. International Journal of Heat and Mass Transfer, 115, 886–896.

    Article  Google Scholar 

  79. Zhang, Y., Sprittles, J. E., & Lockerby, D. A. (2020). Nanoscale thin-film flows with thermal fluctuations and slip. Physical Review E, 102, 053105.

    Google Scholar 

  80. Zhao, Y. (2014). Moving contact line problem: Advances and perspectives. Theoretical and Applied Mechanics Letters, 4, 034002.

    Google Scholar 

  81. Zubarev, D., & Morozov, V. (1983). Statistical mechanics of nonlinear hydrodynamic fluctuations. Physica A: Statistical Mechanics and its Applications, 120, 411–467.

    Article  MathSciNet  Google Scholar 

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Acknowledgements

A large part of this work has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No [836693]. The author also acknowledges the CINECA award under the Iscra project (project id: IscrB_HET-NUCL), and the PRACE-DECI16 (project id: WETONB), for the availability of high performance computing resources and support.

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  1. Advanced Engineering Center, School of Computing Engineering and Mathematics, University of Brighton, Lewes Road, Brightong, BN2 4GJ, UK

    Francesco Magaletti

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Correspondence to Francesco Magaletti .

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  1. School of Computing, Engineering and Mathematics, University of Brighton, Brighton, UK

    Marco Marengo

  2. Laboratory of Surfaces and Interfacial Physics, University of Mons, Mons, Belgium

    Joel De Coninck

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Magaletti, F. (2022). A Mesoscale Modeling of Wetting: Theory and Numerical Simulations. In: Marengo, M., De Coninck, J. (eds) The Surface Wettability Effect on Phase Change. Springer, Cham. https://doi.org/10.1007/978-3-030-82992-6_9

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  • DOI: https://doi.org/10.1007/978-3-030-82992-6_9

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