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Dissipation in rapid dynamic wetting

Published online by Cambridge University Press:  24 June 2011

A. CARLSON ,
M. DO-QUANG  and
G. AMBERG
A. CARLSON*
Affiliation:
Linné Flow Center, Department of Mechanics, The Royal Institute of Technology, SE-100 44, Stockholm, Sweden
M. DO-QUANG
Affiliation:
Linné Flow Center, Department of Mechanics, The Royal Institute of Technology, SE-100 44, Stockholm, Sweden
G. AMBERG
Affiliation:
Linné Flow Center, Department of Mechanics, The Royal Institute of Technology, SE-100 44, Stockholm, Sweden
*
†Email address for correspondence: [email protected]
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Abstract

In this article, we present a modelling approach for rapid dynamic wetting based on the phase field theory. We show that in order to model this accurately, it is important to allow for a non-equilibrium wetting boundary condition. Using a condition of this type, we obtain a direct match with experimental results reported in the literature for rapid spreading of liquid droplets on dry surfaces. By extracting the dissipation of energy and the rate of change of kinetic energy in the flow simulation, we identify a new wetting regime during the rapid phase of spreading. This is characterized by the main dissipation to be due to a re-organization of molecules at the contact line, in a diffusive or active process. This regime serves as an addition to the other wetting regimes that have previously been reported in the literature.

JFM classification

Interfacial Flows (free surface): Contact lines Drops and Bubbles: Drops Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
Papers
Information
Journal of Fluid Mechanics , Volume 682 , 10 September 2011 , pp. 213 - 240
Copyright
Copyright © Cambridge University Press 2011

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Footnotes

‡

Present address: Osquars Backe 18, SE-100 44 Stockholm, Sweden.

References

REFERENCES

Aarts, D. G. A. L., Lekkerkerker, H. N. W., Guo, H., Wegdam, G. H. & Bonn, D. 2005 Hydrodynamics of droplet coalescence. Phys. Rev. Lett. 95 (16), 164503.CrossRefGoogle ScholarPubMed
Amberg, G., Tonhardt, R. & Winkler, C. 1999 Finite element simulations using symbolic computing. Maths. Comput. Simul. 49 (4–5), 257–274.CrossRefGoogle Scholar
Biance, A. L., Clanet, C. & Quere, D. 2004 First steps in the spreading of a liquid droplet. Phys. Rev. E 69 (1), 016301.Google ScholarPubMed
Bird, J. C., Mandre, S. & Stone, H. A. 2008 Short-time dynamics of partial wetting. Phys. Rev. Lett. 100 (23), 234501.CrossRefGoogle ScholarPubMed
Blake, T. D. 2006 The physics of moving wetting lines. J. Colloid and Interface Sci. 299, 1–13.CrossRefGoogle ScholarPubMed
Blake, T. D. & Haynes, J. M. 1969 Kinetics of liquid/liquid displacement. J. Colloid and Interface Sci. 30 (3), 421–423.CrossRefGoogle Scholar
Blake, T. D. & Shikhmurzaev, Y. D. 2002 Dynamic wetting by liquids of different viscosity. J. Colloid and Interface Sci. 253 (1), 196–202.CrossRefGoogle ScholarPubMed
Bonn, D., Eggers, J., Indekeu, J., Meunier, J. & Rolley, E. 2009 Wetting and spreading. Rev. Mod. Phys. 81 (2), 739–805.CrossRefGoogle Scholar
Briant, A. J. & Yeomans, J. M. 2004 Lattice Boltzmann simulations of contact line motion. Part II. Binary fluids. Phys. Rev. E 69 (3), 031603.Google Scholar
Cahn, J. W. & Hilliard, J. E. 1958 Free energy of a nonuniform system. I. Interfacial free energy. J. Chem. Phys. 28 (2), 258–267.CrossRefGoogle Scholar
Carlson, A., Do-Quang, M. & Gustav, A. 2009 Modeling of dynamic wetting far from equilibrium. Phys. Fluids 21 (12), 12170 (1–4).CrossRefGoogle Scholar
Carlson, A., Do-Quang, M. & Amberg, G. 2010 Droplet dynamics in a bifurcating channel. Intl J. Multiphase Flow.CrossRefGoogle Scholar
Courbin, L., Bird, J. C. & Stone, H. A. 2009 Dynamics of wetting: From inertial spreading to viscous imbibtion. J. Physics, Condens. Matter 21, 464127.CrossRefGoogle Scholar
Cox, R. G. 1986 The dynamics of the spreading of liquids on a solid surface. Part 1. Visocus flow. J. Fluid Mech. 168, 169–194.CrossRefGoogle Scholar
De Coninck, J., de Ruijter, M. J. & Voue, M. 2001 Dynamics of wetting. Curr. Opin. Colloid Interface Sci. 6 (1), 49–53.CrossRefGoogle Scholar
Ding, H. & Spelt, P. D. M. 2007 Wetting condition in diffuse interface simulations of contact line motion. Phys. Rev. E 75 (4), 046708.Google ScholarPubMed
Do-Quang, M. & Amberg, G. 2009 The splash of a solid sphere impacting on a liquid surface: Numerical simulation of the influence of wetting. Phys. Fluids 21 (2), 022102.CrossRefGoogle Scholar
Do-Quang, M., Villanueva, W., Singer-Loginova, I. & Amberg, G. 2007 Parallel adaptive computation of some time-dependent materials-related microstructural problems. Bull. Polish Acad. Sci. – Tech. Sci 55 (2), 229–237.Google Scholar
Drelich, J. & Chibowska, D. 2005 Spreading kinetics of water drops on self-assembled monolayers of thiols: Significance of inertial effects. Langmuir 21 (17), 7733–7738.CrossRefGoogle ScholarPubMed
Eggers, J. & Evans, R. 2004 Comment on ‘Dynamic wetting by liquids of different viscosity,’ by T. D. Blake and Y. D. Shikhmurzaev. J. Colloid and Interface Sci. 280 (2), 537–538.CrossRefGoogle Scholar
Eggers, J., Lister, J. R. & Stone, H. A. 1999 Coalescence of liquid drops. J. Fluid Mech. 401, 293–310.CrossRefGoogle Scholar
de Gennes, P. G. 1985 Wetting – statics and dynamics. Rev. Mod. Phys. 57 (3), 827–863.CrossRefGoogle Scholar
Glasstone, S., Laidler, K. J. & Eyring, H. J. 1941 The Theory of Rate Processes. McGraw-Hill.Google Scholar
Guermond, J. L. & Quartapelle, L. 2000 A projection FEM for variable density incompressible flows. J. Comput. Phys. 165 (1), 167–188.CrossRefGoogle Scholar
Hoffman, R. L. 1975 A study of the advancing interface. I. Interface shape in liquid–gas systems. J. Colloid and Interface Sci. 50 (2), 228–241.CrossRefGoogle Scholar
Huh, C. & Scriven, L. E. 1971 Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Colloid and Interface Sci. 35 (1), 85–101.CrossRefGoogle Scholar
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
Matsumoto, S., Maruyama, S. & Saruwatari, H. 1995 A molecular dynamics simulation of a liquid droplet on a solid surface. In Proc. ASME/JSME Therm. Eng. Conf, Maui, Hawaii.Google Scholar
Ngan, C. G., Dussan, V. & Elizabeth, B. 1982 On the nature of the dynamic contact angle: an experimental study. J. Fluid Mech. 118, 27–40.CrossRefGoogle Scholar
Petrov, P. G. & Petrov, J. G. 1992 A combined molecular-hydrodynamic approach to wetting kinetics. Langmuir 8 (7), 1762–1767.CrossRefGoogle Scholar
Qian, B., Loureiro, M., Gagnon, D. A., Tripathi, A. & Breuer, K. S. 2009 a Micron-scale droplet deposition on a hydrophobic surface using a retreating syringe. Phys. Rev. Lett. 102 (16), 164502.CrossRefGoogle ScholarPubMed
Qian, T. Z., Wang, X. P. & Sheng, P. 2003 Molecular scale contact line hydrodynamics of immiscible flows. Phys. Rev. E 68 (1), 016306.Google ScholarPubMed
Qian, T. Z., Wang, X. P. & Sheng, P. 2004 Power-law slip profile of the moving contact line in two-phase immiscible flows. Phys. Rev. Lett. 93 (9), 094501.CrossRefGoogle ScholarPubMed
Qian, T. Z., Wang, X. P. & Sheng, P. 2006 a Molecular hydrodynamics of the moving contact line in two-phase immiscible flows. Commun. Comput. Phys. 1 (1), 1–52.Google Scholar
Qian, T. Z., Wang, X. P. & Sheng, P. 2006 b A variational approach to moving contact line hydrodynamics. J. Fluid Mech. 564, 333–360.CrossRefGoogle Scholar
Qian, T. Z., Wu, C. M., Lei, S. L., Wang, X. P. & Sheng, P. 2009 b Modeling and simulations for molecular scale hydrodynamics of the moving contact line in immiscible two-phase flows. J. Phys., Condens. Matter 21 (46), 464119.CrossRefGoogle ScholarPubMed
Ren, W. Q. & E, W. N. 2007 Boundary conditions for the moving contact line problem. Phys. Fluids 19 (2), 022101.CrossRefGoogle Scholar
de Ruijter, M. J., De Coninck, J. & Oshanin, G. 1999 Droplet spreading: Partial wetting regime revisited. Langmuir 15 (6), 2209–2216.CrossRefGoogle Scholar
Saiz, E. & Tomsia, A. P. 2004 Atomic dynamics and Marangoni films during liquid–metal spreading. Nat. Mater. 3 (12), 903–909.CrossRefGoogle ScholarPubMed
Seveno, D., Vaillant, A., Rioboo, R., Adao, H., Conti, J. & De Coninck, J. 2009 Dynamics of wetting revisited. Langmuir 25 (22), 13034–13044.CrossRefGoogle ScholarPubMed
Shikhmurzaev, Y. D. & Blake, T. D. 2004 Response to the comment on [J. Colloid Interface Sci. 253 (2002) 196] by J. Eggers and R. Evans. J. Colloid and Interface Sci. 280 (2), 539–541.CrossRefGoogle Scholar
Tanner, L. H. 1979 The spreading of silicone oil drops on horizontal surfaces. J. Phys. D 12, 1473–1484.Google Scholar
Villanueva, W. & Amberg, G. 2006 Some generic capillary-driven flows. Intl J. Multiphase Flow 32 (9), 1072–1086.CrossRefGoogle Scholar
Voinov, O. V. 1976 Hydrodynamics of wetting. Izvestiya Akademii Nauk SSSP, Makhanika Zhidkosti i Gaza 5 (76–84).Google Scholar
Wang, X. P., Qian, T. Z. & Sheng, P. 2008 Moving contact line on chemically patterned surfaces. J. Fluid Mech. 605, 59–78.CrossRefGoogle Scholar
Wang, X. P. & Wang, Y. G. 2007 The sharp interface limit of a phase field model for moving contact line problem. Meth. Appl. Anal. 14 (3), 287–294.CrossRefGoogle Scholar
Yue, P., Zhou, C. & Feng, J. J. 2010 Sharp-interface limit of the Cahn–Hilliard model for moving contact lines. J. Fluid Mech. 645 (1), 279–294.CrossRefGoogle Scholar