Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-10T13:09:03.427Z Has data issue: false hasContentIssue false
  • English
  • Français

A Study of Fluid Interfaces and Moving Contact Lines Using the Lattice Boltzmann Method

Published online by Cambridge University Press:  03 June 2015

S. Srivastava ,
P. Perlekar ,
L. Biferale ,
M. Sbragaglia ,
J.H. M. ten Thije Boonkkamp  and
F. Toschi
S. Srivastava*
Affiliation:
Department of Applied Physics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
P. Perlekar*
Affiliation:
Department of Applied Physics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
L. Biferale*
Affiliation:
Department of Physics and INFN, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
M. Sbragaglia*
Affiliation:
Department of Physics and INFN, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
J.H. M. ten Thije Boonkkamp*
Affiliation:
Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
F. Toschi*
Affiliation:
Department of Applied Physics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
*
Corresponding author.Email:s.srivastava@tue.nl
Email:pperlekar@gmail.com
Email:biferale@roma2.infn.it
Email:sbragaglia@gmail.com
Email:j.h.m.tenthijeboonkkamp@tue.nl
Email:f.toschi@tue.nl
Get access

Abstract

We study the static and dynamical behavior of the contact line between two fluids and a solid plate by means of the Lattice Boltzmann method (LBM). The different fluid phases and their contact with the plate are simulated by means of standard Shan-Chen models. We investigate different regimes and compare the multicomponent vs. the multiphase LBM models near the contact line. A static interface profile is attained with the multiphase model just by balancing the hydrostatic pressure (due to gravity) with a pressure jump at the bottom. In order to study the same problem with the multicomponent case we propose and validate an idea of a body force acting only on one of the two fluid components. In order to reproduce results matching an infinite bath, boundary conditions at the bath side play a key role. We quantitatively compare open and wall boundary conditions and study their influence on the shape of the meniscus against static and lubrication theory solution.

Keywords

47.55.np47.55.N-47.11.-jLattice-Boltzmannmultiphase flowmulticomponent flowplunging plate problemLandau-Levich
Type
Research Article
Information
Communications in Computational Physics , Volume 13 , Issue 3 , March 2013 , pp. 725 - 740
Copyright
Copyright © Global Science Press Limited 2013

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

[1]De Gennes, P. G., Rev. Mod. Phys. 57, 827–863 (1985).Google Scholar
[2]Blake, T. D., J. Colloid Interface Sci. 299, 1–13 (2006).CrossRefGoogle Scholar
[3]Oron, A., Davis, S. H. & Bankoff, G., Rev. Mod. Phys. 69, 931–980 (1997).Google Scholar
[4]Eggers, J., Phys. Fluids 17, 082106 (2005).Google Scholar
[5]Ghannum, M. T. & Esmail, M. N., AIChe J. 39, 361–365(1993).Google Scholar
[6]Golestanian, R. & Raphael, E., Phys. Rev. E 64, 031601 (2001);Google Scholar
[7]Hocking, L. M., J. Appl. Maths. 12, 195–208 (2001).Google Scholar
[8]Snoeijer, J. H., Ziegler, J., Andreotti, B., Fermigier, M. & Eggers, J., Phys. Rev. Lett. 100, 244502 (2008)Google Scholar
[9]Snoeijer, J. H., Delon, G., Fermigier, M., & Andreotti, B., Phys. Rev. Lett. 96, 174504 (2006).Google Scholar
[10]Landau, L. D. & Levich, B. V., Acta Physicochim. URSS 17, 42 (1942).Google Scholar
[11]Derjaguin, B. V., Acta Physicochim URSS 20, 349 (1943).Google Scholar
[12]Huh, C. & Scriven, L., J. Colloid Interface Sci. 35, 85–101 (1971).Google Scholar
[13]De Gennes, P. G., Colloid Polym. Sci. 264, 463 (1986).CrossRefGoogle Scholar
[14]Tallmadge, J. A., AIChE J. 16, 925 (1970).Google Scholar
[15]Deryagin, B. M. & Levi, S. M., Film Coating Theory, Focal Press, London, (1964).Google Scholar
[16]de Ryck, A. & Quere, D., J. Colloid Interface Sci. 203, 278 (1998).Google Scholar
[17]Ramdane, O. O. & Quere, D., Langmuir 13, 2911 (1997).CrossRefGoogle Scholar
[18]Eggers, J., Phys. Rev. Lett. 93, 094502 (2004).Google Scholar
[19]Bretherton, F. P., J. Fluid Mech., 10, 166–188 (1961).Google Scholar
[20]Young Phil, T.Trans. R. Soc. Lond 95, 65–87(1805).Google Scholar
[21]De Gennes, P. G., Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves, Springer, New York (2003).Google Scholar
[22]Voinov, O. V., Fluid Dyn. Engl. Transl. 11, 714 (1976).Google Scholar
[23]Cox, R. G., J. Fluid Mech. 168, 169 (1986).Google Scholar
[24]Marchand, A., Chan, T. S., Snoeijer, J. H. & Andreotti, B., arXiv:1110.5274, (2011); and private communication.Google Scholar
[25]Shan, X. & Chen, H., Phys. Rev. E 47, 1815–1819 (1993).Google Scholar
[26]Shan, X. & Chen, H., Phys. Rev. E 49, 2941–2948(1994).Google Scholar
[27]Sbragaglia, M., Benzi, R., Biferale, L., Succi, S., Sugiyama, K. & Toschi, F., Phys. Rev. E 75, 026702 (2007)Google Scholar
[28]Shan, X., Phys. Rev. E 73, 047701 (2006).Google Scholar
[29]Succi, S., The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University Press (2001).Google Scholar
[30]Wolf-Gladrow, D. A., Lattice-Gas Cellular Automata and Lattice Boltzmann Models – An Introduction, Springer-Verlag Berlin Heidelberg (2005).Google Scholar
[31]Shan, X. & Doolen, G., J. Stat. Phys. 81 379 (1995).Google Scholar
[32]Huang, H., Throne, D. T., Schaap, M. G. & Sukop, M. C., Phys. Rev. E 76, 066701 (2007).CrossRefGoogle Scholar
[33]Benzi, R., Biferale, L., Sbragaglia, M., Succi, S. & Toschi, F., Phys. Rev. E 74, 021509 (2006).Google Scholar
[34]Sbragaglia, M., Benzi, R., Biferale, L., Succi, S. & Toschi, F., Phys. Rev. Lett. 97, 204503 (2006).Google Scholar
[35]Briant, A. J., Wagner, A. J., & Yeomans, J. M., Phys. Rev. E 69, 031602 (2004).Google Scholar
[36]Guo, Z., Shi, B. & Zheng, C., Phil. Trans. R. Soc. A 369, 2283 (2011).Google Scholar
[37]Scarbolo, L., Molin, D., Perlekar, P., Sbragaglia, M., Soldati, A. & Toschi, F., J. Comput. Phys., submitted (2011).Google Scholar
[38]Sbragaglia, M., Sugiyama, K. & Biferale, L., J. Fluid Mech. 614, 471 (2008).CrossRefGoogle Scholar
[39]Srivastava, S., Biferale, L., Perlekar, P., & Sbragaglia, M., in preparation (2011).Google Scholar