Skip to Main Content

Access Provided by Xinjiang University

Physical Review E

Access by Xinjiang University

Finite-element lattice Boltzmann simulations of contact line dynamics

Rastin Matin^*, Marek Krzysztof Misztal^†, Anier Hernández-García, and Joachim Mathiesen

Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark

^*rastin@nbi.ku.dk
^†misztal@nbi.ku.dk

Phys. Rev. E 97, 013307 – Published 19 January, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.013307

Abstract

The lattice Boltzmann method has become one of the standard techniques for simulating a wide range of fluid flows. However, the intrinsic coupling of momentum and space discretization restricts the traditional lattice Boltzmann method to regular lattices. Alternative off-lattice Boltzmann schemes exist for both single- and multiphase flows that decouple the velocity discretization from the underlying spatial grid. The current study extends the applicability of these off-lattice methods by introducing a finite element formulation that enables simulating contact line dynamics for partially wetting fluids. This work exemplifies the implementation of the scheme and furthermore presents benchmark experiments that show the scheme reduces spurious currents at the liquid-vapor interface by at least two orders of magnitude compared to a nodal implementation and allows for predicting the equilibrium states accurately in the range of moderate contact angles.

Physics Subject Headings (PhySH)

Article Text

References (42)

A. Briant, Phil. Trans. R. Soc. Lond. A 360, 485 (2002).
A. J. Briant, A. J. Wagner, and J. M. Yeomans, Phys. Rev. E 69, 031602 (2004).
A. J. Briant and J. M. Yeomans, Phys. Rev. E 69, 031603 (2004).
T. Lee and L. Liu, Phys. Rev. E 78, 017702 (2008).
L. Liu and T. Lee, Int. J. Mod. Phys. C 20, 1749 (2009).
T. Lee and L. Liu, J. Comput. Phys. 229, 8045 (2010).
K. Connington and T. Lee, J. Comput. Phys. 250, 601 (2013).
H. Huang, D. T. Thorne, M. G. Schaap, and M. C. Sukop, Phys. Rev. E 76, 066701 (2007).
S. Schmieschek and J. Harting, Commun. Comput. Phys. 9, 1165 (2011).
H. P. Jansen, K. Sotthewes, J. van Swigchem, H. J. W. Zandvliet, and E. S. Kooij, Phys. Rev. E 88, 013008 (2013).
S. Son, L. Chen, D. Derome, and J. Carmeliet, Comput. Fluids 117, 42 (2015).
L. Wang, H.-B. Huang, and X.-Y. Lu, Phys. Rev. E 87, 013301 (2013).
H. Liu, A. J. Valocchi, Q. Kang, and C. Werth, Transp. Porous Media 99, 555 (2013).
A. Ghassemi and A. Pak, J. Petrol. Sci. Eng. 77, 135 (2011).
A. G. Yiotis, J. Psihogios, M. E. Kainourgiakis, A. Papaioannou, and A. K. Stubos, Colloids Surfaces A 300, 35 (2007).
K. Langaas and P. Papatzacos, Transp. Porous Media 45, 241 (2001).
H. Huang and X. Y. Lu, Phys. Fluids 21, 092104 (2009).
H. Huang, Z. Li, S. Liu, and X.-Y. Lu, Intl. J. Num. Methods Fluids 61, 341 (2009).
H. Liu, Q. Kang, C. R. Leonardi, S. Schmieschek, A. Narváez, B. D. Jones, J. R. Williams, A. J. Valocchi, and J. Harting, Comput. Geosci. 20, 777 (2016).
H. Huang, C. M. Sukop, and X.-Y. Lu, Multiphase Lattice Boltzmann Methods: Theory and Application (Wiley, New York, 2015).
A. Montessori, P. Prestininzi, M. L. Rocca, and S. Succi, Phys. Fluids 29, 092103 (2017).
K. W. Connington, T. Lee, and J. F. Morris, J. Comput. Phys. 283, 453 (2015).
H. Xi, G. Peng, and S.-H. Chou, Phys. Rev. E 59, 6202 (1999).
N. Rossi, S. Ubertini, G. Bella, and S. Succi, Intl. J. Num. Methods Fluids 49, 619 (2005).
S. Ubertini and S. Succi, Commun. Comput. Phys. 3, 342 (2008).
D. V. Patil and K. Lakshmisha, J. Comput. Phys. 228, 5262 (2009).
J. Ghasemi and S. Razavi, Comput. Math. Appl. 60, 1135 (2010).
A. Zarghami, S. Ubertini, and S. Succi, Intl. J. Num. Methods Heat Fluid Flow 24, 270 (2014).
M. K. Misztal, A. Hernandez-Garcia, R. Matin, H. O. Sørensen, and J. Mathiesen, J. Comput. Phys. 297, 316 (2015).
T. Lee and C.-L. Lin, J. Comput. Phys. 171, 336 (2001).
T. Lee and C.-L. Lin, J. Comput. Phys. 185, 445 (2003).
A. Bardow, I. V. Karlin, and A. A. Gusev, Europhys. Lett. 75, 434 (2006).
M. K. Misztal, A. Hernandez-Garcia, R. Matin, D. Müter, D. Jha, H. O. Sørensen, and J. Mathiesen, Front. Phys. 3, 50 (2015).
K. E. Wardle and T. Lee, Comput. Math. Appl. 65, 230 (2013).
R. Matin, M. K. Misztal, A. Hernandez-Garcia, and J. Mathiesen, Comput. Math. Appl. 74, 281 (2017).
L. Amaya-Bower and T. Lee, Phil. Trans. R. Soc. Lond. A 369, 2405 (2011).
P. G. de Gennes, Rev. Mod. Phys. 57, 827 (1985).
H. Ding and P. D. M. Spelt, Phys. Rev. E 75, 046708 (2007).
T. Lee, C.-L. Lin, and L.-D. Chen, J. Comput. Phys. 215, 133 (2006).
P. Yue, C. Zhou, and J. J. Feng, J. Fluid Mech. 645, 279 (2010).
E. W. Washburn, Phys. Rev. 17, 273 (1921).
D. V. Patil and K. N. Lakshmisha, Intl. J. Num. Methods Fluids 69, 1149 (2012).