We study the dynamics of the interface between two immiscible fluids in contact with a chemically homogeneous moving solid plate. We consider the generic case of two fluids with any viscosity ratio and of a plate moving in either directions (pulled or pushed in the bath). The problem is studied by a combination of two models, namely, an extension to finite viscosity ratio of the lubrication theory and a Lattice Boltzmann method. Both methods allow to resolve, in different ways, the viscous singularity at the triple contact between the two fluids and the wall. We find a good agreement between the two models particularly for small capillary numbers. When the solid plate moves fast enough, the entrainment of one fluid into the other one can occur. The extension of the lubrication model to the case of a non-zero air viscosity, as developed here, allows us to study the dependence of the critical capillary number for air entrainment on the other parameters in the problem (contact angle and viscosity ratio).
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July 2013
Research Article|
July 22 2013
Hydrodynamics of air entrainment by moving contact lines
T. S. Chan;
T. S. Chan
1Physics of Fluids Group, Faculty of Science and Technology and MESA+ Institute,
University of Twente
, 7500AE Enschede, The Netherlands
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S. Srivastava;
S. Srivastava
2Department of Applied Physics,
Eindhoven University of Technology
, 5600 MB Eindhoven, The Netherlands
3Department of Mathematics and Computer Science,
Eindhoven University of Technology
, 5600 MB Eindhoven, The Netherlands
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A. Marchand;
A. Marchand
4Physique et Mécanique des Milieux Hétérogènes, UMR 7636 ESPCI -CNRS,
Université Paris-Diderot
, 10 rue Vauquelin, 75005 Paris, France
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B. Andreotti;
B. Andreotti
4Physique et Mécanique des Milieux Hétérogènes, UMR 7636 ESPCI -CNRS,
Université Paris-Diderot
, 10 rue Vauquelin, 75005 Paris, France
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L. Biferale;
L. Biferale
5Department of Physics and INFN,
University of Tor Vergata
, Via della Ricerca Scientifica 1, 00133 Rome, Italy
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F. Toschi;
F. Toschi
2Department of Applied Physics,
Eindhoven University of Technology
, 5600 MB Eindhoven, The Netherlands
3Department of Mathematics and Computer Science,
Eindhoven University of Technology
, 5600 MB Eindhoven, The Netherlands
6
CNR-IAC
, Via dei Taurini 19, 00185 Rome, Italy
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J. H. Snoeijer
J. H. Snoeijer
1Physics of Fluids Group, Faculty of Science and Technology and MESA+ Institute,
University of Twente
, 7500AE Enschede, The Netherlands
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Physics of Fluids 25, 074105 (2013)
Article history
Received:
March 06 2013
Accepted:
June 28 2013
Citation
T. S. Chan, S. Srivastava, A. Marchand, B. Andreotti, L. Biferale, F. Toschi, J. H. Snoeijer; Hydrodynamics of air entrainment by moving contact lines. Physics of Fluids 1 July 2013; 25 (7): 074105. https://doi.org/10.1063/1.4814466
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