Skip to main content Accessibility help
×
Home

Boundary conditions in the vicinity of the contact line at a vertically oscillating upright plate: an experimental investigation

  • Chao-Lung Ting (a1) and Marc Perlin (a1)

Abstract

To determine a suitable boundary-condition model for the contact line in oscillatory flow, an upright plate, oscillated vertically with sinusoidal motion in dye-laden water with an air interface, is considered experimentally. Constrained by the desirability of a two-dimensional flow field, eight frequencies in the 1–20 Hz range, each with seven different stroke amplitudes (0.5–6 mm) are chosen. The Reynolds number varies from 1.6 to 1878.3 in the experiments, large relative to the Reynolds number in the conventional uni-directional contact-line experiments (e.g. Dussan V.'s 1974 experiments). To facilitate prediction, a high-speed video system is used to record the plate displacement, the contact-line displacement, and the dynamic behaviour of the contact angle. Several interesting contact-line phenomena are shown in the present results. An expression for λ, the dimensionless capillary coefficient, is formulated such that the dynamic behaviour at the contact line is predicted reasonably well. A particle-tracking-velocimetry (PTV) technique is used to detect particle trajectories near the plate such that the boundary condition along the entire plate can be modelled. Two sets of PTV experiments are conducted. One set is for stick contact-line motion, the other set is for stick–slip contact-line motion. The results from the PTV experiments show that a vortex is formed near the meniscus in the stick-slip contact-line experiments; however, in the stick contact-line experiments, no such vortex is present. Using the present experimental results, a model is developed for the boundary condition along the vertically oscillating vertical plate. In this model, slip occurs within a specific distance from the contact line while the flow obeys the no-slip condition outside this slip region. Also, the mean slip length is determined for each experimental stroke amplitude.

Copyright

References

Hide All
Ablett, R. 1923 An investigation of the angle of contact between paraffin wax and water. Phil. Mag. 46, 244256.
Benjamin, T. B. & Scott, J. C. 1979 Gravity–capillary waves with edge constraints. J. Fluid Mech. 92, 241267.
Cocciaro, B., Faetti, S. & Nobili, M. 1991 Capillary effects on surface gravity waves in a cylindrical container: wetting boundary conditions. J. Fluid Mech. 231, 325343.
Cocciaro, B., Faetti, S. & Festa, C. 1993 Experimental investigation of capillary effects on surface gravity waves: non-wetting boundary conditions. J. Fluid Mech. 246, 4366.
Dussan, V., E. B. 1979 On the spreading of liquids on solid surfaces: static and dynamic contact lines. Ann. Rev. Fluid Mech. 11, 371400.
Dussan, V., E. B. & Davis, S. H. 1974 On the motion of a fluid–fluid interface along a solid surface. J. Fluid Mech. 77, 7195.
Goldstein, S. 1938 Modern Developments in Fluid Dynamics, Vol. 2. Oxford University Press.
Graham-Eagle, J. 1983 A new method for calculating eigenvalues with application to gravity–capillary waves with edge constraints. Math. Proc. Camb. Phil. Soc. 94, 553564.
Graham-Eagle, J. 1984 Gravity—capillary waves with edge constraints. D.Phil. thesis, University of Oxford.
Hocking, L. M. 1987a The damping of capillary–gravity waves at a rigid boundary. J. Fluid Mech. 179, 253266.
Hocking, L. M. 1987b Waves produced by a vertically oscillating plate. J. Fluid Mech. 179, 267281.
Hocking, L. M. & Mahdmina, D. 1991 Capillary–gravity waves produced by a wavemaker. J. Fluid Mech. 224, 217226.
Joo, S. W., Schultz, W. W. & Messiter, A. F. 1990 An analysis of the initial-value wavemaker problem. J. Fluid Mech. 214, 161183.
Miles, J. W. 1967 Surface-wave damping in closed basins. Proc. R. Soc. Lond. A 297, 459475.
Miles, J. W. 1990 Capillary–viscous forcing of surface waves. J. Fluid Mech. 219, 635646.
Miles, J. W. 1991 Wave motion in a viscous fluid of variable depth. Part 2. Moving contact line. J. Fluid Mech. 223, 4755.
Miles, J. W. 1992 On surface waves with zero contact angle. J. Fluid Mech. 245, 485492.
Perlin, M., Lin, H. & Ting, C. 1993 On parasitic capillary waves generated by steep gravity waves: an experimental investigation with spatial and temporal measurements. J. Fluid Mech. 255, 597620.
Sulman 1920 Trans. Inst. Min. & Met., Nov.
Ting, C. 1994 Boundary conditions in the vicinity of the contact line at a vertically oscillating plate: an experimental investigation. PhD dissertation, University of Michigan.
Young, G. W. & Davis, S. H. 1987 A plate oscillating across a liquid interface: effect of contact angle hysteresis. J. Fluid Mech. 174, 327356.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Related content

Powered by UNSILO

Boundary conditions in the vicinity of the contact line at a vertically oscillating upright plate: an experimental investigation

  • Chao-Lung Ting (a1) and Marc Perlin (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.