The damping of capillary–gravity waves at a rigid boundary

1987 ◽  
Vol 179 ◽  
pp. 253-266 ◽  
Author(s):  
L. M. Hocking
Keyword(s):  
Free Surface ◽  
Gravity Waves ◽  
Contact Angle Hysteresis ◽  
Edge Condition ◽  
Experimental Investigations ◽  
Rigid Boundary ◽  
Moving Contact ◽  
Moving Contact Lines ◽  
Damping Rate ◽  
Pure Gravity

The frequency and damping rate of surface capillary-gravity waves in a bounded region depend on the conditions imposed where the free surface makes contact with the boundary. Extreme cases are when the free surface meets the boundary orthogonally, as in the case of pure gravity waves, and when the contact line remains fixed throughout the motion. An edge condition that models to some extent the dynamics associated with moving contact lines, but not contact-angle hysteresis, is given by making the slope of the free surface at contact proportional to its velocity. This model, which includes the two extreme cases, is used to obtain the frequency and damping rate of a standing wave between two parallel vertical walls. The effect of viscosity in the boundary layers on the walls is included and it is shown that the dissipation associated with the surface forces can exceed that produced by viscosity. The results are compared with those obtained from a number of experimental investigations, in which damping rates too large to be attributed to viscous action have been measured.

Moving contact lines on a two-dimensional rough surface

1985 ◽  
Vol 154 ◽  
pp. 1-28 ◽  
Author(s):  
Kalvis M. Jansons
Keyword(s):  
Contact Angle ◽  
Rough Surface ◽  
Rough Surfaces ◽  
Contact Angle Hysteresis ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Contact Lines ◽  
Stick Slip ◽  
Moving Contact ◽  
Moving Contact Lines

The dynamic contact angle for a contact line moving over a solid surface with random sparse spots of roughness is determined theoretically in the limit of zero capillary number. The model exhibits many of the observed characteristics of moving contact lines on real rough surfaces, including contact-angle hysteresis and stick-slip. Several types of rough surface are considered, and a comparison is made between periodic and random rough surfaces.

scholarly journals Capillary damping of inviscid surface waves in a circular cylinder

2009 ◽  
Vol 627 ◽  
pp. 323-340 ◽  
Author(s):  
R. KIDAMBI
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Surface Waves ◽  
Contact Line ◽  
Simple Procedure ◽  
Edge Condition ◽  
Complex Frequency ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Static Contact

We consider the effect of a wetting condition at the moving contact line on the frequency and damping of surface waves on an inviscid liquid in a circular cylinder. The velocity potential φ and the free surface elevation η are sought as complex eigenfunction expansions. The φ eigenvalues are the classical ones whereas the η eigenvalues are unknown and have to be computed so as to satisfy the wetting condition on the contact line and the other free surface conditions – these turn out to be complex in general. A projection of the latter conditions on to an appropriate basis leads to an eigenvalue problem, for the complex frequency Ω, which has to be solved iteratively with the wetting condition. The variation of Ω with liquid depth h, Bond number Bo, capillary coefficient λ and static contact angle θc0 is explored for the (1, 0),(2, 0),(0, 1),(3, 0) and (4, 0) modes. The damping vanishes for λ = 0 (pinned-end edge condition) and λ = ∞ (free-end edge condition) with a maximum in the interior while the frequency decreases with increasing λ, approaching limiting values at the endpoints. A comparison with the analytic results of Miles (J. Fluid Mech., vol. 222, 1991, p. 197) for the no-meniscus case and the experimental results of Cocciaro, Faetti, & Festa (J. Fluid Mech., vol. 246, 1993, p. 43), where a meniscus is present, is good. The study provides a simple procedure for calculating the inviscid capillary damping associated with the moving contact line in a circular cylinder of finite depth with meniscus effects also being considered.

Streams with moving contact lines: Complex dynamics due to contact-angle hysteresis

1991 ◽  
Vol 43 (2) ◽  
pp. 811-818 ◽  
Author(s):  
Miguel A. Rubio ◽  
Bruce J. Gluckman ◽  
A. Dougherty ◽  
J. P. Gollub
Keyword(s):  
Contact Angle ◽  
Complex Dynamics ◽  
Contact Angle Hysteresis ◽  
Contact Lines ◽  
Moving Contact ◽  
Moving Contact Lines

scholarly journals An algorithm for the use of the Lagrangian specification in Newtonian fluid mechanics and applications to free-surface flow

1985 ◽  
Vol 152 ◽  
pp. 173-190 ◽  
Author(s):  
Poul Bach ◽  
Ole Hassager
Keyword(s):  
Contact Angle ◽  
Free Surface ◽  
Fluid Mechanics ◽  
Newtonian Fluid ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Contact Lines ◽  
Moving Contact ◽  
Moving Contact Lines ◽  
Plate Geometry

An algorithm is constructed for the use of the Lagrangian kinematic specification in Newtonian fluid mechanics. The algorithm is implemented with a finite-element method, and it is demonstrated that the method accurately describes free-surface flow, including the effects of surface tension, with the use of just bilinear isoparametric elements. Moving contact lines are modelled with a small amount of slip near the contact lines. The contact angle boundary condition is included in the form of a net interfacial force specified at the contact line. Simulations of measurements in a parallel-plate geometry show that the measured apparent contact angle is not the true angle, and that the true angle is always very close to the equilibrium value.

Experimental investigation of capillarity effects on surface gravity waves: non-wetting boundary conditions

1993 ◽  
Vol 246 ◽  
pp. 43-66 ◽  
Author(s):  
Bruno Cocciaro ◽  
Sandro Faetti ◽  
Crescenzo Festa
Keyword(s):  
Contact Angle ◽  
Experimental Investigation ◽  
Free Surface ◽  
Boundary Conditions ◽  
Gravity Waves ◽  
Contact Line ◽  
Surface Gravity ◽  
Surface Gravity Waves ◽  
Damping Rate ◽  
Vertical Walls

Damping and eigenfrequencies of surface capillary—gravity waves greatly depend on the boundary conditions. To the best of our knowledge, so far no direct measurement has been made of the dynamic behaviour of the contact angle at the three-phase interface (fluid—vapour—solid walls) in the presence of surface oscillation. Therefore, theoretical models of surface gravity–capillary waves involve ad hoc phenomenological assumptions as far as the behavior of the contact angle is concerned. In this paper we report a systematic experimental investigation of the static and dynamic properties of surface waves in a cylindrical container where the free surface makes a static contact angle $\theta_{\rm c} = 62^{\circ}$ with the vertical walls. The actual boundary condition relating the contact angle to the velocity of the contact line is obtained using a new stroboscopic optical method. The experimental results are compared with the theoretical expressions to be found in the literature. Two different regimes are observed: (i) a low-amplitude regime, where the contact line always remains at rest and the contact angle oscillates during the oscillation of the free surface; (ii) a higher-amplitude regime, where the contact line slides on the vertical walls. The profile, the eigenfrequency and the damping rate of the first non-axisymmetric mode of the surface gravity waves are investigated. The eigenfrequency and damping rate in regime (i) are in satisfactory agreement with the predictions of the Graham-Eagle theory (1983) of pinned-end edge conditions. The eigenfrequency and damping rate in regime (ii) show a strongly nonlinear dependence on the oscillation amplitude of the free surface. All the experimental results concerning regime (ii) can be explained in terms of the Hocking (1987 a) and Miles (1967, 1991) models of capillary damping by introducing an ‘effective’ capillary coefficient $\lambda_{\rm eft}$. This coefficient is directly obtained for the first time in our experiment from dynamic measurements on the contact line. A satisfactory agreement is found to exist between theory and experiment.

scholarly journals New exact relations for steady irrotational two-dimensional gravity and capillary surface waves

2017 ◽  
Vol 376 (2111) ◽  
pp. 20170220 ◽  
Author(s):  
Didier Clamond
Keyword(s):  
Free Surface ◽  
Gravity Waves ◽  
Water Waves ◽  
Two Dimensional ◽  
Physical Plane ◽  
Theme Issue ◽  
Nonlinear Water Waves ◽  
Dimensional Gravity ◽  
Irrotational Motion ◽  
Exact Relations

Steady two-dimensional surface capillary–gravity waves in irrotational motion are considered on constant depth. By exploiting the holomorphic properties in the physical plane and introducing some transformations of the boundary conditions at the free surface, new exact relations and equations for the free surface only are derived. In particular, a physical plane counterpart of the Babenko equation is obtained. This article is part of the theme issue ‘Nonlinear water waves’.

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