On forced three-dimensional surface waves in a channel in the presence of surface tension

1974 ◽  
Vol 75 (3) ◽  
pp. 405-426 ◽  
Author(s):  
P. F. Rhodes-Robinson
Keyword(s):  
Surface Tension ◽  
Velocity Potential ◽  
Rectangular Channel ◽  
Three Dimensional ◽  
Vertical Plane ◽  
Dimensional Solution ◽  
Surface Slopes ◽  
Infinite Region ◽  
Wave Maker ◽  
Effect Of Surface

AbstractIn this paper wave-maker theory including the effect of surface tension is determined for three-dimensional motion of water in a semi-infinite rectangular channel with outgoing surface wave modes allowed for at infinity; the motion is generated by a harmonically oscillating vertical plane wave-maker at the end of the channel and the cases of both infinite and finite constant depth are treated. The solution of the boundary-value problem for the velocity potential is more complicated in the presence of surface tension due mainly to the additional effect of the channel walls at which the normal free surface slopes are prescribed—as also is the slope at the wave-maker—to ensure uniqueness. The simpler three-dimensional solution for a semi-infinite region—obtained long ago by Sir Thomas Havelock in the absence of surface tension for the case of infinite depth—is also noted.

Note on the reflexion of water waves at a wall in the presence of surface tension

1982 ◽  
Vol 92 (2) ◽  
pp. 369-374 ◽  
Author(s):  
P. F. Rhodes-Robinson
Keyword(s):  
Surface Tension ◽  
Water Waves ◽  
Wave Motion ◽  
Velocity Potential ◽  
Vertical Plane ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Time Harmonic ◽  
Initial Assumption ◽  
Effect Of Surface

AbstractIn this note we examine the influence of surface tension on surface waves incident against a fixed vertical plane wall. The motion is time harmonic and is determined by making the initial assumption that the free-surface slope at the wall is prescribed. From the unique solution obtained for the velocity potential, the parameter involved in this specification can be determined, for small laboratory-scale waves at least, using some longstanding experimental results on meniscus behaviour at a moving contact line. The effect of surface tension is to produce a motion wherein reflexion from the wall is not complete and there is a local disturbance, in contrast to the classical standing-wave motion in the absence of surface tension.

On the forced surface waves due to a vertical wave-maker in the presence of surface tension

1971 ◽  
Vol 70 (2) ◽  
pp. 323-337 ◽  
Author(s):  
P. F. Rhodes-Robinson
Keyword(s):  
Surface Tension ◽  
Surface Waves ◽  
Wave Motion ◽  
Velocity Potential ◽  
Vertical Plane ◽  
Finite Depth ◽  
Cylindrical Wave ◽  
Constant Depth ◽  
Classical Wave ◽  
Wave Maker

AbstractThe classical wave-maker problem to determine the forced two-dimensional wave motion with outgoing surface waves at infinity generated by a harmonically oscillating vertical plane wave-maker immersed in water was solved long ago by Sir Thomas Havelock. In this paper we reinvestigate the problem, making allowance for the presence of surface tension which was excluded before, and obtain a solution of the boundary-value problem for the velocity potential which is made unique by prescribing the free surface slope at the wave-maker. The cases of both infinite and finite constant depth are treated, and it is essential to employ a method which is new to this problem since the theory of Havelock cannot be extended in the latter case of finite depth. The solution of the corresponding problem concerning the axisymmetric wave motion due to a vertical cylindrical wave-maker is deduced in conclusion.

Experimental Investigation of the Effect of Surface Tension and the Correlation on Void Fraction and Frictional Pressure Drop of an Air-Liquid Two-Phase Flow in a Horizontal Flat Capillary Rectangular Channel

2003 ◽  
Author(s):  
Hideo Ide ◽  
Tohru Fukano
Keyword(s):  
Surface Tension ◽  
Pressure Drop ◽  
Void Fraction ◽  
Two Phase Flow ◽  
Rectangular Channel ◽  
Surfactant Solution ◽  
Phase Flow ◽  
Two Phase ◽  
Frictional Pressure Drop ◽  
Effect Of Surface

Air-liquid two-phase flow in a horizontal flat capillary rectangular channel has been studied to clarify the effects of concentration of surfactant solution on the flow phenomena, such as flow patterns, pressure drop, void fraction and so on. The concentrations of surfactant solution were 0, 10, 50 and 100 ppm and the surface tension of each solution was reduced to about 34mN/m from that of pure water of about 72mN/m. The dimension of the channel used was 10.0 mm × 1.0 mm. The drag reduction by mixing the surfactant was examined in both the single phase flow and the two-phase flow. The experimental data of two-phase frictional pressure drop and holdup were compared with the respective correlations which were previously proposed by the other researchers and the present authors. Finally, we proposed new correlations of two-phase frictional pressure drop and holdup in which the effect of surface tension and the aspect ratio of cross section of channel were taken into account.

Breakup of electrified jets

2007 ◽  
Vol 588 ◽  
pp. 75-129 ◽  
Author(s):  
ROBERT T. COLLINS ◽  
MICHAEL T. HARRIS ◽  
OSMAN A. BASARAN
Keyword(s):  
Surface Tension ◽  
Three Dimensional ◽  
Surface Tension Force ◽  
Radial Electric Field ◽  
Temporal Analysis ◽  
Tension Force ◽  
Satellite Drops ◽  
Wide Range ◽  
Electrified Jets ◽  
Effect Of Surface

Breakup of electrified jets is important in applications as diverse as electrospraying, electroseparations and electrospray mass spectrometry. Breakup of a perfectly conducting, incompressible Newtonian liquid jet surrounded by a passive insulating gas that is stressed by a radial electric field is studied by a temporal analysis. An initially quiescent jet is subjected to axially periodic shape perturbations and the ensuing dynamics are followed numerically until pinch-off by both a three-dimensional but axisymmetric (two-dimensional) and a one-dimensional slender-jet algorithm. Results computed with these algorithms are verified against predictions from linear theory for short times. Breakup times, ratios of the sizes of the primary to satellite drops formed at pinch-off, and the Coulombic stability of these drops are reported over a wide range of electrical Bond numbers, NE (ratio of electric to surface tension force), Ohnesorge numbers, NOh (ratio of viscous to surface tension force), and disturbance wavenumbers, k. Effect of surface charge on interface overturning is investigated. Furthermore, the influence of electrostatic stresses on the dynamics of pinch-off and the mechanisms of satellite drop formation is also addressed.

The influence of surface tension on the reflection of water waves by a plane vertical barrier

1968 ◽  
Vol 64 (3) ◽  
pp. 795-810 ◽  
Author(s):  
D. V. Evans
Keyword(s):  
Surface Tension ◽  
Water Waves ◽  
Related Problem ◽  
Velocity Potential ◽  
Surface Tension Force ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Reflected Wave ◽  
Vertical Barrier ◽  
Effect Of Surface

AbstractIn this paper the effect of surface tension is included in a well-known problem in the theory of two-dimensional infinitesimal water waves. The problem is that of the reflection of waves from a fixed vertical barrier immersed to a depth a into deep water. It is shown how the solution for the velocity potential may be determined uniquely when simple assumptions are made concerning the behaviour of the free surface near the barrier. In particular, expressions are derived for the reflection coefficient, defined as the ratio of the amplitude of the reflected wave to that of the incident wave, at infinity, and the transmission coefficient, defined similarly. It is shown how these coefficients, for small values of the surface tension force, tend to the values obtained by Ursell (4) when surface tension is ignored. The related problem of a completely immersed vertical barrier extending to a distance a from the surface may be solved in a similar manner. Expressions for the reflection and transmission coefficients for this case are given.

scholarly journals The effect of surface tension in porous wave maker problems

1998 ◽  
Vol 39 (4) ◽  
pp. 539-556 ◽  
Author(s):  
A. Chakrabarti ◽  
T. Sahoo
Keyword(s):  
Surface Tension ◽  
Water Waves ◽  
Eigenfunction Expansion ◽  
Mixed Type ◽  
Finite Depth ◽  
Time Harmonic ◽  
Surface Water Waves ◽  
Wave Maker ◽  
Porous Walls ◽  
Effect Of Surface

AbstractUsing a mixed-type Fourier transform of a general form in the case of water of infinite depth and the method of eigenfunction expansion in the case of water of finite depth, several boundary-value problems involving the propagation and scattering of time harmonic surface water waves by vertical porous walls have been fully investigated, taking into account the effect of surface tension also. Known results are recovered either directly or as particular cases of the general problems under consideration.

Experimental Study on the Effect of Surface Tension on Void Fraction and Frictional Pressure Drop of an Air-Liquid Two-Phase Flow in a Horizontal Flat Narrow Rectangular Channel

2003 ◽  
Author(s):  
Hideo Ide ◽  
Tohru Fukano
Keyword(s):  
Surface Tension ◽  
Pressure Drop ◽  
Void Fraction ◽  
Two Phase Flow ◽  
Pure Water ◽  
Rectangular Channel ◽  
Phase Flow ◽  
Two Phase ◽  
Frictional Pressure Drop ◽  
Effect Of Surface

Air-liquid two-phase flow in a horizontal flat capillary rectangular channel has been studied to clarify the effects of surface tension on the flow phenomena, such as flow patterns, holdup and frictional pressure drop and so on. The concentrations of surfactant solution were 0, 10, 50 and 100 ppm and the surface tension of each solution was reduced to about 34mN/m from that of pure water of about 72mN/m. The dimension of the channel used was 10.0 mm×1.0 mm. The drag reduction by mixing the surfactant was examined in both the single phase flow and the two-phase flow. The experimental data of void fraction and two-phase frictional pressure drop were compared with the respective correlations which were previously proposed by the other researchers. Finally, we proposed new correlations of two-phase frictional pressure drop in which the effect of surface tension and the aspect ratio of cross section of channel were taken into account.

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