scholarly journals A cylindrical wave-maker problem in a liquid of finite depth with an inertial surface in the presence of surface tension

1991 ◽  
Vol 33 (1) ◽  
pp. 111-121
Author(s):  
N. K. Ghosh
Keyword(s):  
Surface Tension ◽  
Circular Cross Section ◽  
Finite Depth ◽  
Angular Frequency ◽  
Cylindrical Wave ◽  
Forced Oscillations ◽  
Radial Coordinate ◽  
Time Harmonic ◽  
Inertial Surface ◽  
Wave Maker

AbstractThe problem of generation of waves in a liquid of uniform finite depth with an inertial surface composed of a thin but uniform distribution of disconnected floating particles, due to forced axisymmetric motion prescribed on the surface of an immersed vertical cylindrical wave-maker of circular cross section under the influence of surface tension at the inertial surface, is discussed. The techniques of Laplace transform in time and the modified Weber transform involving Bessel functions in the radial coordinate have been employed to obtain the velocity potential. The steady-state development to the potential function as well as the inertial surface depression due to time-harmonic forced oscillations of the wave-maker are deduced. It is found that the presence of surface tension at the inertial surface ensures the propagation of time-harmonic progressive waves of any angular frequency.

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.

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.

The effect of surface tension on the progressive waves due to incomplete vertical wave-makers in water of infinite depth

1991 ◽  
Vol 435 (1894) ◽  
pp. 293-319 ◽  
Keyword(s):  
Surface Tension ◽  
Reduction Method ◽  
Edge Condition ◽  
Infinite Depth ◽  
Transmitted Waves ◽  
Time Harmonic ◽  
Vertical Barriers ◽  
Wave Maker ◽  
Progressive Waves ◽  
Effect Of Surface

In this paper the influence of surface tension is allowed for in deriving formulas that determine the velocity potentials describing the outgoing progressive waves for two-dimensional time-harmonic motion due to both partially immersed and completely submerged vertical wave-makers in water of infinite depth. For this purpose an effective reduction method is developed to extend a known method suitable only in the absence of surface tension. The two results are used to find the reflected and transmitted waves due to waves incident upon partially immersed and completely submerged fixed vertical barriers, after reformulation as wave-maker problems; and to find the outgoing waves due to a partially immersed vertical hinged plate as a standard example. Certain edge-slope constants needed for the partially immersed wave-maker problem are evaluated using an appropriate dynamical edge condition.

scholarly journals On waves in the presence of vertical porous boundaries

1997 ◽  
Vol 39 (1) ◽  
pp. 104-120 ◽  
Author(s):  
P. F. Rhodes-Robinson
Keyword(s):  
Surface Tension ◽  
Finite Depth ◽  
Wave Source ◽  
Lack Of Information ◽  
Infinite Extent ◽  
Wave Maker ◽  
Incident Waves ◽  
Standard Techniques ◽  
Porous Boundaries ◽  
Effect Of Surface

AbstractIn this paper various wave motions in water of infinite depth containing vertical porous boundaries are determined when the water is of infinite extent on one or both sides. Initially surface tension is ignored and simple solutions for incident waves are obtained before going on to harder wave source and wave-maker solutions. A reduction method is developed to obtain solutions for two-sided boundaries from those for one-sided, which are obtained by standard techniques. The effect of surface tension that precludes simple solutions is also considered, although a present lack of information on dynamical edge behaviour for porous boundaries means that the formal mathematical solutions must be left in terms of arbitrary edge constants. In conclusion, some solutions are noted for finite depth.

Mechanical impedances of lungs and chest wall in the cat

1992 ◽  
Vol 73 (2) ◽  
pp. 427-433 ◽  
Author(s):  
Z. Hantos ◽  
A. Adamicza ◽  
E. Govaerts ◽  
B. Daroczy
Keyword(s):  
Chest Wall ◽  
Respiratory System ◽  
Small Volume ◽  
Angular Frequency ◽  
Forced Oscillations ◽  
Amplitude Dependence ◽  
Volume Changes ◽  
The Real ◽  
Output Flow ◽  
Frequency Independent

In nine anesthetized and paralyzed cats, the mechanical impedances of the total respiratory system (Zrs) and the lungs (ZL) were measured with small-volume pseudorandom forced oscillations between 0.2 and 20 Hz. ZL was measured after thoracotomy, and chest wall impedance (Zw) was calculated as Zw = Zrs-ZL. All impedances were determined by using input airflow [input impedance (Zi)] and output flow measured with a body box [transfer impedance (Zt)]. The differences between Zi and Zt were small for Zrs and negligible for ZL. At 0.2 Hz, the real and imaginary parts of ZL amounted to 33 +/- 4 and 35 +/- 3% (SD), respectively, of Zrs. Up to 8 Hz, all impedances were consistent with a model containing a frequency-independent resistance and inertance and a constant-phase tissue part (G-jH)/omega alpha, where G and H are coefficients for damping and elastance, respectively, omega is angular frequency, and alpha determines the frequency dependence of the real and imaginary parts. G/H was higher for Zw than for ZL (0.29 +/- 0.05 vs. 0.22 +/- 0.04, P less than 0.01). In four cats, the amplitude dependence of impedances was studied: between oscillation volumes of 0.8 and 3 ml, GL, HL, Gw, and Hw decreased on average by 3, 9, 26, and 29%, respectively, whereas the change in G/H was small for both ZL (7%) and Zw (-4%). The values of H were two to three times higher than the quasistatic elastances estimated with greater volume changes (greater than 20 ml).

EFFECTS OF SURFACE TENSION ON TRAPPED MODES IN A TWO-LAYER FLUID

2015 ◽  
Vol 57 (2) ◽  
pp. 189-203 ◽  
Author(s):  
S. SAHA ◽  
S. N. BORA
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Circular Cylinder ◽  
Boundary Value Problems ◽  
Finite Depth ◽  
Trapped Modes ◽  
Trapped Waves ◽  
Linearized Theory ◽  
Horizontal Circular Cylinder ◽  
Effect Of Surface

We consider a two-layer fluid of finite depth with a free surface and, in particular, the surface tension at the free surface and the interface. The usual assumptions of a linearized theory are considered. The objective of this work is to analyse the effect of surface tension on trapped modes, when a horizontal circular cylinder is submerged in either of the layers of a two-layer fluid. By setting up boundary value problems for both of the layers, we find the frequencies for which trapped waves exist. Then, we numerically analyse the effect of variation of surface tension parameters on the trapped modes, and conclude that realistic changes in surface tension do not have a significant effect on the frequencies of these.

Reverse Marangoni surfing

2016 ◽  
Vol 811 ◽  
pp. 612-621 ◽  
Author(s):  
Vahid Vandadi ◽  
Saeed Jafari Kang ◽  
Hassan Masoud
Keyword(s):  
Surface Tension ◽  
Liquid Layer ◽  
Scalar Fields ◽  
Finite Depth ◽  
Lower Surface ◽  
Temperature Fields ◽  
Spherical Particles ◽  
Surface Tension Gradient ◽  
Oblate Spheroidal ◽  
Active Particles

We theoretically study the surfing motion of chemically and thermally active particles located at a flat liquid–gas interface that sits above a liquid layer of finite depth. The particles’ activity creates and maintains a surface tension gradient resulting in the auto-surfing. It is intuitively perceived that Marangoni surfers propel towards the direction with a higher surface tension. Remarkably, we find that the surfers may propel in the lower surface tension direction depending on their geometry and proximity to the bottom of the liquid layer. In particular, our analytical calculations for Stokes flow and diffusion-dominated scalar fields (i.e. chemical concentration and temperature fields) indicate that spherical particles undergo reverse Marangoni propulsion under confinement whereas disk-shaped surfers always move in the expected direction. We extend our results by proposing an approximate formula for the propulsion speed of oblate spheroidal particles based on the speeds of spheres and disks.

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