Surface tension effects on the nonlinear behavior of long waves in a two layer flow

2001 ◽  
Vol 27 (3) ◽  
pp. 265-269
Author(s):  
M. Ballas ◽  
D. Valougeorgis
Keyword(s):  
Surface Tension ◽  
Nonlinear Behavior ◽  
Long Waves ◽  
Layer Flow

Water Waves in a Nonhomogeneous Incompressible Fluid

1977 ◽  
Vol 44 (4) ◽  
pp. 523-528 ◽  
Author(s):  
A. E. Green ◽  
P. M. Naghdi
Keyword(s):  
Surface Tension ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Incompressible Fluid ◽  
Water Waves ◽  
Nonlinear Differential Equations ◽  
Long Waves ◽  
Direct Approach ◽  
Hydraulic Jumps ◽  
Two Dimensional

After a brief discussion of some undesirable features of a number of different partial differential equations often employed in the existing literature on water waves, a relatively simple restricted theory is constructed by a direct approach which is particularly suited for applications to problems of fluid sheets. The rest of the paper is concerned with a derivation of a system of nonlinear differential equations (which may include the effects of gravity and surface tension) governing the two-dimensional motion of incompressible in-viscid fluids for propagation of fairly long waves in a nonhomogeneous stream of water of variable initial depth, as well as some new results pertaining to hydraulic jumps. The latter includes an additional class of possible solutions not noted previously.

scholarly journals Foaming of Binary Mixtures: Link with the Nonlinear Behavior of Surface Tension in Asymmetric Mixtures

Langmuir ◽  
2021 ◽  
Author(s):  
H. P. Tran ◽  
L. Delance ◽  
N. Passade-Boupat ◽  
E. Verneuil ◽  
F. Lequeux ◽  
...  
Keyword(s):  
Surface Tension ◽  
Binary Mixtures ◽  
Nonlinear Behavior

scholarly journals Effects of Surface Tension and General Rotation on the Rayleigh-Taylor Instability of Three-Layer Flow

2013 ◽  
Vol 3 (1) ◽  
pp. 87
Author(s):  
G. A. Hoshoudy
Keyword(s):  
Surface Tension ◽  
Taylor Instability ◽  
Constant Density ◽  
Stable Case ◽  
General Rotation ◽  
Special Cases ◽  
General Dispersion ◽  
Rayleigh Taylor Instability ◽  
Layer Flow ◽  
The Stability

The stability of two interfaces separating three fluids, where the fluids are assumed to be incompressible, inviscid, and of constant density, has been investigated for a system that is acted upon by a general rotation. The effect of surface tension at the two interfaces is taken into account. A general dispersion relation for the system is obtained analytically by formulating the problem in terms of complex variables. Numerical calculations were performed for a hexane-NaCl-CCl4 system to investigate stable case, and special cases that isolate the effect of various parameters on the growth rate of the Rayleigh-Taylor instability are discussed. It is found that the two cutoff wave numbers for the system with surface tension are unchanged by the addition of a general rotation, and that for the system considered, all growth rates are reduced in the presence of a general rotation.

On the evolution of packets of water waves

1979 ◽  
Vol 92 (4) ◽  
pp. 691-715 ◽  
Author(s):  
Mark J. Ablowitz ◽  
Harvey Segur
Keyword(s):  
Surface Tension ◽  
Water Waves ◽  
Evolution Equations ◽  
Wave Packets ◽  
Short Wave ◽  
Similarity Solutions ◽  
Two Dimensions ◽  
Long Waves ◽  
Two Dimensional ◽  
One Dimensional

We consider the evolution of packets of water waves that travel predominantly in one direction, but in which the wave amplitudes are modulated slowly in both horizontal directions. Two separate models are discussed, depending on whether or not the waves are long in comparison with the fluid depth. These models are two-dimensional generalizations of the Korteweg-de Vries equation (for long waves) and the cubic nonlinear Schrödinger equation (for short waves). In either case, we find that the two-dimensional evolution of the wave packets depends fundamentally on the dimensionless surface tension and fluid depth. In particular, for the long waves, one-dimensional (KdV) solitons become unstable with respect to even longer transverse perturbations when the surface-tension parameter becomes large enough, i.e. in very thin sheets of water. Two-dimensional long waves (‘lumps’) that decay algebraically in all horizontal directions and interact like solitons exist only when the one-dimensional solitons are found to be unstable.The most dramatic consequence of surface tension and depth, however, occurs for capillary-type waves in sufficiently deep water. Here a packet of waves that are everywhere small (but not infinitesimal) and modulated in both horizontal dimensions can ‘focus’ in a finite time, producing a region in which the wave amplitudes are finite. This nonlinear instability should be stronger and more apparent than the linear instabilities examined to date; it should be readily observable.Another feature of the evolution of short wave packets in two dimensions is that all one-dimensional solitons are unstable with respect to long transverse perturbations. Finally, we identify some exact similarity solutions to the evolution equations.

Role of pulmonary surfactant in airway closure: a computational study

1993 ◽  
Vol 75 (3) ◽  
pp. 1323-1333 ◽  
Author(s):  
D. R. Otis ◽  
M. Johnson ◽  
T. J. Pedley ◽  
R. D. Kamm
Keyword(s):  
Surface Tension ◽  
Liquid Layer ◽  
Pulmonary Surfactant ◽  
Computational Study ◽  
Surface Shape ◽  
Airway Closure ◽  
Velocity Surface ◽  
The Mean ◽  
Layer Flow

A numerical model that simulates airway closure by liquid bridging during expiration has been developed. The effects of both surfactant and time-varying geometry have been included; the model determines the liquid layer flow resulting from a surface tension (Rayleigh) instability, and the computation traces the film's development to closure, yielding pressure, velocity, surface shape, and surfactant concentration distributions. It is found that surfactant is effective in retarding or eliminating liquid bridging through the reduction of the mean surface tension and the action of surface tension gradients. The former effect is also critical in minimizing the magnitude of the negative pressure in the liquid layer and thus presumably in reducing the tendency for airway compliant collapse.

scholarly journals Surface tension effects on fully developed liquid layer flow over a convex corner

AIP Advances ◽  
2018 ◽  
Vol 8 (4) ◽  
pp. 045206
Author(s):  
Ifrah Bhatti ◽  
Saadia Farid ◽  
Saif Ullah ◽  
Samia Riaz ◽  
Maimoona Faryad
Keyword(s):  
Surface Tension ◽  
Liquid Layer ◽  
Convex Corner ◽  
Layer Flow
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