Effect of surface tension on the onset of convection in a layer of liquid with a free surface

1972 ◽  
Vol 10 (3) ◽  
pp. 412-415
Author(s):  
V. Kh. Izakson
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Onset Of Convection ◽  
Effect Of Surface

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.

scholarly journals Onset of Buoyancy and Surface-Tension Driven Instabilities in Presence of Random Vibrations

1990 ◽  
Vol 45 (11-12) ◽  
pp. 1235-1240
Author(s):  
B. S. Dandapat
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Fluid Layer ◽  
Heat Conducting ◽  
Rigid Plate ◽  
Stability Zone ◽  
Random Vibrations ◽  
White Noise Process ◽  
Onset Of Convection ◽  
The Stability

AbstractOnset of thermal convection in an incompressible fluid layer bounded between a perfectly heat conducting lower rigid plate and an upper free surface is analysed when the layer is subject to random vibrations. It is shown that when the vibrations are characterized by a white noise process, they hasten the onset of convection. Further it is shown that the stability zone is demarcated by an inverted parabola in the (R, M) plane.

scholarly journals The effect of surface tension on free surface flow induced by a point sink in a fluid of finite depth

2017 ◽  
Vol 156 ◽  
pp. 526-533
Author(s):  
G.C. Hocking ◽  
H.H.N. Nguyen ◽  
T.E. Stokes ◽  
L.K. Forbes
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Free Surface Flow ◽  
Finite Depth ◽  
Surface Flow ◽  
Effect Of Surface

scholarly journals THE EFFECT OF SURFACE TENSION ON FREE-SURFACE FLOW INDUCED BY A POINT SINK

2016 ◽  
Vol 57 (4) ◽  
pp. 417-428
Author(s):  
G. C. HOCKING ◽  
H. H. N. NGUYEN ◽  
L. K. FORBES ◽  
T. E. STOKES
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Axisymmetric Flow ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Limiting Factor ◽  
Inviscid Fluid ◽  
Steady Solutions ◽  
Determining Factor ◽  
Effect Of Surface

The steady, axisymmetric flow induced by a point sink (or source) submerged in an inviscid fluid of infinite depth is computed and the resulting deformation of the free surface is obtained. The effect of surface tension on the free surface is determined and is the new component of this work. The maximum Froude numbers at which steady solutions exist are computed. It is found that the determining factor in reaching the critical flow changes as more surface tension is included. If there is zero or a very small amount of surface tension, the limiting factor appears to be the formation of small wavelets on the free surface; but, as the surface tension increases, this is replaced by a tendency for the lowest point on the free surface to descend sharply as the Froude number is increased.

scholarly journals The effect of surface tension on free-surface flow induced by a point sink

2016 ◽  
Vol 57 ◽  
pp. 417
Author(s):  
Graeme Charles Hocking ◽  
Ha H. N. Nguyen ◽  
Lawrence K. Forbes ◽  
Timothy E. Stokes
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Effect Of Surface

Effects of interaction between Marangoni and double-diffusive instabilities

1995 ◽  
Vol 303 ◽  
pp. 1-21 ◽  
Author(s):  
J. Tanny ◽  
C. C. Chen ◽  
C. F. Chen
Keyword(s):  
Surface Tension ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Vertical Temperature ◽  
Onset Of Convection ◽  
Bottom Region ◽  
The Stability ◽  
Double Diffusive ◽  
Effect Of Surface

The effect of surface tension on the onset of convection in horizontal double-diffusive layer was studied both experimentally and by linear stability analysis. The experiments were conducted in a rectangular tank with base dimension of 25×13 cm and 5 cm in height. A stable solute (NaCl) stratification was first established in the tank, and then a vertical temperature gradient was imposed. Vertical temperature and concentration profiles were measured using a thermocouple and a conductivity probe and the flow patterns were visualized by a schlieren system. Two types of experiments were carried out which illustrate the effect of surface tension on the onset of convection. In the rigid–rigid experiments, when the critical thermal Rayleigh number, RT, is reached, large double-diffusive plumes were seen simultaneously to rise from the heated bottom and descend from the cooled top. In the rigid–free experiments, owing to surface tension effects, the first instability onset was of the Marangoni type. Well-organized small plumes were seen to emerge and persist close to the top free surface at a relatively small RTM (where subscript M denotes ‘Marangoni’). At larger RTt > RTM (where subscript t denotes ‘top’) these plumes evolved into larger double-diffusive plumes. The onset of double-diffusive instability at the bottom region occurred at a still higher RTb > RTt (where subscript b denotes ‘bottom‘). A series of stability experiments was conducted for a layer with an initial top concentration of 2 wt% and different concentration gradients. The stability map shows that in the rigid–free case the early Marangoni instability in the top region reduces significantly the critical RT for the onset of double-diffusive convection. Compared with the rigid–rigid case, the critical RT in the top region is reduced by about 60% and in the bottom region by about 30%. The results of the linear stability analysis, which takes into account both surface tension and double-diffusive effects, are in general agreement with the experiments. The analysis is then applied to study the stability characteristics of such a layer as gravity is reduced to microgravity level. Results show that even at 10 −4g0, where g0 is the gravity at sea level, the double-diffusive effect is of equal importance to the Marangoni effect.

The effect of surface tension on the waves produced by a heaving circular cylinder

1968 ◽  
Vol 64 (3) ◽  
pp. 833-847 ◽  
Author(s):  
D. V. Evans
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Circular Cylinder ◽  
Water Waves ◽  
Wave Amplitude ◽  
Velocity Potential ◽  
Linearized Theory ◽  
The Waves ◽  
Energy Argument ◽  
Effect Of Surface

AbstractIn this paper the effect of surface tension on water waves is considered. The usual assumptions of the linearized theory are made. A uniqueness theorem is derived for the waves at infinity for a general class of bounded two-dimensional obstacles in a free surface by means of an energy argument. It is shown how the wave amplitude at infinity depends on the prescribed angle at which the free surface meets the normal to the obstacle. The particular case of a heaving half-immersed circular cylinder is considered in detail, and an expression obtained for the velocity potential in terms of a convergent infinite series, the coefficients of which may be computed.

scholarly journals Fundamental singularities in the theory of water waves with surface tension

1970 ◽  
Vol 2 (3) ◽  
pp. 317-333 ◽  
Author(s):  
P. F. Rhodes-Robinson
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Water Waves ◽  
Potential Functions ◽  
Fundamental Wave ◽  
Harmonic Waves ◽  
Constant Depth ◽  
Wave Source ◽  
Time Harmonic ◽  
Effect Of Surface

In this paper the forms are obtained for the harmonic potential functions describing the fundamental wave-source and multipole singularities which pertain to the study of infinitesimal time-harmonic waves on the free surface of water when the effect of surface tension is included. Line and point singularities are considered for both the cases of infinite and finite constant depth of water. The method used is an extension of that which has been used to obtain these potentials in the absence of surface tension.

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