Effect of surface tension on the stability of a binary fluid layer under reduced gravity

1994 ◽  
Vol 6 (4) ◽  
pp. 1482-1490 ◽  
Author(s):  
C. F. Chen ◽  
C. C. Chen
Keyword(s):  
Surface Tension ◽  
Fluid Layer ◽  
Reduced Gravity ◽  
Binary Fluid ◽  
The Stability ◽  
Effect Of Surface

Instability of a gravity-modulated fluid layer with surface tension variation

2001 ◽  
Vol 434 ◽  
pp. 243-271 ◽  
Author(s):  
J. RAYMOND LEE SKARDA
Keyword(s):  
Surface Tension ◽  
Fluid Layer ◽  
Modulation Frequency ◽  
Galerkin Approximation ◽  
Neutral Stability ◽  
Modulation Amplitude ◽  
Neutral Stability Curve ◽  
Stability Curve ◽  
The Stability ◽  
Rayleigh Benard

Gravity modulation of an unbounded fluid layer with surface tension variations along its free surface is investigated. The stability of such systems is often characterized in terms of the wavenumber, α and the Marangoni number, Ma. In (α, Ma) parameter space, modulation has a destabilizing effect on the unmodulated neutral stability curve for large Prandtl number, Pr, and small modulation frequency, Ω, while a stabilizing effect is observed for small Pr and large Ω. As Ω → ∞ the modulated neutral stability curves approach the unmodulated neutral stability curve. At certain values of Pr and Ω, multiple minima are observed and the neutral stability curves become highly distorted. Closed regions of subharmonic instability are also observed. In (1/Ω, g1Ra)-space, where g1 is the relative modulation amplitude, and Ra is the Rayleigh number, alternating regions of synchronous and subharmonic instability separated by thin stable regions are observed. However, fundamental differences between the stability boundaries occur when comparing the modulated Marangoni–Bénard and Rayleigh–Bénard problems. Modulation amplitudes at which instability tongues occur are strongly influenced by Pr, while the fundamental instability region is weakly affected by Pr. For large modulation frequency and small amplitude, empirical relations are derived to determine modulation effects. A one-term Galerkin approximation was also used to reduce the modulated Marangoni–Bénard problem to a Mathieu equation, allowing qualitative stability behaviour to be deduced from existing tables or charts, such as Strutt diagrams. In addition, this reduces the parameter dependence of the problem from seven transport parameters to three Mathieu parameters, analogous to parameter reductions of previous modulated Rayleigh–Bénard studies. Simple stability criteria, valid for small parameter values (amplitude and damping coefficients), were obtained from the one-term equations using classical method of averaging results.

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 Instability of co-flow in a Hele-Shaw cell with cross-flow varying thickness

2021 ◽  
Vol 927 ◽  
Author(s):  
John C. Grenfell-Shaw ◽  
Edward M. Hinton ◽  
Andrew W. Woods
Keyword(s):  
Surface Tension ◽  
Cross Flow ◽  
Simple Expression ◽  
Immiscible Fluids ◽  
Density Difference ◽  
Varying Thickness ◽  
The Stability ◽  
Wetting Fluid ◽  
Gap Width ◽  
Effect Of Surface

We analyse the stability of the interface between two immiscible fluids both flowing in the horizontal direction in a thin cell with vertically varying gap width. The dispersion relation for the growth rate of each mode is derived. The stability is approximately determined by the sign of a simple expression, which incorporates the density difference between the fluids and the effect of surface tension in the along- and cross-cell directions. The latter arises from the varying channel width: if the non-wetting fluid is in the thinner part of the channel, the interface is unstable as it will preferentially migrate into the thicker part. The density difference may suppress or complement this effect. The system is always stable to sufficiently large wavenumbers owing to the along-flow component of surface tension.

Film flow over heated wavy inclined surfaces

2010 ◽  
Vol 665 ◽  
pp. 418-456 ◽  
Author(s):  
S. J. D. D'ALESSIO ◽  
J. P. PASCAL ◽  
H. A. JASMINE ◽  
K. A. OGDEN
Keyword(s):  
Surface Tension ◽  
Stokes Equations ◽  
Fluid Layer ◽  
Bottom Topography ◽  
Marangoni Effect ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Inclined Surfaces ◽  
Variable Surface ◽  
The Stability

The two-dimensional problem of gravity-driven laminar flow of a thin layer of fluid down a heated wavy inclined surface is discussed. The coupled effect of bottom topography, variable surface tension and heating has been investigated both analytically and numerically. A stability analysis is conducted while nonlinear simulations are used to validate the stability predictions and also to study thermocapillary effects. The governing equations are based on the Navier–Stokes equations for a thin fluid layer with the cross-stream dependence eliminated by means of a weighted residual technique. Comparisons with experimental data and direct numerical simulations have been carried out and the agreement is good. New interesting results regarding the combined role of surface tension and sinusoidal topography on the stability of the flow are presented. The influence of heating and the Marangoni effect are also deduced.

Experimental Study on the Physico-Chemical Properties of Bio-Oil and Diesel Emulsification

2012 ◽  
Vol 433-440 ◽  
pp. 94-99 ◽  
Author(s):  
Yue Ling Gu ◽  
Qian Qian Yin ◽  
Shu Rong Wang ◽  
Xin Bao Li ◽  
Zuo Gang Guo ◽  
...  
Keyword(s):  
Experimental Study ◽  
Surface Tension ◽  
Oil Content ◽  
Chemical Properties ◽  
Experimental Results ◽  
Physico Chemical ◽  
Bio Oil ◽  
Optimal Value ◽  
The Stability ◽  
Effect Of Surface

Experimental study on the physico-chemical properties of bio-oil and diesel emulsification has been carried out in this paper, which was based on the preliminary experiment. The effect of surface tension and viscosity on the stability of emulsions were particular concerned. It was found that the longest stable time, the lowest viscosity and lowest surface tension can be obtained simultaneously when the hydrophile and lipophile balance (HLB) value was of the optimal value, i.e. 6.5. Experimental results indicated that the stable time of emulsion decreased rapidly with the increase of bio-oil content, while the value of surface tension and viscosity increased. Meantime, it was shown that the most stable emulsions had the lowest value of viscosity and surface tension.

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.

scholarly journals The effect of surface tension on the shape of fingers in a Hele Shaw cell

1981 ◽  
Vol 102 ◽  
pp. 455-469 ◽  
Author(s):  
J. W. McLean ◽  
P. G. Saffman
Keyword(s):  
Surface Tension ◽  
Experimental Results ◽  
Two Dimensional ◽  
Singular Perturbation Analysis ◽  
Linearized Stability ◽  
Finger Width ◽  
The Stability ◽  
Hele Shaw Cell ◽  
Effect Of Surface ◽  
Small Disturbances

The experimental results of Saffman & Taylor (1958) and Pitts (1980) on fingering in a Hele Shaw cell are modelled by two-dimensional potential flow with surface-tension effects included at the interface. Using free streamline techniques, the shape of the free surface is expressed as the solution of a nonlinear integro-differential equation. The equation is solved numerically and the solutions are compared with experimental results. The shapes of the profiles are very well predicted, but the dependence of finger width on surface tension is not quantitatively accurate, although the qualitative behaviour is correct. A conflict between the numerics and a formal singular perturbation analysis is noted but not resolved. The stability of the steady finger to small disturbances is also examined. Linearized stability analysis indicates that the two-dimensional fingers are not stabilized by the surface-tension effect, which disagrees with the experimental observations. A possible reason for the discrepancy between theory and experiment is suggested.

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