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.

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 Effects of Suction–Injection–Combination (SIC) on the onset of Rayleigh–Bénard Electroconvection in a Micropolar Fluid

2015 ◽  
Vol 14 (3) ◽  
pp. 23-42 ◽  
Author(s):  
S Pranesh ◽  
Tarannum Sameena ◽  
Baby Riya
Keyword(s):  
Stability Analysis ◽  
Micropolar Fluid ◽  
Fluid Layer ◽  
Suspended Particles ◽  
Wave Number ◽  
Critical Wave Number ◽  
Onset Of Convection ◽  
Temperature Boundary ◽  
The Stability ◽  
Rayleigh Benard

The effect of Suction – injection combination on the onset of Rayleigh – Bénard electroconvection micropolar fluid is investigated by making a linear stability analysis. The Rayleigh-Ritz technique is used to obtain the eigenvalues for different velocity and temperature boundary combinations. The influence of various parameters on the onset of convection has been analysed. It is found that the effect of Prandtl number on the stability of the system is dependent on the SIC being pro-gravity or anti-gravity. A similar Pe-sensitivity is found in respect of the critical wave number. It is observed that the fluid layer with suspended particles heated from below is more stable compared to the classical fluid layer without suspended particles.

Stability of Hadley Circulations in a Viscoelastic Fluid With Deformable Free Surface

2003 ◽  
Author(s):  
P. N. Kaloni ◽  
J. X. Lou
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Stability Analysis ◽  
Eigenvalue Problem ◽  
Viscoelastic Fluid ◽  
Lower Surface ◽  
Horizontal Layer ◽  
Convective Stability ◽  
Rigid Plate ◽  
Temperature Dependent

This paper deals with liner convective stability analysis of Oldroyd B fluid in a thin horizontal layer with a deformable free surface. The lower surface of the layer is in contact with an adiabatic rigid plate and the upper deformable surface is subject to a temperature dependent surface tension. The eigenvalue problem is solved by the Chebyshev Tau-QZ method and the results for various different forms of upper surfaces are presented.

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.

Effects of a Magnetic Modulation on the Stability of a Magnetic Liquid Layer Heated From Above

2001 ◽  
Vol 123 (3) ◽  
pp. 428-433 ◽  
Author(s):  
Saı¨d Aniss ◽  
Mohamed Belhaq ◽  
Mohamed Souhar
Keyword(s):  
Floquet Theory ◽  
Fluid Layer ◽  
Mathieu Equation ◽  
Magnetic Liquid ◽  
Damping Term ◽  
Onset Of Convection ◽  
First Order ◽  
Gravitational Forces ◽  
Sinusoidal Magnetic Field ◽  
The Stability

The effect of a time-sinusoidal magnetic field on the onset of convection in a horizontal magnetic fluid layer heated from above and bounded by isothermal non magnetic boundaries is investigated. The analysis is restricted to static and linear laws of magnetization. A first order Galerkin method is performed to reduce the governing linear system to the Mathieu equation with damping term. Therefore, the Floquet theory is used to determine the convective threshold for the free-free and rigid-rigid cases. With an appropriate choice of the ratio of the magnetic and gravitational forces, we show the possibility to produce a competition between the harmonic and subharmonic modes at the onset of convection.

scholarly journals A pinned or free-floating rigid plate on a thin viscous film

2014 ◽  
Vol 760 ◽  
pp. 407-430 ◽  
Author(s):  
Philippe H. Trinh ◽  
Stephen K. Wilson ◽  
Howard A. Stone
Keyword(s):  
Thin Film ◽  
Surface Tension ◽  
Free Surface ◽  
Viscous Fluid ◽  
Substrate Surface ◽  
Rigid Plate ◽  
Viscous Film ◽  
Structure Interaction ◽  
Horizontal Substrate ◽  
The Right

AbstractA pinned or free-floating rigid plate lying on the free surface of a thin film of viscous fluid, which itself lies on top of a horizontal substrate that is moving to the right at a constant speed is considered. The focus of the present work is to describe how the competing effects of the speed of the substrate, surface tension, viscosity, and, in the case of a pinned plate, the prescribed pressure in the reservoir of fluid at its upstream end, determine the possible equilibrium positions of the plate, the free surface, and the flow within the film. The present problems are of interest both in their own right as paradigms for a range of fluid–structure interaction problems in which viscosity and surface tension both play an important role, and as a first step towards the study of elastic effects.

scholarly journals Thermosolutal Natural Convection in Partially Porous Domains

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Dominique Gobin ◽  
Benoît Goyeau
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Heat And Mass Transfer ◽  
Fluid Layer ◽  
Horizontal Layer ◽  
Clear Fluid ◽  
Onset Of Convection ◽  
The Stability ◽  
Double Diffusive

In many industrial processes or natural phenomena, coupled heat and mass transfer and fluid flow take place in configurations combining a clear fluid and a porous medium. Since the pioneering work by Beavers and Joseph (1967), the modeling of such systems has been a controversial issue, essentially due to the description of the interface between the fluid and the porous domains. The validity of the so-called one-domain approach—more intuitive and numerically simpler to implement—compared to a two-domain description where the interface is explicitly accounted for, is now clearly assessed. This paper reports recent developments and the current state of the art on this topic, concerning the numerical simulation of such flows as well as the stability studies. The continuity of the conservation equations between a fluid and a porous medium are examined and the conditions for a correct handling of the discontinuity of the macroscopic properties are analyzed. A particular class of problems dealing with thermal and double diffusive natural convection mechanisms in partially porous enclosures is presented, and it is shown that this configuration exhibits specific features in terms of the heat and mass transfer characteristics, depending on the properties of the porous domain. Concerning the stability analysis in a horizontal layer where a fluid layer lies on top of a porous medium, it is shown that the onset of convection is strongly influenced by the presence of the porous medium. The case of double diffusive convection is presented in detail.

The effects of thermal modulation upon the onset of Marangoni–Bénard convection

2002 ◽  
Vol 456 ◽  
pp. 161-182 ◽  
Author(s):  
A. C. OR ◽  
R. E. KELLY
Keyword(s):  
Heat Flux ◽  
Free Surface ◽  
Fluid Layer ◽  
Linear Stability Theory ◽  
Modulation Amplitude ◽  
Thermal Modulation ◽  
Onset Of Convection ◽  
Long Wavelength ◽  
Critical Marangoni Number ◽  
The Mean

The effects of thermal modulation with time on the thermocapillary instability of a thin horizontal fluid layer with a deformable free surface are investigated on the basis of linear stability theory. First, a sinusoidal heating with a mean component is applied at the lower wall, corresponding to boundary conditions either in the form of prescribed temperature or heat flux. For finite-wavelength convection the thermal modulation exerts a strong effect, giving rise to a family of looped regions of instability corresponding to alternating synchronous or subharmonic responses. In the case of prescribed heat flux, the critical curve consists of significantly fewer loops than in the case of prescribed temperature. Thermal modulation with moderate modulation amplitude tends to stabilize the mean basic state, and optimal values of frequency and amplitude of modulation are determined to yield maximum stabilization. However, large-amplitude modulation can be destabilizing. A basic state with zero mean is then considered and the critical Marangoni number is obtained as a function of frequency. The effects of modulation are also investigated in the long-wavelength limit. For the case of prescribed temperature, the modulation does not affect the onset of the long-wavelength mode associated with the mean basic state and a purely oscillating basic state is always stable with respect to long-wavelength disturbances. For the case of prescribed heat flux both at the wall and free surface, by contrast, thermal modulation exerts a significant effect on the onset of convection from a mean basic state and long-wavelength convection can occur even for a purely oscillating basic state. The modulation can be stabilizing or destabilizing, depending on the frequency.

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