The onset of convection in a porous layer induced by viscous dissipation: A linear stability analysis

2009 ◽  
Vol 52 (1-2) ◽  
pp. 337-344 ◽  
Author(s):  
A. Barletta ◽  
M. Celli ◽  
D.A.S. Rees
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Viscous Dissipation ◽  
Porous Layer ◽  
Linear Stability Analysis ◽  
Onset Of Convection

Onset of convection in a layered porous medium heated from below

1980 ◽  
Vol 96 (2) ◽  
pp. 375-393 ◽  
Author(s):  
R. Mckibbin ◽  
M. J. O'Sullivan
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Homogeneous System ◽  
Onset Of Convection

The formalism required to determine the criterion for the onset of convection in a multi-layered porous medium heated from below is developed using a straightforward linear stability analysis. Detailed results for two- and three-layer configurations are presented. These results show that large permeability differences between the layers are required to force the system into an onset mode different from a homogeneous system.

Washing wedges: capillary instability in a gradient of confinement

2016 ◽  
Vol 790 ◽  
pp. 619-633 ◽  
Author(s):  
Ludovic Keiser ◽  
Rémy Herbaut ◽  
José Bico ◽  
Etienne Reyssat
Keyword(s):  
Surface Tension ◽  
Stability Analysis ◽  
Linear Stability ◽  
Viscous Dissipation ◽  
Linear Stability Analysis ◽  
Theoretical Description ◽  
Oil Droplets ◽  
Bulk Viscous ◽  
Open Question ◽  
Wetting Liquid

We present experimental results on the extraction of oil trapped in the confined region of a wedge. Upon addition of a more wetting liquid, we observe that oil fingers develop into this extracting liquid. The fingers eventually pinch off and form droplets that are driven away from the apex of the wedge by surface tension along the gradient of confinement. During an experiment, we observe that the size of the expelled oil droplets decreases as the unstable front recedes towards the wedge. We show how this size can be predicted from a linear stability analysis reminiscent of the classical Saffman–Taylor instability. However, the standard balance of capillary and bulk viscous dissipation does not account for the dynamics found in our experiments, leaving as an open question the detailed theoretical description of the instability.

Unicellular natural circulation in a shallow horizontal porous layer heated from below by a constant flux

1995 ◽  
Vol 294 ◽  
pp. 231-257 ◽  
Author(s):  
S. Kimura ◽  
M. Vynnycky ◽  
F. Alavyoon
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Linear Stability ◽  
Porous Layer ◽  
Linear Stability Analysis ◽  
Natural Circulation ◽  
Stable Mode ◽  
Constant Flux

Natural convection in a saturated horizontal porous layer heated from below and cooled at the top with a constant flux is studied both analytically and numerically. Linear stability analysis indicates that unicellular recirculation remains a stable mode of flow as the aspect ratio (A) of the layer is increased, in contrast to the situation for an isothermally heated and cooled layer. An analytical solution is presented for fully developed counterflow in the infinite-aspect-ratio limit; this flow is found to be linearly stable to transverse disturbances for Rayleigh number (Ra) as high as 506, at which point a Hopf bifurcation sets in; however, further analysis indicates that an exchange of stability due to longitudinal disturbances will occur much sooner at Ra ≈ 311.53. The velocity and temperature profiles of the counterflow solution, whilst not strictly speaking valid in the extreme end regions of the layer, otherwise agree very well with full numerical computations conducted for the ranges 25 [les ] Ra [les ] 1050, 2 [les ] A [les ] 10. However, for sufficiently high Rayleigh number (Ra between 630 and 650 for A = 8 and Ra between 730 and 750 for A = 4, for example), the computations indicate transition from steady unicellular to oscillatory flow, in line with the Hopf bifurcation predicted by the linear stability analysis for infinite aspect ratio.

scholarly journals Linear Stability Effect of Densely Distributed Porous Medium and Coriolis Force on Soret Driven Ferrothermohaline Convection

2018 ◽  
Vol 23 (4) ◽  
pp. 911-928
Author(s):  
R. Sekar ◽  
D. Murugan
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Linear Stability ◽  
Normal Mode ◽  
Coriolis Force ◽  
Linear Stability Analysis ◽  
Stationary Convection ◽  
Onset Of Convection ◽  
Stability Effect ◽  
Mode Technique

Abstract The effect of Coriolis force on the Soret driven ferrothermohaline convection in a densely packed porous medium has been studied. A linear stability analysis is carried out using normal mode technique. It is found that stationary convection is favorable for the Darcy model, therefore oscillatory instability is studied. A small thermal perturbation is applied to the basic state and linear stability analysis is used for which the normal mode technique is applied. It is found that the presence of a porous medium favours the onset of convection. The porous medium is assumed to be variable and the effect of the permeable parameter is to destabilize the system. The present work has been carried out both for oscillatory as well as stationary instabilities. The results are depicted graphically.

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.

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