Onset of Surface-Tension-Driven Bénard Convection

Schatz, Michael F.; VanHook, Stephen J.; McCormick, W. D.; Swift, J. B.; Swinney, Harry L.

doi:10.1103/physrevlett.75.1938

Cited by 128 publications

(123 citation statements)

References 18 publications

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“…The dynamic viscosity µ and the density ρ were measured in the laboratory and the value of the surface tension σ * was determined on the basis of the the manufacturer's data and the temperature coefficient of surface tension quoted by Schatz et al (1995) for silicone oil. Figure 5.…”

Section: Experimental Methodsmentioning

confidence: 99%

The reopening of a collapsed fluid-filled elastic tube

Juel¹,

Heap²

2007

J. Fluid Mech.

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We present an experimental study of the reopening mechanics of a collapsed liquidfilled elastic tube. The experiment is a simple mechanical model of pulmonary airway reopening and aims to assess the robustness of existing theoretical models. A metrelong horizontal elastic tube of inner radius R i = 4.88 ± 0.14 mm is filled with silicone oil and is carefully collapsed mechanically. The injection of nitrogen at a constant flow rate results in the steady propagation of an air finger, after the decay of initial transients. This behaviour is observed over the realizable range of the capillary numbers Ca, which measures the ratio of viscous and capillary forces. With increasing Ca, the transition region between the collapsed and reopened sections of the tube shortens, and the height of the tube behind the bubble tip increases. We also find that air fingers can propagate in partially reopened tubes, in which the transmural pressure is negative far behind the finger tip.

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Section: Experimental Methodsmentioning

confidence: 99%

The reopening of a collapsed fluid-filled elastic tube

Juel¹,

Heap²

2007

J. Fluid Mech.

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“…[16]), Marangoni convection (e.g. [17]), Turing structures in chemical systems [18], crystal growth (e.g. [19]), and surface waves on vertically vibrated liquid or granular layers (Faraday experiment) [20,21].…”

Section: Introductionmentioning

confidence: 99%

Mean flow in hexagonal convection: stability and nonlinear dynamics

Young¹,

Riecke²

2002

Physica D: Nonlinear Phenomena

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Weakly nonlinear hexagon convection patterns coupled to mean flow are investigated within the framework of coupled Ginzburg-Landau equations. The equations are in particular relevant for non-Boussinesq Rayleigh-Bénard convection at low Prandtl numbers. The mean flow is found to (1) affect only one of the two longwave phase modes of the hexagons and (2) suppress the mixing between the two phase modes. As a consequence, for small Prandtl numbers the transverse and the longitudinal phase instability occur in sufficiently distinct parameter regimes that they can be studied separately. Through the formation of penta-hepta defects, they lead to different types of transient disordered states. The results for the dynamics of the penta-hepta defects shed light on the persistence of grain boundaries in such disordered states.

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“…The dimensionless heat flux across the interface, which is uniform below the onset of convection, is given by the Biot number B = Λ + /ΛL, where Λ + (Λ) is the thermal conductivity of the upper (lower) fluid [17]. In contrast to previous liquid/gas experiments [8,9,10,11,12,13], for which B ∼ 0.1, in our experiment Λ + > Λ so that most of the total temperature drop ∆T falls across the thinner lower layer and B = 4.31 ± 0.08 at onset.Water, at a constant temperature T 0 , bathed the top surface of a sapphire window which formed the top boundary of the cell. The base plate of the cell was 1…”

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confidence: 99%

Bénard-Marangoni Convection in Two-Layered Liquids

2000

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We describe experiments on Bénard-Marangoni convection in horizontal layers of two immiscible liquids. Unlike previous experiments, which used gases as the upper fluid, we find a square planform close to onset which undergoes a secondary bifurcation to rolls at higher temperature differences. The scale of the convection pattern is that of the thinner lower fluid layer for which buoyancy and surface tension forces are comparable. The wavenumber of the pattern near onset agrees with the prediction of the linear stability analysis for the full two-layer problem. The square planform is in qualitative agreement with recent one-and two-layer nonlinear theories, which fail however to predict the transition to rolls.Submitted to Physical Review Letters, June 29, 1998. See also http://mobydick.physics.utoronto.ca.Convection in fluids has been a fruitful system for the study of nonlinear, nonequilibrium patterns for almost 100 years. [1,2,3] The original experiments of Bénard [1] used shallow layers of whale oil, heated from below and open to the air above. Many years passed before it was conclusively shown that surface tension gradients, or "Marangoni", forces were crucial. [4,5] In general, both Marangoni and buoyancy forces are present. [6,7] Beginning with Pearson [5], theories of this instability have traditionally neglected the dynamics of the upper fluid (air in Bénard's experiments), replacing it by a constant heat flux boundary condition on the lower fluid. This condition is experimentally unrealizable, however. In wellcontrolled experiments [8,9,10,11,12,13], the upper fluid is bounded above by a plate, on which a constant temperature boundary condition is maintained. The heat flux across the interface is then the result of conduction and convection in both fluids, and is not constant above the onset of convection. The two-fluid interface is deformable, and its distance from the upper plate also changes the local heat flux. [13] In addition, buoyancy forces in the upper fluid may actively assist or impede convection in the lower fluid via surface stresses. [7,14,15] Recent experiments have found it necessary to treat the dynamics of both fluids in order the quantitatively explain the data. [13] In order to gain insight into the more complex, but experimentally better posed, two-layer problem, we have undertaken an experimental study of convection in a system of two immiscible fluids sharing a deformable interface. To our knowledge, only one previous experiment has been done on this system, and it was restricted to locating the onset of convection, without visualization [14]. On the theoretical side, the two-layer problem has been the subject of a complete linear stability analysis [7,14,15] and some weakly nonlinear analyses [7,24] in certain limiting cases. The general problem, including surface deformations, should however be well within the range of modern weakly nonlinear theory and of numerical simulations.In our experiment, both fluids were liquids, and the conditions were such that the Marangoni forces w...

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Onset of Surface-Tension-Driven Bénard Convection

Cited by 128 publications

References 18 publications

The reopening of a collapsed fluid-filled elastic tube

The reopening of a collapsed fluid-filled elastic tube

Mean flow in hexagonal convection: stability and nonlinear dynamics

Bénard-Marangoni Convection in Two-Layered Liquids

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