Instabilities of dynamic thermocapillary liquid layers. Part 2. Surface-wave instabilities

Smith, Marc K.; Davis, Stephen H.

doi:10.1017/s0022112083001524

Cited by 194 publications

(126 citation statements)

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“…Smith and Davis [3,4] performed a linear stability analysis of thermocapillary instability. When the free surface is assumed to be flat and non-deformable, they found two types of thermocapillary instabilities: stationary longitudinal rolls and hydrothermal waves.…”

Section: Introductionmentioning

confidence: 99%

Transition to chaos in thermocapillary convection

Zhu

Kang

2013

International Journal of Heat and Mass Transfer

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a b s t r a c tWe present experiments on transition to chaos in thermocapillary convection in a rectangular pool of silicone oil. The applied temperature difference between the two sidewalls is adjusted in the range of 0-43°C to observe various dynamic states. The applied temperature gradient along the fluid-gas interface drives shear flow along the free surface from hot to cold and a back flow in the underlying layer. With the increase of the temperature gradient, the thermocapillary convection will transit from steady flow to regularly oscillatory flow, and finally to chaos. A temperature measurement system, which consists of thermocouple, voltmeter and data-acquiring computer, is used to record the temperature of the liquid dynamically. In order to identify the different dynamic regimes from steady flow to chaos, fast Fourier transform and fractal theory are used to analyze the experimental data. The critical conditions for transition have been obtained and discussed by non-dimensional analysis. The quasi-periodic route and Feigenbaum route were observed for different experimental conditions, and the relationship between oscillatory frequency and Marangoni number Ma has been discussed.

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Section: Introductionmentioning

confidence: 99%

Transition to chaos in thermocapillary convection

Zhu

Kang

2013

International Journal of Heat and Mass Transfer

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“…, we got the same form as described in Davis's paper [6], and Q was defined as an imposed heat flux in [4,5]. Here, we assumed h 1 = h int = Àx, which implied an constant heat flux Q should be imposed by the particula r considerat ion.…”

Section: The Base Statementioning

confidence: 99%

“…Linear stability analysis of Pearson predicts the threshold value of Marango ni number, Ma = 79.6, which coincides with experiments. Smith and Davis [4,5] and Davis [6] considered thermocapillary instabilities in a single layer system with a non-deformabl e interface. Sen and Davis [7] studied steady thermocapi llary flows in two-dimensi onal slots.…”

Section: Introductionmentioning

confidence: 99%

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Linear instability analysis of thermocapillary convection in a bilayer system

Ding

Liu

2013

International Journal of Heat and Mass Transfer

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a b s t r a c tThe linear instability analysis of thermocapillary conve ction in a bila yer system consisting of silicon oil 10cS and fluorinert FC70 liquids was discussed in this paper. The bilayer system was bound below by a rigid plate and above by a free surface with a passive gas. The two immiscible liquids were separated by an interface. A constant horizontal temperature gradient was imposed along the interfaces. Two typical cases were studied: (i) streamwise homogeneou s disturbances (the streamwise disturbance wave number a = 0); (ii) spanwis e homogeneou s disturbances (the spanwis e disturbance wave number b = 0). When a = 0, it was found that convection in the two layers may occur in the form of stationary mode or oscillatory mode. The oscillatory mode takes the form of traveling wave, which propagates in either spanwis e direction. When b = 0, convection in the two layers occurs in the form of oscillatory mode, which takes the form of traveling wave propagating in the same direction as base flow. The three dimensional analysis suggested that disturbance in the spanwis e direction was the major cause of destabilization in the system. The influences of Biot number Bi and the depth ratio h on the unstable modes in the bilayer system were discussed.

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“…Several investigators have also studied the flow phenomena in a twodimensional slot with different temperatures specified on the side walls (Lai, 1984;Sen and Davis, 1982;Strani, Piva and Graziani, 1983). The thermocapillary convections in a two-dimensional thin liquid layer with specified surface temperature distributions were also studied in the past (Lai, 1984;Pimputka and Ostrach, 1980;Smith andDavis, 1983a, 1983b). However, the coupling among the flow field, the temperature field and the imposed heat flux was not taken into consideration.…”

Section: Introductionmentioning

confidence: 99%