Thermocapillary drift of a droplet of viscous liquid

Bratukhin, Yu. K.

doi:10.1007/bf01015460

Cited by 32 publications

(13 citation statements)

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“…The regular expansion in NRr assumed by Bratukhin (1975) in solving a similar problem retaining inertial effects (and including deformation), while it appears to yield correct results to O(N,,), is likely to encounter difficulties at higher orders since the structure of the energy equation is very similar to that in the present problem. Furthermore, in similar problems, singular perturbation techniques are necessaryfor the solution of the momentum equation as well.…”

Section: 400mentioning

confidence: 82%

Slow migration of a gas bubble in a thermal gradient

Subramanian

1981

AIChE Journal

144

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The steady migration velocity of a gas bubble placed in a liquid with a linear temperature field in the absence of gravity is obtained for small Marangoni Numbers using a matched asymptotic expansion procedure for solving the governing equations. A result good to O(N&,) is obtained, and in the limiting case of zero Marangoni Number, the results of Young, Goldstein and Block are recovered. R. S. SUBRAMANIAN Deportment of Chemical EngineeringClorkron College of Technology Potsdom, NY 13676 SCOPEWith the advent of orbital facilities for experimentation such as Spacelab to be flown aboard the Space Shuttle, and "Space Processing" applications, the migration of droplets and bubbles in a continuous phase due to forces other than buoyancy will become a subject of considerable interest.A theoretical development is presented for the description of bubble migration in a free fall environment due to interfacial tension gradients generated on the bubble surface by a temperature gradient in the surrounding liquid. The objective is to obtain a result for the migration velocity as a function of system parameters for a class of systems characteristic of glasses suggested for Space Processing. These systems, because of their high viscosities, possess very low Reynolds Numbers SO that the inertial terms in the equations of motion may be ignored* However, the Prandtl can be large; therefore, the convective transport terms in the energy equation are not usually negligible. CONCLUSIONS AND SIGNIFICANCEThe principal result of this work is Eq. 53 for the scaled migration velocity of the bubble. In addition to providing a quantitative expression for the buhhle velocity, this result identifies the influence of convective transport of energy in the system. The effect of such transport is to reduce the migration velocity over the value which would prevail were conduction to be the only mechanism. In the limit of zero Marangoni Number, when convective transport is negligible, the result derived here reduces to that of Young, Goldstein and Block utility in the description of bubble migration in space processing applications. Also, applications may be anticipated in the areas of bubble elimination in glass furnaces and in sealing operations where large thermal gradients are encountered. It is expected that this work will haveThe migration of a gas bubble (or a droplet in general) d u e to forces other than buoyancy in a surrounding fluid medium is a subject which so far has received only a small amount of attention. However, with the advent of the Space Shuttle, and the opportunity it provides for the conduct of experiments in a free fall environment, there is a need for developing improved descriptions of this process. In space experiments, it is expected that many occasions will arise where liquid bodies containing droplets of a second fluid, either liquid or gaseous, will be encountered. An example is in the manufacture of spaceprocessed glasses.It has been suggested that the containerless environment available in orbit can be used to make...

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Section: 400mentioning

confidence: 82%

Slow migration of a gas bubble in a thermal gradient

Subramanian

1981

AIChE Journal

144

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“…Some of the restrictive hypotheses largely adopted in the classical theoretical and numerical literature on thermo-capillary migration of bubbles and drops [3][4][5][6][7][8] are removed in the present paper. The ow develops in a cavity and not in an unbounded medium so that the boundary conditions for the external phase are correctly imposed.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of thermo‐solutal‐capillary migration of a dissolving drop in a cavity

Bassano¹

2003

Numerical Methods in Fluids

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SUMMARYIn the present paper the thermo-solutal-capillary migration of a dissolving liquid drop, composed by a binary mixture having a miscibility gap, injected in a closed cavity with di erentially heated end walls, is studied. The main goal of the analysis is to clarify if and how the drop migration is a ected by the dissolution process. The numerical code is based on a ÿnite volume formulation. A level-set technique is used for describing the dynamics of the interface separating the di erent phases. A thermodynamic constraint ÿxes the concentration jump between the interface sides. This jump, together with that of the concentration normal derivatives, in turn deÿnes the entity of the dissolution cross-ow through the interface and the interface velocity relative to the uid. Since the jump singularity of normal derivatives cannot be easily molliÿed, while retaining the necessary accuracy, a scheme for the species equation is elaborated that allows sharp jumps and has subcell resolution. Steady migration speeds are determined after the start-up phase for di erent radii and temperature di erences. The results will be used for the preparation of a sounding rocket space experiment.

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“…If the particle moves with constant velocity the transformation of a laboratory coordinate system to a coordinate system moving with the particle frame will simplify the solution (2,3,5). Let us denote the particle coordinate system moving with the droplet velocity U by O and the laboratory coordinate system by O respectively.…”

Section: On the Thermocapillary Motion Of Deformable Dropletsmentioning

confidence: 99%

On the Thermocapillary Motion of Deformable Droplets

Berejnov¹

2001

Journal of Colloid and Interface Science

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Thermocapillary drift of a droplet of viscous liquid

Cited by 32 publications

References 2 publications

Slow migration of a gas bubble in a thermal gradient

Slow migration of a gas bubble in a thermal gradient

Numerical simulation of thermo‐solutal‐capillary migration of a dissolving drop in a cavity

On the Thermocapillary Motion of Deformable Droplets

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