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Thermocapillary Convection Due to a Stationary Bubble - A ParadoxWe analyze the velocity and temperature fields at steady state due to thermocapillary convection around a gas bubble that is stationary in a liquid. A linear temperature field is imposed in the undisturbed liquid. Our interest is in investigating the effect of convective transport of momentum and energy on the velocity and temperature fields. We assume the pertinent physical properties to be constant, and that buoyant convection is negligible. Suitably defined Reynolds and Marangoni numbers are assumed to be small compared with unity. When both the Reynolds and Marangoni numbers are set equal to zero, a solution can be found. In this solution, far from the bubble, the velocity field decays as the inverse of the distance from the bubble, and the disturbance temperature field decays as the inverse of the square of this distance. We now attempt to obtain a solution when the Reynolds number is zero, but the Marangoni number is small, but non-zero, by a perturbation expansion in the Marangoni number. When the temperature field is expanded in a regular perturbation series in the Marangoni number, we show that the problem for the first correction field is ill-posed. The governing equation for this perturbation field contains an inhomogeneity, and the corresponding particular solution neither decays far from the bubble, nor can be canceled by a homogeneous solution. Additional information is included in the original extended abstract.
Document ID
20040111427
Acquisition Source
Glenn Research Center
Document Type
Preprint (Draft being sent to journal)
Authors
Balasubramaniam, R.
(National Center for Microgravity Research on Fluids and Combustion Cleveland, OH, United States)
Subramanian, R. S.
(Clarkson Univ. Potsdam, NY, United States)
Date Acquired
August 21, 2013
Publication Date
January 1, 2003
Subject Category
Fluid Mechanics And Thermodynamics
Meeting Information
Meeting: Annual Meeting American Institute of Chemical Engineers
Location: Ann Arbor, MI
Country: United States
Start Date: October 13, 2003
End Date: October 14, 2003
Sponsors: American Inst. of Chemical Engineers
Funding Number(s)
CONTRACT_GRANT: NCC3-975
OTHER: 101-58-09
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
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