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Unsteady thermocapillary migration of bubblesUpon the introduction of a gas bubble into a liquid possessing a uniform thermal gradient, an unsteady thermo-capillary flow begins. Ultimately, the bubble attains a constant velocity. This theoretical analysis focuses upon the transient period for a bubble in a microgravity environment and is restricted to situations wherein the flow is sufficiently slow such that inertial terms in the Navier-Stokes equation and convective terms in the energy equation may be safely neglected (i.e., both Reynolds and Marangoni numbers are small). The resulting linear equations were solved analytically in the Laplace domain with the Prandtl number of the liquid as a parameter; inversion was accomplished numerically using a standard IMSL routine. In the asymptotic long-time limit, the theory agrees with the steady-state theory of Young, Goldstein, and Block. The theory predicts that more than 90 percent of the terminal steady velocity is achieved when the smallest dimensionless time, i.e., the one based upon the largest time scale-viscous or thermal-equals unity.
Document ID
19890012683
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Dill, Loren H.
(NASA Lewis Research Center Cleveland, OH, United States)
Balasubramaniam, R.
(Case Western Reserve Univ. Cleveland, OH., United States)
Date Acquired
September 5, 2013
Publication Date
January 1, 1988
Subject Category
Fluid Mechanics And Heat Transfer
Report/Patent Number
NASA-TM-101338
NAS 1.15:101338
E-4357
Meeting Information
Meeting: International Colloquium on Drops and Bubbles
Location: Monterey, CA
Country: United States
Start Date: September 18, 1988
End Date: September 21, 1988
Sponsors: JPL
Accession Number
89N22054
Funding Number(s)
PROJECT: RTOP 674-25-05-08
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
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