We develop a mathematical model of a long vapor bubble in a micro-channel with given temperature distributions on the walls. We assume that the shape of the bubble is dominated by capillary forces everywhere except near the walls of the channel and use a lubrication-type analysis to find the local vapor-liquid interface shapes and mass fluxes near the walls. Both two- and three-dimensional steady-state solutions are found such that evaporation near the heated bottom is balanced by condensation in colder areas of the vapor-liquid interface. The total length in this steady regime is found from the integral mass balance and investigated as a function of heating conditions. Steady-state conditions can no longer be satisfied when the intensity of heating is above a certain level. In this regime the bubble is expanding. We investigate such expansion in the framework of a two-dimensional model in the limit of small capillary number.
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ASME 2003 1st International Conference on Microchannels and Minichannels
April 24–25, 2003
Rochester, New York, USA
Conference Sponsors:
- Nanotechnology Institute
ISBN:
0-7918-3667-3
PROCEEDINGS PAPER
Mathematical Modeling of Constrained Vapor Bubbles
Vladimir S. Ajaev,
Vladimir S. Ajaev
Southern Methodist University, Dallas, TX
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G. M. Homsy
G. M. Homsy
University of California at Santa Barbara, Santa Barbara, CA
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Vladimir S. Ajaev
Southern Methodist University, Dallas, TX
G. M. Homsy
University of California at Santa Barbara, Santa Barbara, CA
Paper No:
ICMM2003-1072, pp. 589-594; 6 pages
Published Online:
February 24, 2009
Citation
Ajaev, VS, & Homsy, GM. "Mathematical Modeling of Constrained Vapor Bubbles." Proceedings of the ASME 2003 1st International Conference on Microchannels and Minichannels. 1st International Conference on Microchannels and Minichannels. Rochester, New York, USA. April 24–25, 2003. pp. 589-594. ASME. https://doi.org/10.1115/ICMM2003-1072
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