The Unsteady expansion and contraction of a two-dimensional vapour bubble confined between superheated or subcooled plates

K.S. Das, S.K. Wilson

Research output: Contribution to conferencePaper

Abstract

This talk describes the results of a theoretical investigation of the unsteady expansion and contraction of a vapour bubble in a narrow channel. Specifically we construct and analyse a mathematical model for a long, two-dimensional bubble confined between superheated or subcooled parallel plates, whose motion is driven by mass transfer between the liquid and the vapour. The present model is similar to that previously proposed by Wilson, Davis and Bankoff (1999), but differs from it in one crucial respect, namely that, unlike the earlier work, it includes significant mass transfer from and/or to the semi-circular cap regions at the nose of the bubble as well as from and/or to the thin liquid films attached to the plates. The inclusion of this additional contribution to the overall mass transfer significantly alters the dynamics of the bubble. When both plates are superheated the bubble always expands. In this case there are two possible constant-velocity travelling-wave solutions for the expansion of the bubble, namely an unstable fast mode and a stable slow mode. The evolution of the bubble is calculated numerically for a range of values of the parameters. In particular, these calculations show that eventually the bubble expands either with the constant velocity of the slow mode or exponentially. When both plates are subcooled the bubble always collapses to zero length in a finite time.When one plate is subcooled and the other plate is superheated the situation is rather more complicated.
LanguageEnglish
Pages489-493
Number of pages4
Publication statusPublished - Nov 2004
Event57th Annual Meeting of the Division of Fluid Dynamics - Seattle, Washington
Duration: 21 Nov 200423 Nov 2004

Conference

Conference57th Annual Meeting of the Division of Fluid Dynamics
CitySeattle, Washington
Period21/11/0423/11/04

Fingerprint

contraction
bubbles
vapors
expansion
mass transfer
liquids
parallel plates
caps
traveling waves
mathematical models
inclusions

Keywords

  • vapour bubble
  • superheated plates
  • subcooled plates
  • fluid dynamics

Cite this

Das, K. S., & Wilson, S. K. (2004). The Unsteady expansion and contraction of a two-dimensional vapour bubble confined between superheated or subcooled plates. 489-493. Paper presented at 57th Annual Meeting of the Division of Fluid Dynamics, Seattle, Washington, .
Das, K.S. ; Wilson, S.K. / The Unsteady expansion and contraction of a two-dimensional vapour bubble confined between superheated or subcooled plates. Paper presented at 57th Annual Meeting of the Division of Fluid Dynamics, Seattle, Washington, .4 p.
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Das, KS & Wilson, SK 2004, 'The Unsteady expansion and contraction of a two-dimensional vapour bubble confined between superheated or subcooled plates' Paper presented at 57th Annual Meeting of the Division of Fluid Dynamics, Seattle, Washington, 21/11/04 - 23/11/04, pp. 489-493.

The Unsteady expansion and contraction of a two-dimensional vapour bubble confined between superheated or subcooled plates. / Das, K.S.; Wilson, S.K.

2004. 489-493 Paper presented at 57th Annual Meeting of the Division of Fluid Dynamics, Seattle, Washington, .

Research output: Contribution to conferencePaper

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N2 - This talk describes the results of a theoretical investigation of the unsteady expansion and contraction of a vapour bubble in a narrow channel. Specifically we construct and analyse a mathematical model for a long, two-dimensional bubble confined between superheated or subcooled parallel plates, whose motion is driven by mass transfer between the liquid and the vapour. The present model is similar to that previously proposed by Wilson, Davis and Bankoff (1999), but differs from it in one crucial respect, namely that, unlike the earlier work, it includes significant mass transfer from and/or to the semi-circular cap regions at the nose of the bubble as well as from and/or to the thin liquid films attached to the plates. The inclusion of this additional contribution to the overall mass transfer significantly alters the dynamics of the bubble. When both plates are superheated the bubble always expands. In this case there are two possible constant-velocity travelling-wave solutions for the expansion of the bubble, namely an unstable fast mode and a stable slow mode. The evolution of the bubble is calculated numerically for a range of values of the parameters. In particular, these calculations show that eventually the bubble expands either with the constant velocity of the slow mode or exponentially. When both plates are subcooled the bubble always collapses to zero length in a finite time.When one plate is subcooled and the other plate is superheated the situation is rather more complicated.

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Das KS, Wilson SK. The Unsteady expansion and contraction of a two-dimensional vapour bubble confined between superheated or subcooled plates. 2004. Paper presented at 57th Annual Meeting of the Division of Fluid Dynamics, Seattle, Washington, .