### Abstract

Language | English |
---|---|

Article number | 046314 |

Number of pages | 13 |

Journal | Physical Review E |

Volume | 81 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 2010 |

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### Keywords

- two-dimensional vapor bubble
- subcooled parallel plates
- superheating

### Cite this

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*Physical Review E*, vol. 81, no. 4, 046314. https://doi.org/10.1103/PhysRevE.81.046314

**Dynamics of a two-dimensional vapor bubble confined between superheated or subcooled parallel plates.** / Das, K.S.; Wilson, S.K.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Dynamics of a two-dimensional vapor bubble confined between superheated or subcooled parallel plates

AU - Das, K.S.

AU - Wilson, S.K.

PY - 2010/4

Y1 - 2010/4

N2 - The dynamics of a long, two-dimensional vapor bubble confined in the gap between two superheated or subcooled parallel plates is analyzed theoretically. The unsteady expansion and/or contraction of the bubble is driven by mass transfer between the liquid and the vapor. The analysis uses the approach developed by Wilson et al. J. Fluid Mech. 391, 1 1999 for a situation with 'large' gaps and 'small' superheating or subcooling to consider a situation with small gaps and large superheating or subcooling in which the mass transfer from or to the semicircular nose of the bubble is comparable to that from or to the thin liquid films on the plates. In order to permit a semi- analytical treatment the analysis is restricted to low Prandtl number liquids. When both plates are superheated the bubble always expands. In this case there are two possible constant-velocity continuous-film 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. If the magnitude of the subcooling is less than that of the superheating then if the magnitude of the subcooling is greater than a critical value then a variety of complicated behaviors including the possibility of an unexpected 'waiting time' behavior in which the bubble remains almost stationary for a finite period oftime can occur before the bubble eventually collapses to a finite length in an infinite time, whereas if it is less than this critical value then the bubble always expands and eventually does so exponentially. If the magnitude of the subcooling is greater than that of the superheating then the bubble always collapses to zero length in a finite time.

AB - The dynamics of a long, two-dimensional vapor bubble confined in the gap between two superheated or subcooled parallel plates is analyzed theoretically. The unsteady expansion and/or contraction of the bubble is driven by mass transfer between the liquid and the vapor. The analysis uses the approach developed by Wilson et al. J. Fluid Mech. 391, 1 1999 for a situation with 'large' gaps and 'small' superheating or subcooling to consider a situation with small gaps and large superheating or subcooling in which the mass transfer from or to the semicircular nose of the bubble is comparable to that from or to the thin liquid films on the plates. In order to permit a semi- analytical treatment the analysis is restricted to low Prandtl number liquids. When both plates are superheated the bubble always expands. In this case there are two possible constant-velocity continuous-film 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. If the magnitude of the subcooling is less than that of the superheating then if the magnitude of the subcooling is greater than a critical value then a variety of complicated behaviors including the possibility of an unexpected 'waiting time' behavior in which the bubble remains almost stationary for a finite period oftime can occur before the bubble eventually collapses to a finite length in an infinite time, whereas if it is less than this critical value then the bubble always expands and eventually does so exponentially. If the magnitude of the subcooling is greater than that of the superheating then the bubble always collapses to zero length in a finite time.

KW - two-dimensional vapor bubble

KW - subcooled parallel plates

KW - superheating

U2 - 10.1103/PhysRevE.81.046314

DO - 10.1103/PhysRevE.81.046314

M3 - Article

VL - 81

JO - Physical Review E

T2 - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 4

M1 - 046314

ER -