### Abstract

The unsteady thermocapillary flow and the free surface variation in a two-dimensional, thin liquid layer are investigated theoretically. The temperature is fixed at one end and sinusoidally varied at the other. By employing sine series expansions, the asymptotically oscillatory solutions of the u-velocity distribution and the free surface deformation are solved exactly. It is found that there exists an inversely proportional relation between τ_{u}, the u-velocity time scale and τ_{s}, the free-surface variation time scale, when the free surface has a maximum oscillation. Near the maximum oscillation conditions, the u-velocity may assume a uni-directional distribution across the layer depth. Furthermore, the deformation of the free surface becomes smaller when the gravity effect becomes more important.

Original language | English |
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Pages (from-to) | 629-640 |

Number of pages | 12 |

Journal | Acta Astronautica |

Volume | 21 |

Issue number | 9 |

DOIs | |

Publication status | Published - 1990 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Aerospace Engineering

### Cite this

*Acta Astronautica*,

*21*(9), 629-640. https://doi.org/10.1016/0094-5765(90)90074-U

}

*Acta Astronautica*, vol. 21, no. 9, pp. 629-640. https://doi.org/10.1016/0094-5765(90)90074-U

**Unsteady thermocapillary flows and free surface oscillations.** / Lai, Chun Liang; Yang, Tian-Shiang.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Unsteady thermocapillary flows and free surface oscillations

AU - Lai, Chun Liang

AU - Yang, Tian-Shiang

PY - 1990/1/1

Y1 - 1990/1/1

N2 - The unsteady thermocapillary flow and the free surface variation in a two-dimensional, thin liquid layer are investigated theoretically. The temperature is fixed at one end and sinusoidally varied at the other. By employing sine series expansions, the asymptotically oscillatory solutions of the u-velocity distribution and the free surface deformation are solved exactly. It is found that there exists an inversely proportional relation between τu, the u-velocity time scale and τs, the free-surface variation time scale, when the free surface has a maximum oscillation. Near the maximum oscillation conditions, the u-velocity may assume a uni-directional distribution across the layer depth. Furthermore, the deformation of the free surface becomes smaller when the gravity effect becomes more important.

AB - The unsteady thermocapillary flow and the free surface variation in a two-dimensional, thin liquid layer are investigated theoretically. The temperature is fixed at one end and sinusoidally varied at the other. By employing sine series expansions, the asymptotically oscillatory solutions of the u-velocity distribution and the free surface deformation are solved exactly. It is found that there exists an inversely proportional relation between τu, the u-velocity time scale and τs, the free-surface variation time scale, when the free surface has a maximum oscillation. Near the maximum oscillation conditions, the u-velocity may assume a uni-directional distribution across the layer depth. Furthermore, the deformation of the free surface becomes smaller when the gravity effect becomes more important.

UR - http://www.scopus.com/inward/record.url?scp=38249016630&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249016630&partnerID=8YFLogxK

U2 - 10.1016/0094-5765(90)90074-U

DO - 10.1016/0094-5765(90)90074-U

M3 - Article

VL - 21

SP - 629

EP - 640

JO - Acta Astronautica

JF - Acta Astronautica

SN - 0094-5765

IS - 9

ER -