Wave Phenomena pp 231-248 | Cite as

Interfacial Waves in Hele-Shaw Cells of Liquid Crystal-Air Systems

  • Song Ling Yang
  • Zhong Cheng Liang
  • Ren Fan Shao
  • Lui Lam
Part of the Woodward Conference book series (WOODWARD)


When a liquid is pushed by a less viscous fluid (e.g. air) in a thin linear cell, instability of the interface develops and a viscous finger is formed. This problem was first studied by SAFFMAN and TAYLOR [1] in theory and in experiment; it is thus called the Saffman-Taylor problem [2,3]. The cell in which the two fluids move consists of two plates with very small separation between them and is called a Hele-Shaw cell. The flow may be considered approximately two-dimensional. When the less viscous fluid has very small viscosity there is a single dimensionless control parameter [4,5],
$$\frac{1}{B} = 12\frac{{\mu U}}{T}{\left( {\frac{w}{b}} \right)^2}$$
where U is the velocity of the more viscous liquid at x = ∞ where the x axis is the long axis of the linear horizontal cell, w the width and b the thickness of the cell, T the interfacial tension, μ the viscosity of the more viscous liquid.


Liquid Crystal Viscous Liquid Dibutyl Phthalate Interfacial Wave Isotropic Liquid 
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Copyright information

© Springer-Verlag New York Inc. 1989

Authors and Affiliations

  • Song Ling Yang
  • Zhong Cheng Liang
  • Ren Fan Shao
  • Lui Lam

There are no affiliations available

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