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

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.