Abstract
Patterns formed by the instabilities in propagating interfaces between different phases have received much attention1 in recent years. One of the well known examples is the Saffman-Taylor problem in a Hele-Shaw cell2, where an unique finger pattern is observed when a viscous fluid is displaced by a less viscous fluid.
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References
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The non-symmetric patterns can be selected when there exists asymmetric forcing in the problem. For some detail, see, “Non-symmetric SafFman-Taylor fingers”, by E. Berner, H. Levine and Y. Tu, to appear in J. Fluid Dynamics.
The non-existence of the lowest branch of solutions at small surface tension was first observed in numerical calculation, M. Ben-Amar in the proceedings of NATO-Asi, Pattern and Growth, Cargese, 1990 (to appear); a qualitative explanation was given by V. Hakim, which is essentially the same as the one we discuss here.
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© 1991 Plenum Press, New York
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Tu, Y. (1991). Saffman-Taylor Problem in Sector Geometry. In: Segur, H., Tanveer, S., Levine, H. (eds) Asymptotics beyond All Orders. NATO ASI Series, vol 284. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0435-8_12
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DOI: https://doi.org/10.1007/978-1-4757-0435-8_12
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