Abstract
The formation of fingers through the Saffman-Taylor instability in Hele-Shaw flow presents one of the simplest of pattern formation problems. The flow is governed by the Poisson equation, and thus should have a close formal connection[1,2] through its similarity to the random walk problem to diffusion-limited aggregation (DLA)[3]. This poses the fascinating simulation problem of how much and which physical properties must be added to the essentially fractal DLA problem to mock up the interfacial conditions which produce the smooth fingering patterns seen in the Saffman-Taylor flow [4,5,6]. The experimental work I will present in this paper[7] exploits the well-established critical properties of binary mixtures to vary the crucial viscosity contrast parameter more precisely and over a greater range than ever before. In addition, the temporal development of the non-linear pattern is determined more accurately than in most earlier work.
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Maher, J.V. (1985). Fingering Patterns in Hele-Shaw Flow. In: Boccara, N., Daoud, M. (eds) Physics of Finely Divided Matter. Springer Proceedings in Physics, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93301-1_32
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DOI: https://doi.org/10.1007/978-3-642-93301-1_32
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