Abstract
My primary aim in this lecture is to bring to your attention a deterministic dynamical system which grows many of the patterns discussed at this school. Daccord and Guyon have discussed the current experimental situation, and I have nothing to add here except to note that the role of randomness of the porous material has been studied experimentally by J. D. Chen. I will start by reviewing some theoretical models which treat small-scale flow through porous media. These models are robust in the sense that they apply to a broad range of flow scenarios ranging from capillary dominance to viscous fingering in the case of unfavorable viscosity ratios. Next, I will discuss how special limiting situations can be treated through the use of simplifying assumptions. Invasion percolation is one example. Emergence of DLA-like viscous patterns is another.
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References
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© 1986 Martinus Nijhoff Publishers,Dordrecht
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Willemsen, J. (1986). Flow through Porous Materials. In: Stanley, H.E., Ostrowsky, N. (eds) On Growth and Form. NATO ASI Series, vol 100. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5165-5_23
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DOI: https://doi.org/10.1007/978-94-009-5165-5_23
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