Journal ArticleDOI
Viscous flows in two dimensions
TLDR
In this paper, the Saffman-Taylor equations for the displacement of one fluid by another in a two-dimensional geometry (a Hele-Shaw cell) are discussed.Abstract:
This review is an expository treatment of the displacement of one fluid by another in a two-dimensional geometry (a Hele-Shaw cell). The Saffman-Taylor equations modeling this system are discussed. They are simulated by random-walk techniques and studied by methods from complex analysis. The stability of the generated patterns (fingers) is studied by a WKB approximation and by complex analytic techniques. The primary conclusions reached are that (a) the fingers are linearly stable even at the highest velocities, (b) they are nonlinearly unstable against noise or an external perturbation, the critical amplitude for the noise being an exponential function of a power of the velocity for high velocities, (c) such exponentials seem to dominate high-velocity behavior, as can be seen from a WKB analysis, and (d) the results of the Saffman-Taylor equations disagree with experiments, apparently because they leave out film-flow phenomena.read more
Citations
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Pattern formation outside of equilibrium
Michael Cross,P. C. Hohenberg +1 more
TL;DR: A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented in this article, with emphasis on comparisons between theory and quantitative experiments, and a classification of patterns in terms of the characteristic wave vector q 0 and frequency ω 0 of the instability.
Journal ArticleDOI
Long-scale evolution of thin liquid films
TL;DR: In this article, a unified mathematical theory is presented that takes advantage of the disparity of the length scales and is based on the asymptotic procedure of reduction of the full set of governing equations and boundary conditions to a simplified, highly nonlinear, evolution equation or to a set of equations.
Journal ArticleDOI
Nonlinear dynamics and breakup of free-surface flows
TL;DR: In this article, the authors review the theoretical development of this field alongside recent experimental work, and outline unsolved problems, as well as a host of technological applications, ranging from printing to mixing and fiber spinning.
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Viscous fingering in porous media
TL;DR: Mecanisme de digitation visqueuse. as discussed by the authors : Deplacements non miscibles en cellules de Hele Shaw. Butteau et al. describe a set of ecoulements in a cellule.
Journal ArticleDOI
Flow phenomena in rocks : from continuum models to fractals, percolation, cellular automata, and simulated annealing
TL;DR: In this article, theoretical and experimental approaches to flow, hydrodynamic dispersion, and miscible and immiscible displacement processes in reservoir rocks are reviewed and discussed, and two different modeling approaches to these phenomena are compared.
References
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Journal ArticleDOI
Diffusion-limited aggregation, a kinetic critical phenomenon
Abstract: A model for random aggregates is studied by computer simulation The model is applicable to a metal-particle aggregation process whose correlations have been measured previously Density correlations within the model aggregates fall off with distance with a fractional power law, like those of the metal aggregates The radius of gyration of the model aggregates has power-law behavior The model is a limit of a model of dendritic growth
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The Penetration of a Fluid into a Porous Medium or Hele-Shaw Cell Containing a More Viscous Liquid
TL;DR: In this paper, it was shown that a flow is possible in which equally spaced fingers advance steadily at very slow speeds, such that behind the tips of the advancing fingers the widths of the two columns of fluid are equal.
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Multidimensional Nonlinear Diffusion Arising in Population Genetics
Journal ArticleDOI
Diffusion-limited aggregation
TL;DR: In this article, the authors show that diffusion-limited aggregation has no upper critical dimension and apply scale invariance to study growth, gelation, and the structure factor of aggregates.