Class of nonsingular exact solutions for Laplacian pattern formation
- 1 July 1994
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 50 (1) , R24-R27
- https://doi.org/10.1103/physreve.50.r24
Abstract
We present a class of exact solutions for the so-called Laplacian growth equation describing the zero-surface-tension limit of a variety of two-dimensional pattern formation problems. These solutions are free of finite-time singularities (cusps) for quite general initial conditions. They reproduce various features of viscous fingering observed in experiments and numerical simulations with surface tension, such as existence of stagnation points, screening, tip splitting, and coarsening. In certain cases the asymptotic interface consists of N separated moving Saffman-Taylor fingers.Keywords
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This publication has 24 references indexed in Scilit:
- A finite polynomial solution of the two-dimensional interface dynamicsPhysica D: Nonlinear Phenomena, 1990
- Viscous flows in two dimensionsReviews of Modern Physics, 1986
- Fingering in Hele-Shaw cellsJournal of Fluid Mechanics, 1986
- Tip-splitting solutions to a Stefan problemPhysical Review A, 1986
- Cusp Development in Hele–Shaw Flow with a Free SurfaceSIAM Journal on Applied Mathematics, 1986
- The instability of long fingers in Hele–Shaw flowsPhysics of Fluids, 1985
- Singularities in nonlocal interface dynamicsPhysical Review A, 1984
- Experimental Studies of Wetting Front Instability Induced by Gradual Change of Pressure Gradient and by Heterogeneous Porous MediaSoil Science Society of America Journal, 1977
- EXACT SOLUTIONS FOR THE GROWTH OF FINGERS FROM A FLAT INTERFACE BETWEEN TWO FLUIDS IN A POROUS MEDIUM OR HELE-SHAW CELLThe Quarterly Journal of Mechanics and Applied Mathematics, 1959
- The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquidProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1958