Diffusion-limited aggregation and the Saffman-Taylor problem
- 1 March 1985
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 31 (3) , 1977-1979
- https://doi.org/10.1103/physreva.31.1977
Abstract
A random-walk model is proposed to simulate Darcy-law two-dimensional flows in hydrodynamics in the limit of zero-surface tension. The simulation is compared with the analytic and numerical results of the latter in steady-state and dynamic cases, respectively. The instabilities of the model in a flat interface are studied in the linear region. It is clear that the mean-field limit of diffusion-limited aggregation is a Saffman-Taylor problem.Keywords
This publication has 6 references indexed in Scilit:
- Singularities in nonlocal interface dynamicsPhysical Review A, 1984
- Diffusion-Limited Aggregation and Two-Fluid Displacements in Porous MediaPhysical Review Letters, 1984
- Diffusion-limited aggregationPhysical Review B, 1983
- Hele-shaw flow with a cusping free boundaryJournal of Computational Physics, 1981
- Instabilities and pattern formation in crystal growthReviews of Modern Physics, 1980
- 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