Dendrites, viscous fingers, and the theory of pattern formation
Abstract
Recent developments in the theory of pattern formation in dendritic crystal growth and viscous fingering in fluids are reviewed. Consideration is given to the discovery that weak capillary forces act as singular perturbations which lead to selection mechanisms in dendritic crystal growth and fingering patterns. Other topics include the conventional thermodynamic model of the solidification of a pure substance from its melt, fingering instability, pattern selection, the solvability theory, dendritic growth rates, the bubble effect discovered by Couder et al. (1986), the dynamics of pattern-forming systems, and snowflake formation.
- Publication:
-
Science
- Pub Date:
- March 1989
- DOI:
- 10.1126/science.243.4895.1150
- Bibcode:
- 1989Sci...243.1150L
- Keywords:
-
- Crystal Growth;
- Dendritic Crystals;
- Liquid-Solid Interfaces;
- Snow;
- Solidification;
- Viscous Fluids;
- Thermodynamics and Statistical Physics