Boundary-Layer Formulation of Dendritic Growth: Existence of a Family of Steady-State Needle Solutions
- 14 October 1985
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 55 (16) , 1685-1688
- https://doi.org/10.1103/physrevlett.55.1685
Abstract
We develop a systematic boundary-layer-type formalism for diffusion-controlled dendritic growth, which yields an expression for the shape of steady-state needle solutions valid at large undercoolings. Both physical and analytical considerations suggest the general existence of a continuous family of steady-state needlelike solutions of the heat-flow equations. Simple modifications of the boundary-layer model of Ben-Jacob et al. exhibit this behavior.Keywords
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