The Problem of Directional Solidification Revisited
The connection of directional solidification at low velocity with Saffman-Taylor fingering is discussed. We put forward some quantitative predictions concerning the shape of solidification cells, which can be gained from this analogy. We present also some numerical results without surface tension, which seem to go against the existence of wavelength selection by a solvability mechanism in this problem.
KeywordsDirectional Solidification Wavelength Selection Amplitude Steady State Solidification Cell Directional Solidification Experiment
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- 1.K.A. Jackson, J.D. Hunt: Trans. Met. Soc. AIME 236, 1929 (1966)Google Scholar
- 3.D.J. Wollkind, L.A. Segel: Philos. Trans. R. Soc. Lond. 51, 268 (1970)Google Scholar
- 9.In order to derive (22), we calculate ∫∫ dx dz div[z G(po,p)] as -∫ ds(f n.∇G(po,p)), where the surface integration area is limited by the two lines (x=±0.5) and by an arbitrary smooth profile called here f. Alternatively, we may estimate the first quantity by using the diffusion equation of the Green’s function.Google Scholar
- 10.We define dilog(z) as dilog(z) = ∫0 Z du log(1-u)/uGoogle Scholar