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Phenomenological Approach to Cellular Pattern Formed during Directional Solidification
Author(s) -
Wolczyński W.,
Kloch J.
Publication year - 1997
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/1521-3951(199710)203:2<387::aid-pssb387>3.0.co;2-8
Subject(s) - physics , geometry , mathematics
The approach to the solid/liquid (s/l) interface geometry for a 1D experiment of cellular growth is presented. It is based on a periodical function which comprises fundamental undulation of the planar s/l interface and some disfigurements of this undulation. Four regions of the cellular structure formation are distinguished versus growth rate: finite cells, doublets, deep cells and gothic cells (predendritic region). The fundamental undulation is expressed by the same formula within all the regions and the intercellular spacing is treated as equal to the wavelength of undulation. The differentiation among the regions is expressed by some terms responsible for the disfigurements of undulation. The fitting of the presented equations to the observed cellular morphology is the subject of the method. The selection of the intercellular spacing with the use of the criterion of minimum entropy production is suggested. However, only the formal calculation of the undulation amplitude is presented.