PHENOMENOLOGICAL APPROACH TO CELLULAR-PATTERN FORMED DURING DIRECTIONAL SOLIDIFICATION

The approach to the solid/liquid (s/l) interface geometry for a 1D exp eriment of cellular growth is presented. It is based on a periodical f unction which comprises fundamental undulation of the planar s/l inter face and some disfigurements of this undulation. Four regions of the c ellular structure formation are distinguished versus growth rate: fini te cells, doublets, deep cells and gothic cells (predendritic region). The fundamental undulation is expressed by the same formula within al l the regions and the intercellular spacing is treated as equal to the wavelength of undulation. The differentiation among the regions is ex pressed by some terms responsible for the disfigurements of undulation . The fitting of the presented equations to the observed cellular morp hology is the subject of the method. The selection of the intercellula r spacing with the use of the criterion of minimum entropy production is suggested. However, only the formal calculation of tl-ie undulation amplitude is presented.