Numerical modeling of cellular dendritic array growth: Spacing and structure predictions

A numerical model of cellular and dendritic growth has been developed that can predict cellular and dendritic spacings, undercoolings, and the transition between structures. Fully self-consistent solutions are produced for axisymmetric interface shapes. An important feature of the model is that the spacing selection mechanism has been treated. A small, stable range of spacings is predicted for both cells and dendrites, and these agree well with experiment at both low and high velocities. By suitable nondimensionalization, relatively simple analytic expressions can be used to fit the numerical results. These expressions provide an insight into the cellular and dendritic growth processes and are useful for comparing theory with experiment.