Numerical modeling of cellular/dendritic array growth: Spacing and undercooling predictions

A numerical model of cellular and dendritic growth has been developed which can predict cellular and dendritic spacing, 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 both for cells and dendrites and these agree well with experiment both at low and at high velocities. By suitable non-dimensionalization relatively simple analytic expressions can be used to fit the numerical results.