A Simplified Scaling Law of Cell-Dendrite Transition in Directional Solidification

To describe the cell-dendrite transition (CDT) during directional solidification, a new simplified scaling law is proposed and verified by quantitative phase field simulations. This scaling law bears clear physical foundation with consideration of the overall effects of primary spacing, pulling velocity, and thermal gradient on the onset of sidebranches. The analysis results show that the exponent parameters in this simplified scaling law vary within different systems, which mediates the discrepancy of exponent parameters in previous experiments. The scaling law also presents an explanation for the destabilizing mechanism of thermal gradient in sidebranching dynamics.