Cellular tip splitting instability during transient growth

In this work, cellular growth under transient conditions is investigated by using a developed quantitative phase-field model in which both the pulling speed and thermal gradient are time-dependent variables. Cellular tip shapes during transient growth are first characterized using the three-dimensional Saffman-Taylor viscous finger shape equation. Simulation results show that cellular tip and shoulders under non-steady-state conditions can be described by this simple mathematical model even at large Peclet number. The problem of cellular pattern evolution during directional solidification in the laser molten pool is possibly that of viscous finger in fluid mechanics. Previous tip splitting criterion is not applicable in our work. The mechanism of cellular tip splitting and later tip crack deepening under transient conditions is first studied, this interesting phenomenon may result from the coupling effect between morphological instabilities which can be measured by the shape factor and cellular spacing, and non-equilibrium of tip solute concentration which provides the driving force for deepening of the bifurcation.