Dendritic shape at high undercoolings

The complete shape of dendrites grown in regimes of high undercooling has been studied by means of a phase-field model. The integral parameters surface area and contour length have been used to characterize the dendrite. The dependence on the undercooling of the behaviour of both parameters gives some insight in the role played by the radius of the tip as a length scale. It is found that in regimes dominated by kinetics, lengths far from the tip cannot be scaled by the tip radius. This is significantly different to what has been previously observed in experiments and simulations of dendrites mainly determined by surface tension.