We have analyzed, in the context of a boundary-layer model, the problem of pattern selection in dendritic growth in a situation where impurities are present in the undercooled liquid. We find that the tip-velocity selection criterion that has been proposed recently for the geometrical model and the boundary-layer model of a pure substance can be extended, in a nontrivial way, to this more complex situation where two coupled diffusion fields (temperature and solute) determine the interface dynamics. Our model predicts a sharp enhancement of tip velocity in good qualitative agreement with experiment. This agreement is consistent with the conjecture that a solvability condition can be used to determine the operating point of the dendrite in the full nonlocal problem.

• Received 5 December 1984

DOI:https://doi.org/10.1103/PhysRevA.31.3266