Abstract
The physical location of the first side branch instability during steady state directional solidification is studied. A new model which allows for the coarsening of the dendrite is considered for the prediction of the location of the first perturbation. The accepted growth law for liquid phase sintering is integrated into the existing dendrite model. Thus, it is inferred that the dendrite fixes its tip radius because of marginal stability considerations, but the coarsening driven solute flow modifies the concentration gradient experienced by the dendrite envelope thereby influencing the location of the first secondary instability. A test of the model for the succinonitrile-acetone system is carried out by comparing the predicted behavior with the numerous experimental measurements previously reported. A reasonable match of the calculated values for the location of the first side branch instability in relation to the dendrite tip, is noted when compared with the experimentally measured numbers.
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