Validation criterion for noise-induced mechanism of sidebranching in directional solidification

We address the compatibility between the theory of noise-induced sidebranching and the recent experimental evidence of sidebranching enhancement by thermal gradient in directional solidification. For this, the respective roles played by primary instability, cell tip undercooling and cell tip shape in the theory of noise-induced sidebranching are analyzed. It is first noticed that, by its own, the primary instability tends to make thermal gradient reduce sidebranching. It is then found that tip undercooling cannot solely reverse this tendency but that, altogether, tip undercooling and cell form can succeed in making thermal gradient promote sidebranching, depending on the cellular branch of solutions. Applying this result to the branch actually displayed in directional solidification, we obtain a condition on the variation of the tip curvature radius with thermal gradient, for the noise-induced theory to be compatible with thermal gradient-induced sidebranching. Whether this condition is actually satisfied or not provides a validation criterion for the noise-induced theory of sidebranching in directional solidification, simple enough for being accessible to experimental investigation.