Dynamical wavelength selection by tilt domains in thin-film lamellar eutectic growth

Tilt domains are dynamical defects of cellular growth fronts consisting of a group of asymmetric cells traveling laterally along the front. We study the dynamics of these defects in thin-film directional solidification of the ${\mathrm{CBr}}_4$-${\mathrm{C}}_2$ ${\mathrm{Cl}}_6$ eutectic alloy. We show that the sweeping of the growth front by tilt domains, at a given growth velocity V, brings it into a well-defined ‘‘dynamically selected’’ state. Once this state is reached, the tilt domains travel with a constant width. A sudden increase (decrease) of the growth velocity transforms constant-width tilt domains to growing (shrinking) ones. This behavior is in complete agreement with the theoretical predictions made by Coullet et al. [Phys. Rev. Lett. 63, 1954 (1989)] and Caroli et al. [J. Phys. I (Paris) 2, 281 (1992)]. We study the V dependence of the dynamically selected wavelength. It does not follow the ${\mathit{V}}^{\mathrm{-}1/2}$ law, contrary to the ‘‘selected’’ wavelength of lamellar eutectics in the range of velocities and thermal gradients that we use. Above a velocity ${\mathit{V}}_{\mathrm{cr}}$, the dynamically selected basic state is unstable against the lamellar-extinction instability. We describe some dynamical patterns resulting from the interplay between the latter instabiilty and the tilt instability.