Analytical treatment for parity breaking in eutectic growth

Using an ansatz for an asymmetric profile of the solidification front in lamellar eutectic growth, the von Neuman problem is solved. Imposing the Gibbs-Thomson condition, we derive a general expression for the tilt angle as a function of the control parameters. We find that the front undergoes a supercritical parity-breaking bifurcation at a critical value of σ=${\mathit{d}}_0$l/${\lambda }^2$ (${\mathit{d}}_0$ is the capillary length, l the diffusion length, and λ the wavelength of the pattern). We further find that parity-breaking causes a reduction of the average front undercooling. All these features agree with previous numerical results.