Tip-splitting instability in directional solidification based on bias field method

Tip splitting instability of cellular interface morphology in directional solidification is analyzed based on the bias field method proposed recently by Glicksman. The physical mechanism of tip instability is explained by analyzing the interface potential, the tangential energy flux, and the normal energy flux. A rigorous criterion for tip-splitting instability is established analytically, i.e., the ratio of the cellular tip radius to the cellular width α > 3/2/pπ≈ 0.3899, which is in good agreement with simulation results. This study also reveals that the cellular tip splitting instability is attributable to weak Gibbs-Thomson energy acting on the interface.