Morphological stability of rod-shaped continuous phases

Abstract Morphological transition of a rod-shaped phase into a string of spherical particles is commonly observed in the microstructures of alloys during solidification (Ratke and Mueller, 2006). This transition phenomenon can be explained by the classic Plateau-Rayleigh theory which was derived for fluid jets based on the surface area minimization principle. The quintessential work of Plateau-Rayleigh considers tiny perturbations (amplitude much less than the radius) to the continuous phase and for large amplitude perturbations, the breakup condition for the rod-shaped phase is still a knotty issue. Here, we present a concise thermodynamic model based on the surface area minimization principle as well as a non-linear stability analysis to generalize Plateau-Rayleigh’s criterion for finite amplitude perturbations. Our results demonstrate a breakup transition from a continuous phase via dispersed particles towards a uniform-radius cylinder, which has not been found previously, but is observed in our phase-field simulations. This new observation is attributed to a geometric constraint, which was overlooked in former studies. We anticipate that our results can provide further insights on microstructures with spherical particles and cylinder-shaped phases.