Open Access

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.

We present a 3D simulation approach utilising the diffuse interface representation of the phase-field method combined with a heat transfer equation to analyse the thermal conductivity in air-filled aluminium foams with complex cellular structures of different porosity. Algorithmic methods are introduced to create synthetic open-cell foam structures and to compute the thermal conductivity by means of phase-field modelling. A material law for the effective thermal conductivity is derived by determining the appropriate exponent depending on the relative density in the system. The results are compared with the thermal conductivity in massive aluminium and in pure air.