Universality and self-similarity in pinch-off of rods by bulk diffusion

As rodlike domains pinch off owing to Rayleigh instabilities, a finite-time singularity occurs as the interfacial curvature at the point of pinch-off becomes infinite. The dynamics controlling the interface become independent of initial conditions and, in some cases, the interface attains a universal shape. Such behaviour occurs in the pinching of liquid jets and bridges and when pinching occurs by surface diffusion. Here we examine an unexplored class of topological singularities where interface motion is controlled by the diffusion of mass through a bulk phase. We show theoretically that the dynamics are determined by a universal solution to the interface shape (which depends only on whether the high-diffusivity phase is the rod or the matrix) and materials parameters. We find good agreement between theory and experimental observations of pinching liquid rods in an Al-Cu alloy. The universal solution applies to any physical system in which interfacial motion is controlled by bulk diffusion, from the break-up of rodlike reinforcing phases in eutectic composites to topological singularities that occur during coarsening of interconnected bicontinuous structures, thus enabling the rate of topological change to be determined in a broad variety of multiphase systems.