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(1). Such behaviour occurs in the pinching of liquid jets and bridges(2-9) and when pinching occurs by surface diffusion(10-12). 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(13-16) to topological singularities that occur during coarsening of interconnected bicontinuous structures(17-20), thus enabling the rate of topological change to be determined in a broad variety of multiphase systems.