Pinch-off of rods by bulk diffusion

The morphology of a rod embedded in a matrix undergoing pinching by interfacial-energy-driven bulk diffusion is determined near the point of pinching. We find a self-similar solution that gives a unique temporal power law and interfacial shape prior to pinching and self-similar solutions after pinching. The theory is compared to experiments that employ in situ four-dimensional X-ray tomographic microscopy for rods of liquid or solid pinching by solute diffusion in the high-diffusivity liquid phase. The excellent agreement between experiment and theory confirms that the interfacial morphology near the singularity is universal both before and after pinching; the shape holds regardless of the material system and initial condition. This also implies that the predictions of the time-dependence of the process can be used to determine the time to pinching for a wide variety of physical systems, and thus provide estimates of the time required for capillarity-driven break-up of microstructures from the detachment of secondary dendrite arms to polymer blends

EXISTENCE AND STABILITY FOR A NON-LOCAL ISOPERIMETRIC MODEL OF CHARGED LIQUID DROPS

Abstract. We consider a variational problem related to the shape of charged liquid drops at equilibrium. We show that this problem never admits global minimizers with respect to L 1 perturbations preserving the volume. This leads us to study it in more regular classes of competitors, for which we show existence of minimizers. We then prove that the ball is the unique solution for sufficiently small charges. 1