Universal pinch off of rods by capillarity-driven surface diffusion

Abstract

Interfacial energy is a central factor in setting the morphology of phases and in determining the stability of equilibrium morphologies. here the authors examine the morphological evolution of a rod via capillary-driven surface diffusion as it both approaches and departs the topological singularity of pinch off. During the final stages of pinching the neck radius approaches zero, and self-similar solutions are sought. The authors have derived local similarity solutions for the axisymmetric pinch off of rods when the morphological evolution is by capillarity-driven surface diffusion. These local solutions describe the approach to and departure from the topological singularity where a rod pinches into two separate bodies. During pinching, the self-similar surface profile far away from the neck approaches two opposing cones with a unique half-cone angle of 46.04{degree}. It is thus likely that all rods must pinch off with this cone angle. This assertion is supported by several numerical simulations. After pinch off, the smoothening of the cone tip is again self-similar. The results obtained here for rods also apply to the pinch off of cylindrical pore channels.