Diffuse-interface approach to competition between viscous flow and diffusion in pinch-off dynamics

Abstract

Recently it was observed that when interfacial tension is lower by 2-3 orders of magnitude than normal liquids, pinch-off dynamics is dominated by bulk diffusion, with a scaling behavior unlike that of Stokes flow. We use the Cahn-Hilliard--Navier-Stokes model to investigate the pinch-off dynamics of a liquid thread surrounded by a viscous external fluid. A length scale is introduced to characterize the competition between diffusion and viscous flow. The crossover between Stokes and diffusion-dominated regimes is examined numerically and analytically for the change in scaling behaviors of similarity solutions as the pinching neck of the interface accesses the characteristic length scale.