The Late Stages of Approach of Liquid-Liquid Interfaces to Smooth Probes; Rupture by Asperities

The passage of a liquid-liquid interface past a smooth parabolic profile is analysed, with emphasis on the last st ages before rupture. The outer flow is at high Reynolds number, and so boundary-layer theory is relevant. The cases We → ∞, We → 0, and We = O(1) are treated separately, where We is the Weber number based on the far-field approach velocity, the probe-tip curvature, the interfacial tension and the fluid density; density and viscosity are taken equal for the two fluids respectively for simplicity. For smooth prob es and fluids of interest, it is shown that the time taken for th e interface to approach close enough for long-range surface forces to be important at the probe tip, and hence cause rupture, is large compared with the time taken for an undeforming int erface to reach the position of the prob e tip. However, using a fractal mod el for a sharp-tipped probe, it is shown that the time to rupture is close to the latter time.