Boundary Curvature Effect on Thin-film Drainage and Slip Length Measurements

Abstract

The thin-liquid film drainage between two curved surfaces is a fundamental process for many hydrodynamic measurements, for which Vinogradova's formula has played a central role when flow slip occurs at fluid-solid interfaces. By performing a rigorous order-of-magnitude analysis, we reveal the importance of the curvature contribution to boundary flow, neglected sofar. Vinogradova's result is found to considerably underestimate the slip-induced reduction of the hydrodynamic drainage force. Our theory can play a crucial role in distinguishing finite-slip from no-slip and quantifying the degree of flow slip at fluid-solid surfaces, which is a fundamental but controversial issue in fluid dynamics. Moreover, qualitatively different from previous theories, our theory predicts a finite hydrodynamic repulsive force for two hydrophobic particles in touch, thus allowing particle collision to occur in a finite time without any additional attractive surface forces. This finding has deep and immediate implications on particle coagulation, adsorption and sedimentation processes relevant for numerous industrial technologies as well as natural phenomena on the earth.