Visco-elastic drag forces and crossover from no-slip to slip boundary conditions for flow near air-water interfaces

TL;DR

This study investigates how surface contamination affects flow boundary conditions at air-water interfaces by measuring viscous and elastic forces on a vibrating sphere, revealing a transition from no-slip to slip conditions and frequency-dependent elastic behavior.

Contribution

It introduces a novel AFM-based method to detect surface impurities by analyzing force responses, providing insights into boundary condition crossover and impurity concentration estimation.

Findings

Viscous forces exhibit a crossover from no-slip to slip boundary conditions.

Elastic forces vary nontrivially with vibration frequency.

Proposed model explains force behavior and impurity detection.

Abstract

The "free" water surface is generally prone to contamination with surface impurities be they surfactants, particles or other surface active agents. The presence of such impurities can modify flow boundary near such interfaces in a drastic manner. Here we show that vibrating a small sphere mounted on an AFM cantilever near a gas bubble immersed in water, is an excellent probe of surface contamination. Both viscous and elastic forces are exerted by an air-water interface on the vibrating sphere even when very low doses of contaminants are present. The viscous drag forces show a cross-over from no-slip to slip boundary conditions while the elastic forces show a nontrivial variation as the vibration frequency changes. We provide a simple model to rationalize these results and propose a simple way of evaluating the concentration of such surface impurities.