Transient bubble rising in the presence of a surfactant at very low concentrations

TL;DR

This study investigates how tiny amounts of surfactant affect bubble rise dynamics, revealing a three-phase formation of the adsorption layer and the maximum velocity occurring near the desorption rate, even at trace surfactant levels.

Contribution

It provides a detailed analysis of the dynamic adsorption layer formation and its impact on bubble velocity in the presence of very low surfactant concentrations, validated by experiments and simulations.

Findings

Maximum bubble velocity occurs near the inverse of the desorption rate constant.

The dynamic adsorption layer forms in three distinct phases.

Trace surfactant amounts significantly influence bubble dynamics.

Abstract

We study the formation of the dynamic adsorption layer when a bubble is released in a tank containing water with a tiny amount of surfactant. The influence of the sorption kinetic constants is examined by comparing the experiments with Sodium Dodecyl Sulfate (SDS) and Triton X-100. The experiments allowed us to determine the parameter conditions that lead to a stable bubble rising and to validate the simulation. A simple scaling analysis and the simulation show that the formation of the dynamic adsorption layer can be split into three phases characterized by disparate time scales. The mechanisms controlling those phases are surfactant convection, adsorption-desorption, and diffusion. The amount of surfactant adsorbed onto the interface increases monotonously throughout the three phases. The experiments and the simulation show that the rising velocity reaches a maximum at times of the order of $k_d^{-1}$ ($k_d$ is the desorption constant) when the dynamic adsorption layer is practically formed. This occurs even when only traces of surfactant are present in the liquid. The non-monotonous behavior of the maximum surfactant surface concentration is explained in terms of the reverse flow in the rear of the bubble right after the bubble release. This work contributes to the understanding of the complex interplay between hydrodynamics and surfactant transport and kinetics over bubble rising.