A Surfactant Prediction Model for Rising Bubbles

Abstract

Bubbles released from a needle show shape deformations that depend on the surfactant concentration of the surrounding liquid. We develop a model that predicts the surfactant concentration based on experimental early-stage observations of these deformations. Using high-speed imaging, we examine bubbles within the first 144 ms of ascent, corresponding to a vertical rise distance of approximately 40 mm and extract the instantaneous aspect ratio (AR) and analyse its temporal evolution. In clean conditions, bubbles exhibit pronounced shape oscillations resulting from the periodic exchange between surface and kinetic energy. The presence of surfactants leads to an immediate damping of these oscillations, characterised by reduced AR amplitudes and earlier peak deformations. This damping effect intensifies with increasing surfactant concentration until a near-saturation regime is reached, beyond which bubbles remain largely spherical and further increases in concentration produce indistinguishable AR profiles within the early-stage observation window. To develop the prediction model, an aspect-ratio-based analysis methodology is proposed, which yields an empirical relationship capable of estimating surfactant concentrations between 0 ppm and 2.9 ppm. We finally test the reliability of the model on unknown surfactant-laden bubbles. The model successfully detected the presence and relative extent of surfactant contamination as higher concentrations were introduced.