Stress field in the vicinity of a bubble/sphere moving in a dilute surfactant solution

Abstract

In this study, we experimentally investigate the stress field around a bubble rising in a dilute surfactant solution (20 < Re < 220, high Peclet numbers) whose surface gradually becomes contaminated, and compare it with that around a sphere free from surface contamination. We employ a newly developed polarization measurement technique, highly sensitive to stress fields near interfaces. First, we validate this method by measuring the flow around a solid sphere settling at Re = 120 and comparing results with numerical predictions, confirming its accuracy. We then measure the stress field around a bubble whose drag force transitions from that of a clean interface to that of a rigid interface within the observation region. The stress near the bubble's front resembles that of a clean bubble, while the rear behaves like a solid sphere. Between these regions, a discontinuous phase retardation near the cap angle indicates a transition from slip to no-slip boundary conditions. Axisymmetric stress reconstruction reveals localized stress spike at the cap angle, which shifts as surfactant accumulates and increases the drag. Remarkably, the measured cap angle versus normalized drag coefficient agrees well with numerical simulations at Re = 100 (Cuenot et al. 1997) and shows only a slight deviation from the creeping-flow stagnant cap model (Sadhal and Johnson 1983). This work demonstrates that polarization-based stress field measurements effectively capture the interplay between surface contamination and hydrodynamics at intermediate Reynolds numbers.