The effect of surfactant on the rise of a spherical bubble at high Reynolds and Peclet numbers

Experiments and numerical simulations of rising spherical bubbles in quiescent surfactant solutions are presented. The rise velocities versus the concentration in the bulk are measured using three surfactants, Triton X100, Brij30 and SDS for different bubble sizes, between 0.4 and 1 mm equivalent radius. We also present a brief description of the finite-difference numerical method developed to solve the full Navier-Stokes equations around the contaminated bubble for Reynolds numbers ranging from 50 to 200. The distributions of the tangential velocity, the vorticity, the pressure and the surfactant concentration on the bubble surface are calculated. In the case of high Peclet numbers surfactant molecules, which adsorb on the surface are convected and collected at the rear part of the bubble forming a stagnant cap where the no-slip condition holds. The concentration on the bubble interface is obtained for surfactants having a desorption rate much slower than the convective rate. The sudden increase of the shear stress and pressure at the leading edge of the cap contributes mainly to decrease the rise velocity. This rapid slowdown of the bubble occurs when nearly half of the bubble surface is covered by the surfactant layer, and this is due to the particularly high values obtained for the shear stress and the pressure at the leading edge of this cap-angle. Measured and calculated rise velocities for bubbles of 0.4 mm equivalent radius show good agreement when the sorption kinetics controls the surfactant exchange between the bulk and the surface. Calculated critical concentrations needed to cover completely the bubble agree with the measurements even for larger bubbles.