The effect of soluble surfactant on the transient motion of a buoyancy-driven bubble

Abstract

The effect of soluble surfactants on the unsteady motion and deformation of a bubble rising in an otherwise quiescent liquid contained in an axisymmetric tube is computationally studied by using a finite-difference/front-tracking method. The unsteady incompressible flow equations are solved fully coupled with the evolution equations of bulk and interfacial surfactant concentrations. The surface tension is related to the interfacial surfactant concentration by a nonlinear equation of state. The nearly spherical, ellipsoidal, and dimpled ellipsoidal-cap regimes of bubble motion are examined. It is found that the surfactant generally reduces the terminal velocity of the bubble but this reduction is most pronounced in the nearly spherical regime in which the bubble behaves similar to a solid sphere and its terminal velocity approaches that of an equivalent solid sphere. Effects of the elasticity number and the bulk and interfacial Peclet numbers are examined in the spherical and ellipsoidal regimes. It is found that the surface flow and interfacial surfactant concentration profiles exhibit the formation of a stagnant cap at the trailing end of the bubble in the ellipsoidal regime at low elasticity and high interfacial Peclet numbers. Bubble deformation is first reduced due to rigidifying effect of the surfactant but is then amplified when the elasticity number exceeds a critical value due to overall reduction in the surface tension.