Computational Modeling of Adiabatic Bubble Growth Dynamics From Submerged Capillary-Tube Orifices in Aqueous Solutions of Surfactants

Abstract

The growth dynamics of isolated gas bubbles from a submerged capillary-tube orifice in a pool of an aqueous surfactant (sodium dodecyl sulfate or SDS) solution is computationally investigated. The governing equations for surfactant mass transport in the bulk liquid and interfacial adsorption–desorption are solved simultaneously with the Navier–Stokes equations, employing the volume-of-fluid (VOF) technique to track the deforming liquid–air interface. The VOF method tends to spread the liquid–air interface over two to three computational cells, creating an interface region with finite thickness. A new numerical treatment is developed to determine the surfactant transport and adsorption/desorption in the interface region. From the variation of the surfactant interfacial concentration, the spatio-temporal variation in interfacial tension is determined and the shape of the growing bubble is predicted. To validate the numerical model, experimental measurements of bubble shape and size are carried out using high speed videography. Because of the decrease in surface tension with surface age, bubble departure diameters in SDS–water solutions are smaller than those obtained in pure water, and they are a function of bubble frequency. At higher air-flow rates (smaller surface age), the bubble departure diameters tend toward those in pure water, whereas at low flow rates (larger surface age), they are significantly smaller than those in water and are closer in size to those in a pure liquid having surface tension equal to the equilibrium value in SDS solution. Furthermore, the nonuniform surfactant adsorption–desorption at the evolving interface results in variation in interfacial tension around the bubbles, and thus their shapes in surfactant solution are different from those in a pure liquid.