The growth dynamics of isolated gas bubbles (inception → growth → departure) emanating from a capillary-tube orifice submerged in isothermal pools of aqueous solutions of surfactants is computationally investigated. The Navier-Stokes equations are solved in the liquid and the gas phase. The evolution of the gas-liquid interface is tracked using a Volume-of-Fluid (VOF) method. Surfactant molecules in aqueous solutions have a tendency to diffuse towards the gas-liquid interface and are subsequently adsorbed onto it. This time dependent adsorption process gives rise to the dynamic surface tension behavior of the aqueous surfactant solutions. To computationally model this behavior, the species conservation equation for the surfactant is solved in the bulk fluid and is coupled with the dynamic adsorption-desorption of the surfactant on the interface. A new form of the surfactant transport equation is derived that was necessary to incorporate the interfacial transport in the volume-of-fluid method where the interface is spread over multiple grid cells.
Computational results were obtained for bubble growth dynamics from a capillary orifice in a pool of pure water and in an aqueous solution of Sodium Dodecyl Sulphate (SDS). The evolving bubble shape and the flow field in the two phases in the pure liquid and in surfactant solution are compared for a variety of air flow rates (from 4 ml/min to 24 ml/min) in the constant bubble regime. To validate the computational model, the results for the transient shape and size of growing bubbles in pure water were compared with available experimental data and were found to be in excellent agreement. Results show that the dynamic surface tension relaxation gives rise to smaller bubble size at departure in aqueous surfactant solution compared to that in pure water. However, this effect is found to be a function of the air flow rate. At high air flow rates (24 ml/min), the short time for bubble growth allows relatively smaller drop in the surface tension and produces departure diameters similar to bubble diameters in water. At low air flow rates (4 ml/min), the departure time is much larger and allows for complete surface tension relaxation. As such the departure diameters at low air flow rates in aqueous surfactant solution are significantly smaller than those predicted in pure water. Also, the flow patterns around a growing bubble in surfactant solution are altered due to the non-uniform surfactant adsorption along the gas-liquid interface. The computational results elucidate the role of surfactant transport on bubble growth dynamics.