Using surfactants to control the formation and size of wakes behind moving bubbles at order-one Reynolds numbers

Abstract

A bubble translating through a continuous liquid (i.e. Newtonian) phase moves as a sphere when inertial and viscous forces are small relative to capillary forces. Spherical bubbles with stress-free interfaces do not retain wakes at their trailing ends as inertial forces become important (increasing Reynolds number). This is in contrast to translating spheres with immobile interfaces in which flow separation and wake formation occurs at order-one Reynolds number. Surfactants present in the continuous phase adsorb onto a bubble surface as it translates, and affect the interfacial mobility by creating tension gradient forces. Adsorbed surfactant is convected to the trailing end of the bubble, lowers the tension there relative to the front, and creates a tension gradient which reduces the surface flow. For low bulk concentrations of surfactant (or if kinetic exchange between bulk and surface is slow relative to convection), diffusion towards the surface is much slower than convection, and surfactant is swept into an immobile cap at the trailing end. As with solid spheres, these caps entrain wakes at order-one Reynolds number. In adsorptive bubble technologies where solutes transfer between the bubble and the continuous phase, usually through thin boundary layers around the bubble surface (high Péclet number), these wakes generally form owing to the presence of surfactant impurities. The wake presence retards the interphase transfer displacing the thin boundary layer towards the front end of the bubble; as mass transfer through the wake is much slower than through the boundary layer, the mass transfer is reduced.

Our recent theoretical research has demonstrated that at low Reynolds numbers, the mobility of a surfactant-retarded bubble interface can be increased by raising the bulk concentration of a surfactant which kinetically rapidly exchanges between the surface and the bulk. At high bulk concentrations the interface saturates with surfactant, effectively removing the tension gradient. In this paper, we demonstrate theoretically that this interfacial control is still realized at order-one Reynolds numbers, and, more importantly, we show that the control can be used to manipulate the formation, size and ultimately the disappearance of a wake. This wake removal mechanism has the potential to dramatically increase the interphase transfer in adsorptive bubble technologies.