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.
Modelling vertical concentration distributions of solids suspended in turbulent visco-plastic fluid
