A numerical study on mass transfer in buoyancy-driven bubbly flows

The present study investigates the mass transfer of a dilute species from a dispersed bubbly phase to a carrier liquid phase using interface-resolved simulations and proposes a phenomenological model for its transient dynamics. To this end, we individually vary several input parameters, i.e. the species diffusivity (the Schmidt number, ${\textit{Sc}}$ ), the void fraction $(\alpha )$ and the bubble size (which affects the Galilei number ${\textit{Ga}}$ and Bond number ${\textit{Bo}}$ ) – while maintaining conditions representative of air bubbles in water. For the parametric range – ${\textit{Sc}}$ = $1,5$ and 10; $\alpha$ = 0.5 %, 1.9 % and 3.6 %; and three initial bubble diameters $d_0$ = $0.63\, \text{mm}$ $(\text{i.e.}\ Ga$ = $1.75$ and ${\textit{Bo}}$ = $0.0125)$ , $1.2\, \text{mm}$ ( ${\textit{Ga}}$ = $4.6$ and ${\textit{Bo}}$ = 0.045) and $1.58\, \text{mm}$ ( ${\textit{Ga}}$ = $7$ and ${\textit{Bo}}$ = $0.07921$ ) – we show that increasing diffusivity and decreasing bubble size decreases scalar advection as compared with diffusion and hence the time needed for the species concentration to saturate in the carrier phase, which can be well represented by a Péclet number