Micro-convection mass transfer following bubble coalescence on a solid wall
The Volume-of-Fluid implementation in the \href{basilisk.fr}{Basilisk} flow solver is employed to study mass transfer after coalescence-induced jump-off of bubbles on solid substrates at four combinations of bubble radius ($R_m=150$ and 25 $\mu$m, hydrogen-water properties) and Schmidt number ($\text{Sc}=210$ and 1). The results show a relatively strong downward entrainment of low-concentration liquid, induced by a rapid movement of the bubble interface at approximately 0.5 to 1 inertio-capillary time units after the moment of coalescence. At $\text{Sc}=210$, this leads to a highly local increase of the Sherwood number at a core region (roughly an area of radius $R_m/2$) below the south pole of the merged bubble, which persists long after the bubble departure due to the slow diffusion at large $\text{Sc}$. The enhancement factor of the Sherwood number is highly dependent on the state of the mass-transfer boundary layer at the moment of coalescence, increasing with smaller boundary layer thicknesses. Shortly after the jump-off, the velocity of the bubble is considerably damped and rapidly approaches its free-rise terminal velocity. The effect of micro-convection on the wall mass transfer coefficient at this stage is insignificant when isolated, similar to what is reported in the literature for purely buoyancy-driven bubble rise -- but slightly stronger.