Mass transfer and reaction in the liquid phase of gas-liquid multiphase flows usually takes place at a considerably slower rate than the transfer of momentum, so mass flux boundary layers are much thinner than momentum boundary layers. In Direct Numerical Simulations (DNS) the resolution requirement for flows with mass transfer are therefore significantly higher than for flow without mass transfer and reaction. In this work we develop a multi-scale approach and demonstrate its implementation in 2D to compute the mass transfer from buoyant bubbles, using a boundary-layer approximation next to the bubble and a relatively coarse grid for the rest of the flow. This approach greatly reduces the overall grid resolution required. Then we implement our method in 3D and perform validation of the approach by comparing to experimental data and semi-empirical correlations from the literature. We study the effect of void fraction and bubble interactions on the mass transfer from many bubbles using a 3D implementation of the code.
Specifically, we do simulations of single bubbles in periodic boxes and we compare it to the simulation of several bubbles in a larger domain with the same void fraction. Comparisons shows that even though the average Reynolds number of freely moving bubbles drops after a while the mass transfer from the bubbles for most case studies increases slightly when bubbles start wobbling which increases bubble interactions. We also develop a film model to recover the under-resolved viscous forces between colliding non-coalescing droplet.