Mixing structures in bubble wakes of single bubbles and bubble swarms and their influence on gas-liquid mass transfer and chemical reaction

The main objective of this project is to unveil how mixing structures in the wakes of freely rising single bubbles and in bubble swarms can be incorporated into compact mass transfer correlations for process engineering. In this way the impact of the wakes on chemical reactions can be estimated more easily. The knowledge about the detailed mass transfer is crucial to produce a vast proportion of bulk chemicals used in everyday life that are synthesized in gas-liquid reactions like hydrogenation, oxidation, or chlorination. Furthermore, contained high gas concentrations in bubble wakes can also be potentially harmful to microorganisms and enzymes in gassed reactors leading to a substrate inhibition. To predict how much gas is transferred from a bubble to a surrounding liquid the mass transfer coefficient (or the nondimensionalized Sherwood number) has to be determined. Todays mass transfer models (Sherwood correlations) either build on the two-film theory, on the penetration theory, or on the surface-renewal theory with varying parameters in dependence on bubble relative velocity to the surrounding liquid and laminar or turbulent surrounding flow conditions. Adapted models exist to account for the effect of surfactants onto the mass transfer. All theories assume, however, that once the gas is dissolved in the liquid phase it gets immediately well mixed and that all fluid parcels passing the bubble interface experience the same conditions in the bubble wake once they leave the bubble surface. This picture neglects effects of a heterogeneous concentration wake that will likely influence a reaction taking place close to the bubble interface and in the bubble wake for small to intermediate Hatta numbers as according to Levenspiel. So far, the details of the structure of the mixing in the bubble wake are not considered for mass transfer correlations. In this research proposal, the Lagrangian coherent structures (LCS) in the bubble wake of 3D freely rising bubbles and bubble swarms in stagnant liquid will be analyzed by evaluating 4D-PTV measurements using recently developed mathematical tools stemming from dynamical systems theory. Additionally, a quantitative evaluation of the concentration of the dissolved gas will be obtained using Time Resolved Laser Induced Fluorescence (TRS-LIF). The LCS will be compared to the concentration wakes and both measurements supply input for the development of new Sherwood correlations that incorporate the effect of coherent flow structures in bubble wakes.