A continuum thermodynamic model of the influence of non-ionic surfactant on mass transfer from gas bubbles

Mass transfer of gaseous components from rising bubbles to the ambient liquid depends not only on the chemical potential difference of the transfer component but also on the interfacial free energy and composition. The latter is strongly affected by surface active agents that are present in many applications. Surfactants lead to local changes in the interfacial tension, which influence the mass transfer rates in two different ways. On the one hand, inhomogeneous interfacial tension leads to Marangoni stress, which can strongly change the local hydrodynamics. One the other hand, the coverage by surfactant molecules results in a mass transfer resistance. This hindrance effect is not included in current continuum physical models. The present work provides the experimental validation of a recently introduced extended sharp-interface model for two-phase flows with mass transfer that also accounts for the mass transfer hindrance due to adsorbed surfactant. The crucial feature is to account for area-specific concentrations not only of adsorbed constituents but also of transfer species, and to model mass transfer as a series of two bi-directional sorption-type bulk-interface exchange processes. The resulting model is shown to quantitatively describe experimental measurements on mass transfer reduction for the dissolution of CO$_2$ bubbles in different surfactant solutions.