Estimation of gas-liquid mass transfer using a model of gas diffusion around deformable bubbles

A new hybrid modeling approach is presented for predicting the mass transfer rate of sparingly soluble gases in liquid flow over non-spherical bubbles within an elementary mass-exchange cell. Extending the classical theoretical foundation laid by Levich, the proposed model incorporates the bubble's non-spherical, axisymmetric surface geometry and local flow characteristics-factors often encountered in real systems but typically omitted in standard approximations. This framework can integrate advanced image analysis (such as high-speed video segmentation of bubble boundaries) to capture bubble interface contours, which are then parameterized using superformula regression to yield representations of complex axisymmetric bubble shapes. These representations are used to impose shape-sensitive boundary conditions on the convective-diffusive equation, and the governing equation is transformed into a local orthogonal curvilinear coordinate system aligned with the bubble surface, simplifying the convective-diffusive formulation in the bubble boundary layer. Focusing on the actual interface geometry the model yields a detailed description of the local mass flux distribution over the bubble surface. This shape-specific result can be integrated across bubble geometries to improve overall mass transfer estimates in bubbly flows. In the special case of a spherical bubble, the model's predictions agree with Levich's analytical solution for both the total mass transfer and flux distribution along the interface, lending credibility to this generalized approach. The resulting framework not only generalizes Levich's theory but also offers a non-invasive efficient methodology for quantifying absorption processes in bubble-driven multiphase flows-one of the few to explicitly account for deformed bubble geometry.