Investigation of a free rising bubble with mass transfer by an arbitrary Lagrangian–Eulerian method

Abstract

The dissolution of bubbles with large volume change is numerically investigated by employing an arbitrary Lagrangian–Eulerian (ALE) method. To describe the mechanisms of the mass transfer from the bubble to the surrounding liquid, the species conservation equation is solved in the liquid phase, and the interfacial mass transfer is modeled based on the concentration gradient at the interface. Moreover, an accelerating reference method is developed to synchronize the computational domain with the bubble/drop motion and also to minimize the computational cost. The applicability of the proposed numerical approach is verified by benchmark tests, i.e., the dynamic behavior of a free rising bubble/drop and the dissolution of a rising bubble. Then the dissolving processes of an oxygen bubble in silicon oil are simulated, and the calculated shrinkage of the bubble size agrees well with experimental results. Moreover, the bubble motion is found to have a strong effect on the dissolution, and reasonable agreement is obtained between the predicted results and the experimental data in terms of the Sherwood and Reynolds numbers. Furthermore, based on the accurate calculation of the bubble surface and the corresponding transport of the dissolving gas, the thickness of the concentration boundary layer and the local Sherwood number are studied quantitatively. It is found that the thickness increases gradually with the cap angle, while on the contrary, the Sherwood number decreases, indicating that the thickness of the concentration boundary layer dominates the mass transfer behavior at the bubble surface.