Liquid film distribution around long gas bubbles propagating in rectangular capillaries

Magnini, M.; Municchi, F.; El Mellas, I.; Icardi, M.

Abstract

We present a systematic analysis of the bubble and liquid film dynamics corresponding to the propagation of long, isolated gas bubbles, within rectangular capillary channels of cross-sectional aspect-ratio ranging from 1 to 8. Direct numerical simulations of the flow are performed using ESI-OpenFOAM v.1812 and its geometric Volume-Of-Fluid solver isoAdvector. The interface curvature, which enters the calculation of the surface tension force in the momentum equation, is calculated with a parabolic reconstruction method. This study covers a range of capillary and Reynolds numbers of, respectively, 0.005≤Ca≤1 and 1≤Re≲1000. The lubrication film surrounding the bubble is always resolved by the computational mesh, and thus the present results are representative of a perfectly wetting fluid. This study shows that rectangular cross-sections promote the formation of an extended liquid film covering the longer wall of the channel. This liquid film exhibits a saddle-like shape and its streamwise evolution varies depending on the channel shape and flow conditions. Although cross-sectional liquid film profiles and corresponding thicknesses are not constant along the bubble, in general the film deposited upon the shorter wall becomes thicker for increasing values of the aspect-ratio, while the thickness of the film deposited upon the longer wall obeys a Ca2/3/(1+Ca2/3) law which, provided that the channel hydraulic radius is the same, is independent of the aspect-ratio at sufficiently small Ca. An empirical correlation is proposed to predict the cross-sectional gas fraction and bubble speed as a function of a modified capillary number, embedding dependencies on both Ca and aspect-ratio, and converging to the asymptotic limit for a quasi-static flow when Ca→0.

Citation

Magnini, M., Municchi, F., El Mellas, I., & Icardi, M. (2022). Liquid film distribution around long gas bubbles propagating in rectangular capillaries. International Journal of Multiphase Flow, 148, Article 103939. https://doi.org/10.1016/j.ijmultiphaseflow.2021.103939

• Journal Article Type: Article
• Acceptance Date: Dec 14, 2021
• Online Publication Date: Jan 12, 2022
• Publication Date: 2022-03
• Deposit Date: Oct 19, 2022
• Publicly Available Date: Jan 13, 2023
• Journal: International Journal of Multiphase Flow
• Print ISSN: 0301-9322
• Electronic ISSN: 1879-3533
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 148
• Article Number: 103939
• DOI: https://doi.org/10.1016/j.ijmultiphaseflow.2021.103939
• Keywords: Fluid Flow and Transfer Processes; General Physics and Astronomy; Mechanical Engineering
• Public URL: https://nottingham-repository.worktribe.com/output/7285003
• Publisher URL: https://www.sciencedirect.com/science/article/abs/pii/S0301932221003402?via%3Dihub