Liquid film distribution around long gas bubbles propagating in rectangular capillaries

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 less than or similar to 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 Ca-2/3/(1 + Ca-2/3) 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.

Automated summary

This study systematically analyzed the dynamics of bubbles and liquid films in rectangular capillary channels using numerical simulations, providing insights into the evolution of liquid films and the prediction of bubble speed.