Morphology of long gas bubbles propagating in square capillaries

Abstract

We present the results of a systematic analysis of the morphology of the thin lubrication film surround- ing a long gas bubble transported by a liquid flow in a square capillary. Direct numerical simulations of the flow are performed using the Volume-Of-Fluid method implemented in OpenFOAM, for a range of capillary and Reynolds numbers Ca = 0 . 002 −0 . 5 and Re = 1 −20 0 0 , and very long bubbles, up to 20 times the hydraulic diameter of the channel. The lubrication film surrounding the bubbles is always re- solved by the computational mesh, and therefore the results are representative of a fully-wetting liquid. This study shows that when Ca ≥0.05, the long gas bubble exhibits an axisymmetric shape on the chan- nel cross-section, whereas for lower capillary numbers the bubble flattens at the centre of the channel wall and thick liquid lobes are left at the corners. When Ca ≤0.01, the thin film at the centre of the wall assumes a saddle-like shape, which leads to the formation of two constrictions at the sides of the liquid film profile, where minimum cross-sectional values of the film thickness are observed. The result- ing cross-stream capillary pressure gradients drain liquid out of the thin-film, whose thickness decreases indefinitely as a power-law of the distance from the bubble nose. Therefore, the film thickness depends on the length of the bubble, unlike flow in circular channels. We report detailed values of the centre- line, diagonal and minimum film thickness along the bubble, bubble speed, and cross-sectional gas area fraction, at varying Ca and Re. Inertial effects retard the formation of the saddle-shaped thin-film at the channel centre, which may never form if the bubble is not sufficiently long. However, the film thins at a faster rate towards the bubble rear as the Reynolds number of the flow is increased.