Inertial and buoyancy effects on the flow of elongated bubbles in horizontal channels

When a long gas bubble travels in a horizontal liquid-filled channel of circular cross-section, a liquid film is formed between the bubble and the channel wall. At low Reynolds and Bond numbers, inertial and buoyancy effects are negligible, and the liquid film thickness is a function of the capillary number only. However, as the tube diameter is increased to the millimetre scale, both buoyancy and inertial forces may become significant. We present the results of a systematic analysis of the bubble shape, inclination, and liquid film thickness for a wide range of capillary, Bond, and Reynolds numbers, namely   0.024≤Cal≤0.051, 0.11≤Bo≤3.5, and 1≤Rel≤750. Three-dimensional numerical simulations of the flow are performed by employing the Volume-Of-Fluid method implemented in OpenFOAM. In agreement with previous studies, we observe that buoyancy lifts the bubble above the channel axis, making the top liquid film thinner, and thickening the bottom film. As the Bond number approaches unity, the cross-sectional shape of the bubble deviates significantly from a circular shape, due to flattening of the bottom meniscus. The simulations demonstrate the existence of a cross-stream film flow that drains liquid out of the top film and drives it towards the bottom film region. This drainage flow causes inclination of the bubble, with a larger inclination angle along the bottom plane of the bubble than the top. As buoyancy becomes even more significant, draining flows become less effective and the bubble inclination reduces. A theoretical model for the liquid film thickness and bubble speed is proposed embedding dependencies on both capillary and Bond numbers, which shows good agreement with the reported numerical results. Inertial forces tend to shrink the bubble cross-section and further lift the bubble above the channel centreline, so that the bottom film thickness increases significantly with the Reynolds number, whereas the top film thickness is less sensitive to it.