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

Abstract

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 Reynoldsand Bond numbers, inertial and buoyancy effects are negligible, and the liquid film thicknessis a function of the capillary number only. However, as the tube diameter is increased to themillimetre scale, both buoyancy and inertial forces may become significant. We present theresults of a systematic analysis of the bubble shape, inclination, and liquid film thicknessfor 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 floware performed by employing the Volume-Of-Fluid method implemented in OpenFOAM. Inagreement with previous studies, we observe that buoyancy lifts the bubble above the chan-nel axis, making the top liquid film thinner, and thickening the bottom film. As the Bondnumber approaches unity, the cross-sectional shape of the bubble deviates significantly froma circular shape, due to flattening of the bottom meniscus. The simulations demonstratethe existence of a cross-stream film flow that drains liquid out of the top film and drives ittowards the bottom film region. This drainage flow causes inclination of the bubble, witha larger inclination angle along the bottom plane of the bubble than the top. As buoyancybecomes even more significant, draining flows become less effective and the bubble inclina-tion reduces. A theoretical model for the liquid film thickness and bubble speed is proposedembedding dependencies on both capillary and Bond numbers, which shows good agreementwith the reported numerical results. Inertial forces tend to shrink the bubble cross-sectionand further lift the bubble above the channel centreline, so that the bottom film thicknessincreases significantly with the Reynolds number, whereas the top film thickness is less sen-sitive to it.