Inertial and buoyancy effects on the horizontal flow of Taylor bubbles in a circular channel

The effect of gravity on liquid film thickness around an elongated bubble travelling along a horizontal liquid-filled tube is studied numerically. At small Reynolds (Re) and Bond (Bo) numbers buoyancy and inertial effects are negligible and the liquid film thickness is a function of only the capillary number (Ca). As the tube diameter reaches millimetre length scales the buoyancy forces become non-negligible. 2D simulations for Bond and capillary numbers in the ranges 0.05<Bo<0.42 and 5 10⁴<Ca<0.12 have been performed. These simulations capture the asymmetry of the liquid film thickness, where gravitational effects cause the liquid film to be thinner at the top of the tube than the bottom. The 2D simulations do not capture bubble inclination relative to the channel centreline, but this is in agreement with experimental studies on the effect of gravity on a Saffman-Taylor meniscus. 3D simulations can capture transverse flow, and thus film drainage from the top to the bottom of the tube and its effect on bubble inclination. 3D numerical simulations are systematically performed to span a wide range of Ca, Re and Bo and thus investigate how inertial forces impact the flow.