Linear stability of inverted annular gas–liquid two-phase flow in capillaries

Linear stability of creeping inverted-annular gas–liquid two-phase flow (liquid core and gaseous annular film) in microtubes, where buoyancy effect is suppressed by surface tension, is addressed. Using a long-wave linear stability solution [Physics of Fluids 14 (1971) 251], the flow field is shown to be linearly unstable for long-wavelength axisymmetric disturbances. The flow field approaches a neutrally stable state as the gas film thickness approaches zero, and instability is enhanced as the phasic velocities are reduced. A two-dimensional linear-stability analysis is also performed in order to examine the stability characteristics at the limit of zero phasic velocities. The analysis leads to a dispersion relation that results in an expression for the neutral wavelength that coincides with the prediction of the Kelvin–Helmholtz stability theory. The neutral and fastest-growing wavelengths are shown to be relatively insensitive to the liquid viscosity.