  This work deals with stability of two-phase stratified air-water flows in
horizontal circular pipes. For this purpose, we performed a linear stability
analysis, which considers all possible three-dimensional infinitesimal
disturbances and takes into account deformations of the air-water interface.
The main results are presented in form of stability maps, which compare well
with the available experimental data. The neutral stability curves are
accompanied by the corresponding wavenumbers and wave speeds of the critical
perturbations, as well as by spatial patterns of their velocity components.
Accordingly, several modes of the critical perturbation are revealed. Long
waves are found to be the critical perturbation over part of the stability
boundary, and they are affected by the surface tension due to the confinement
effect of the lateral direction. Exploring the effect of pipe diameter on the
stability boundary and critical perturbations shows that for small water
holdups (i.e., thin water film) the scaling of the critical gas velocity by the
gas Froude number is valid for pipe diameters larger than about 0.1m, where the
surface tension effects due to the lateral confinement become negligible.
Comparing results obtained in pipe, square duct, and two-plate geometries, we
show that there are cases where the simplified geometry of two parallel plates
can be employed to model the realistic geometry reasonably well.
