Stability of surfactant-laden coreannular ow and rodannular ow to non-axisymmetric modes

The linear stability of core–annular fluid arrangements are considered in which twoconcentric viscous fluid layers occupy the annular region within a straight pipe with asolid rod mounted on its axis when the interface between the fluids is coated with aninsoluble surfactant. The linear stability of this arrangement is studied in two scenarios:one for core–annular flow in the absence of the rod and the second for rod–annularflow when the rod moves parallel to itself along the pipe axis at a prescribed velocity.In the latter case the effect of convective motion on a quiescent fluid configuration isalso considered. For both flows the emphasis is placed on non-axisymmetric modes;in particular their impact on the recent stabilization to axisymmetric modes at zeroReynolds number discovered by Bassom, Blyth and Papageorgiou (J. Fluid. Mech.,vol. 704, 2012, pp. 333–359) is assessed. It is found that in general non-axisymmetricdisturbances do not undermine this stabilization, but under certain conditions theflow may be linearly stable to axisymmetric disturbances but linearly unstable tonon-axisymmetric disturbances.Key words: core–annular flow, interfacial flows (free surface), multiphase and particle-laden flows