J. Fluid Mech. (2012), vol. 704, pp. 333–359. c  Cambridge University Press 2012 333 doi:10.1017/jfm.2012.243 Using surfactants to stabilize two-phase pipe flows of core–annular type Andrew P. Bassom 1 , M. G. Blyth 2 † and D. T. Papageorgiou 3 1 School of Mathematics & Statistics, The University of Western Australia, Crawley 6009, Australia 2 School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK 3 Department of Mathematics, Imperial College London, London SW7 2AZ, UK (Received 29 September 2011; revised 30 April 2012; accepted 21 May 2012; first published online 2 July 2012) The stability of a core–annular fluid arrangement consisting of two concentric fluid layers surrounding a solid cylindrical rod on the axis of a circular pipe is examined when the interface between the two fluid layers is covered with an insoluble surfactant. The motion is driven either by an imposed axial pressure gradient or by the movement of the rod at a prescribed constant velocity. In the basic state the fluid motion is unidirectional and the interface between the two fluids is cylindrical. A linear stability analysis is performed for arbitrary layer thicknesses and arbitrary Reynolds number. The results show that the flow can be fully stabilized, even at zero Reynolds number, if the base flow shear rate at the interface is set appropriately. This result is confirmed by an asymptotic analysis valid when either of the two fluid layers is thin in comparison to the gap between the pipe wall and the rod. It is found that for a thin inner layer the flow can be stabilized if the inner fluid is more viscous than the outer fluid, and the opposite holds true for a thin outer layer. It is also demonstrated that traditional core–annular flow, for which the rod is absent, may be stabilized at zero Reynolds number if the annular layer is sufficiently thin. Finally, weakly nonlinear simulations of a coupled set of partial differential evolution equations for the interface position and surfactant concentration are conducted with the rod present in the limit of a thin inner layer or a thin outer layer. The ensuing dynamics are found to be sensitive to the size of the curvature of the undisturbed interface. Key words: core-annular flow, instability, thin films 1. Introduction A cylindrical fluid thread is naturally unstable and will tend to disintegrate into droplets under the action of surface tension. The instability responsible for the break-up was first investigated by Plateau (1873) and Rayleigh (1878, 1892) both of whom considered an inviscid fluid thread suspended in a vacuum. Weber (1931) and Tomotika (1935) subsequently performed the corresponding linear stability calculations for a viscous thread suspended in an ambient viscous liquid and confirmed that a small-amplitude perturbation whose wavelength is greater than the circumference of the thread will grow in time. The same instability threshold applies when the liquid layers are bounded by a solid surface. This was demonstrated by Goren (1962), who † Email address for correspondence: m.blyth@uea.ac.uk