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.
|Number of pages||27|
|Journal||Journal of Fluid Mechanics|
|Publication status||Published - 2012|