Stability of core-annular flow of power-law fluids in the presence of interfacial surfactant

The shear-thinning influence on the core-annular flow stability of two immiscible power-law fluids is considered by making a linear stability analysis. The flow is driven by an axial pressure gradient in a straight pipe with the interface between the two fluids occupied by an insoluble surfactant. Given the basic flow for this core-annular arrangement, the analytical solution is obtained with respect to the power-law fluid model. The linearized equations for the evolution of infinitesimal disturbances are derived and the stability problem is formulated as a generalized matrix eigenvalue problem, which is solved by using the software package Matlab based on the QZ algorithm. The shear-thinning property is found to have marked influence on the power-law fluid core-annular flow stability, which is reflected in various aspects. First, the capillary instability is magnified by the shear-thinning property, which may lead to an essential difference between power-law and Newtonian fluid flows. Especially when the interface is close to the pipe wall, the power-law fluid flow may be unstable while the Newtonian fluid flow is stable. Second, under disturbances to the interface a velocity discontinuity at the interface appears which is destabilizing to the flow. The magnitude of this velocity discontinuity is affected by the power-law index and the flow stability is influenced correspondingly. Besides, the shear-thinning property may induce new stability modes which do not appear in the Newtonian fluid flow. The flow stability shows much dependence on the interface location, the role of which was neglected in most previous studies. The shear-thinning fluid flow is more unstable to long wave disturbances when the interface is close to the pipe wall, while the Newtonian fluid flow is more unstable when the interface is close to the pipe centerline. But this trend is changed by the addition of interfacial surfactant, for which the power-law fluid flow is more stable no matter where the interface is located.