Linear instability of two-fluid Taylor–Couette flow in the presence of surfactant

Abstract

The effect of an insoluble surfactant on the centrifugal and shear instability of a pair of radially stratified immiscible liquids in the annular gap between concentric two-fluid Taylor–Couette flow is investigated by a normal-mode linear analysis and complementary energy analysis. The interface is assumed to be concentric with the cylinders. The gravitational effects are ignored. Influences of density and viscosity stratification, surface tension, surfactant concentration distribution and Taylor–Couette shearing are considered comprehensively. The instability characteristics due to competition and interaction between various physical instability mechanisms are of principal concern. Neutral curves with upper and lower branches in the Reynolds number (Re1)/axial wavenumber (k) plane are obtained. A window of parameters is identified in which the flow is linearly stable. The Marangoni traction force caused by the gradient of surfactant concentration stabilizes the axisymmetric perturbations but initiates an instability corresponding to non-axisymmetric modes in the presence of basic Couette shearing flow. Co-rotation of the outer cylinder has a stabilizing effect in expanding the stable region, which dwindles in the counter-rotation situation.