| The stability of miscible core-annular flows with viscosity stratification is investigated in this dissertation. In the first part of the investigation, we perform the linear temporal stability analysis of variable viscosity, miscible core-annular flows. Consistent with pipe flow of a single fluid, the flow is stable at any Reynolds number when the magnitude of the viscosity ratio is less than a critical value. This is in contrast to the immiscible case without interfacial tension, which is unstable at any viscosity ratio. Beyond the critical value of the viscosity ratio, the flow can be unstable even when the more viscous fluid is in the core. This is in contrast to plane channel flows with finite interface thickness, which are always stabilized relative to single fluid flow when the less viscous fluid is in contact with the wall. If the more viscous fluid occupies the core, the axisymmetric mode usually dominates over the corkscrew mode. It is demonstrated that, for a less viscous core, the corkscrew mode is inviscidly unstable, while the axisymmetric mode is unstable for small Reynolds numbers at high Schmidt numbers. The occurrence of inviscid instability for the corkscrew mode is shown to be consistent with the Rayleigh criterion for pipe flows. In some parameter ranges, the miscible flow is seen to be more unstable than its immiscible counterpart, and the physical reasons for this behavior are discussed.; The second emphasis of the dissertation is to investigate the convective/absolute nature of miscible core-annular flows through both linear spatio-temporal analysis and nonlinear simulations. The stability transition curves from convective to absolute instability, obtained in the parameter space of Reynolds number (Re) and core radius (RI), show that miscible core-annular flows exhibit absolute instability for a limited range of RI, at high viscosity ratios. Direct numerical simulations performed in a long periodic domain show that the front velocities of the perturbation wave packet agree with those obtained from the linear impulse response. This indicates that the trailing edge front dynamics are dominated by linear mechanisms. In the case of a semi-infinite domain with an upstream boundary, absolutely unstable systems give rise to nonlinear global modes. The global frequency is seen to match the linear absolute frequency for the parameters prescribed at the upstream boundary, in accordance with the theoretical predictions. The simulation results are compared with the recent experiments, wherein the miscible core-annular flows are shown to exhibit global instability. |
