Studies On The Stability Of Flows With Wall Suction/Injection And Surfactant

Effects of wall suctioin/injection and surfactants play an important role in the stability of flows involved in a wide range of engineering applications.In a majority of previous studies on these topics,the basic flow configuration is usually treated as a steady system or has only one interface.This dissertation is devoted to the stability of periodic flows with the suction/injection,surfactant-laden multiple-layer films,and oscillatory fluid layer with surfactants.Four typical problems are investigated in detail and described briefly as follows:(1)The stability of plane Poiseuille flow modulated by oscillatory wall suction/injection is investigated based on linear stability analysis together with Floquet theory. The basic flow and the stability characteristics are analyzed using a Chebyshev collocation method.When the amplitudeΔof suction/injection is sufficiently small,asymptotic solutions of the basic velocity profile and the growth rate of disturbances are also obtained.For the parameters considered,the critical Reynolds number is always lower than one for the pure Poiseuille flow,and hence the flow becomes more unstable.The asymptotic results show that the correction terms for the growth rate are of O(Δ~2)and positive,indicating a destabilizing effect of the suction/injection.Moreover,it is found that the destabilizing effect is mainly connected to the steady corrections of the mean flow profile in the O(Δ~2)terms.(2)Effects of uniform wall suction/injection on the linear stability of flat Stokes layers are studied.A semi-analytical method is developed to examine the stability of time-periodic boundary flows in the presence of wall suction/injection.Typical growth rates,neutral curves and critical Reynolds numbers are obtained.Results show that the critical Reynolds number decreases monotonically as the velocity of suction/injection increases.Thus,the onset of instability of the flat Stokes layers can be suppressed by wall suction and enhanced by wall injection.The values of the critical Reynolds number predicted by the quasi-parallel approximation of the basic flow agree quite well with the exact results,indicating a negligible influence of the normal component of the basic velocity on the flow instability.It is also revealed that the critical Reynolds number is approximately dependent on the suction/injection velocity with an exponential relation. (3)The inertialess instability of a two-layer film flow is analyzed by interpreting the underlying mechanism of the long-wave instability in an intuitive way as well as examining the influence of insoluble surface and interfacial surfatants on the flow stability.In the limit of long waves,two coupled advection-diffusion equations for the surface and interracial displacements are derived.A normalmode analysis of the equations yields very tractable formulas for the growth rates and eigenfunctions,and the stability/instability can be readily identified.The surface and interfacial waves of the normal modes are not exactly in phase or out of phase byπ.Instead,there exists an additional phase shift.It is found that the coexistence of the disturbance flows related to this additional phase shift and the normal component of gravity leads to the inertialess instability.In the presence of surface and interfacial surfactants,four normal modes are detected,and at most one of the four modes may be unstable for a group of specified flow parameters. Both the surface and interfacial surfactants can act as stabilizing or destabilizing role.In particular,when the viscosity of the upper layer is much higher than that of the lower layer,the surface surfactant can enhance the intertialess instability of the flow.Note that the destabilizing effect of surfactants on a zero-shear free surface is revealed for the first time.(4)The linear stability of an oscillatory fluid layer covered by an insoluble surfactant is studied.In the limit of long-wavelength perturbations,two particular Floquet modes associated with the instability are identified and the corresponding growth rates are obtained by solving a quadratic equation.The surfactant tends to shrink the unstable regions for the stability parameters,and thus plays a stabilizing role in the long-wave disturbances.The stability of arbitrary-wavelength disturbances is numerically analyzed using a Chebyshev collocation method,and the critical Reynolds numbers are calculated for a wide range of amplitude and frequency of the modulation as well as surfactant elasticity.Results show that the flow is stabilized for small surfactant elasticity and can be destabilized for relatively large surfactant elasticity.The disturbance modes in the form of traveling waves may be induced by the surfactant and dominate the instability of the flow.