Linear stability of stratified two-phase flows in horizontal channels to arbitrary wavenumber disturbances is studied. The problem is reduced to Orr-Sommerfeld equations for the stream function disturbances, defined in each sublayer and coupled via boundary conditions that account also for possible interface deformation and capillary forces. Applying the Chebyshev collocation method, the equations and interface boundary conditions are reduced to the generalized eigenvalue problems solved by standard means of numerical linear algebra for the entire spectrum of eigenvalues and the associated eigenvectors. Some additional conclusions concerning the instability nature are derived from the most unstable perturbation patterns. The results are summarized in the form of stability maps showing the operational conditions at which a stratified-smooth flow pattern is stable. It is found that for gas-liquid and liquid-liquid systems the stratified flow with a smooth interface is stable only in confined zone of relatively low flow rates, which is in agreement with experiments, but is not predicted by long-wave analysis. Depending on the flow conditions, the critical perturbations can originate mainly at the interface (so-called "interfacial modes of instability") or in the bulk of one of the phases (i.e., "shear modes"). The present analysis revealed that there is no definite correlation between the type of instability and the perturbation wavelength

Linear stability of horizontal and inclined stratified channel flows of Newtonian/non-Newtonian shearthinning fluids is investigated with respect to all wavelength perturbations. The Carreau model has been chosen for the modeling of the rheology of a shear-thinning fluid, owing to its capability to describe properly the constant viscosity limits (Newtonian behavior) at low and high shear rates. The results are presented in the form of stability boundaries on flow pattern maps (with the phases' superficial velocities as coordinates) for several practically important gas-liquid and liquid-liquid systems. The stability maps are accompanied by spatial profiles of the critical perturbations, along with the distributions of the effective and tangent viscosities in the non-Newtonian layer, to show the influence of the complex rheological behavior of shear-thinning liquids on the mechanisms responsible for triggering instability. Due to the complexity of the considered problem, a working methodology is proposed to alleviate the search for the stability boundary. Implementation of the proposed methodology helps to reveal that in many cases the investigation of the simpler Newtonian problem is sufficient for the prediction of the exact (non-Newtonian) stability boundary of smooth stratified flow (i.e., in case of horizontal gas-liquid flow). Therefore, the knowledge gained from the stability analysis of Newtonian fluids is applicable to those (usually highly viscous) non-Newtonian systems. Since the stability of stratified flow involving highly viscous Newtonian liquids has not been researched in the literature, interesting findings on the viscosity effects are also obtained. The results highlight the limitations of applying the simpler and widely used power-law model for characterizing the shear-thinning behavior of the liquid. That model would predict a rigid layer (infinite viscosity) at the interface, where the shear rates in the viscous liquid are low, and thereby unphysical representation of the interaction between the phases.

Linear stability of stratified gas-liquid and liquid-liquid plane-parallel flows in inclined channels is studied with respect to all wavenumber perturbations. The main objective is to predict parameter regions in which stable stratified configuration in inclined channels exists. Up to three distinct base states with different holdups exist in inclined flows, so that the stability analysis has to be carried out for each branch separately. Special attention is paid

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The transport of liquid and of small rigid spherical particles in a high-Prandtl-number (Pr = 68) thermocapillary liquid bridge under zero gravity is studied by highly resolved numerical simulations when the flow arises as an azimuthally traveling hydrothermal wave with azimuthal wave number one. The Langrangian transport of fluid elements reveals the coexistence of regular and chaotic streamlines in the frame of reference rotating with the wave. The structure of the KAM (Kolmogorov-Arnold-Moser) tori is unraveled for several Reynolds numbers for which the flow is periodic in time and space. Based on the streamline topology the segregation of small rigid spherical particles of a dilute suspension into particle accumulation structures (PASs) is studied, based on the steric finite-particlesize effect when the particles moves close to the free surface. It is shown that the intricate KAM structures have their counterparts in a multitude of different attractors for the particle motion. Examples of PASs are provided, and their dependence on particle size, particle-tofluid density ratio, and Reynolds number are discussed. A large parametric study reveals the most probable combinations of particle size and density ratio which lead to particle clustering.

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The non-modal transient growth of perturbations in horizontal and inclined channel flows of two immiscible fluids is studied. 3D perturbations are examined in order to find the optimal perturbations that attain the maximum amplification of perturbation energy at relatively short times. Definition of the energy norm is extended to account for the gravitational potential energy along with the kinetic energy and interfacial capillary energy. Contrarily to the fastest exponential growth, which is reached by essentially 2D perturbations, the maximal non-modal energy growth is attained mostly by three-dimensional spanwise perturbations. Significant transient energy growth is found to occur in linearly stable flow configurations, which, similarly to single phase shear flows, may trigger non-linear destabilizing mechanisms within one of the phases. It is shown that the transient energy growth in linearly stable cases can be accompanied by noticeable interface deformations.Therefore, flow pattern transition due to non-modal transient growth and reduction of the range of operational conditions for which stratified-smooth flow remains stable cannot be ruled out.