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
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