Suppression of the Kapitza instability in falling liquid films by confining the gas phase
Résumé
We address the linear stability of inclined falling liquid films in confined channels. We
revisit the two-phase temporal Orr-Sommerfeld problem and investigate the role of
the confinement upon the Kapitza instability with both aerostatic and counter-current
gas flow.
Increasing the confinement provides a strong stabilizing effect on the liquid film,
with a reduction of the cut-off wavenumber along with an increase of the critical
Reynolds number, as shown in Figure 1. In the presence of a counter-current gas
flow, the increase of the gas flow rate induces interfacial stability at strong confine-
ment. We show that the Kapitza instability can be fully suppressed at low angles of
inclination and relatively strong confinements. A parametric study of the influence
of the confinement by varying the Reynolds number, the inclination angle and the
Kapitza number is also provided.
We validate the numerical solution of the Orr-Sommerfeld temporal linear stabil-
ity problem by comparison with experimental data of cut-off frequency and spatial
growth rate, as well as with previous numerical works. The stabilizing effect of the
confinement is due to the perturbation of the interfacial tangential shear stress which,
in fact, attenuates the growth of the wave crest by reducing the inertial effects, which
in turn are responsible for the instability.