Title: Effect of viscosity ratio on the self-sustained instabilities in planar immiscible jets,
Abstract: Previous studies have shown that intermediate surface tension has a
counterintuitive destabilizing effect on 2-phase planar jets. Here, the
transition process in confined 2D jets of two fluids with varying viscosity
ratio is investigated using DNS. Neutral curves for persistent oscillations are
found by recording the norm of the velocity residuals in DNS for over 1000
nondimensional time units, or until the signal has reached a constant level in
a logarithmic scale - either a converged steady state, or a "statistically
steady" oscillatory state. Oscillatory final states are found for all viscosity
ratios (0.1-10). For uniform viscosity (m=1), the first bifurcation is through
a surface tension-driven global instability. For low viscosity of the outer
fluid, there is a mode competition between a steady asymmetric Coanda-type
attachment mode and the surface tension-induced mode. At moderate surface
tension, the Coanda-type attachment dominates and eventually triggers
time-dependent convective bursts. At high surface tension, the surface
tension-dominated mode dominates. For high viscosity of the outer fluid,
persistent oscillations appear due to a strong convective instability. Finally,
the m=1 jet remains unstable far from the inlet when the shear profile is
nearly constant. Comparing this to a parallel Couette flow (without inflection
points), we show that in both flows, a hidden interfacial mode brought out by
surface tension becomes temporally and absolutely unstable in an intermediate
Weber and Reynolds regime. An energy analysis of the Couette setup shows that
surface tension, although dissipative, induces a velocity field near the
interface which extracts energy from the flow through a viscous mechanism. This
study highlights the rich dynamics of immiscible planar uniform-density jets,
where several self-sustained and convective mechanisms compete depending on the
exact parameters.