Effect of viscosity ratio on the self-sustained instabilities in planar immiscible jets

TLDR: In this paper, the transition process in confined two-dimensional jets of two fluids with varying viscosity ratio is investigated using direct numerical simulations (DNSs), where the outer fluid coflow velocity is 17% of that of the central jet.

Abstract: Previous studies have shown that intermediate magnitude of surface tension has a counterintuitive destabilizing effect on two-phase planar jets. In the present study, the transition process in confined two-dimensional jets of two fluids with varying viscosity ratio is investigated using direct numerical simulations (DNSs). The outer fluid coflow velocity is 17% of that of the central jet. Neutral curves for the appearance of 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 ranging from 10−1 to 10. For uniform viscosity (m=1), the first bifurcation is through a surface-tension-driven global instability. On the other hand, 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 first bifurcation is through the Coanda-type attachment, which eventually triggers time-dependent convective bursts. At high surface tension, the first bifurcation is through the surface-tension-dominated mode. For high viscosity of the outer fluid, persistent oscillations appear due to a strong convective instability, although it is shown that absolute instability may be possible at even higher viscosity ratios. Finally, we show that the jet is still convectively and absolutely unstable far from the inlet when the shear profile is nearly constant. Comparing this situation 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. By an energy analysis of the Couette flow case, we show that surface tension, although dissipative, can induce a velocity field near the interface that extracts energy from the flow through a viscous mechanism. This study highlights the rich dynamics of immiscible planar uniform-density jets, where different self-sustained and convective mechanisms compete and the nature of the instability depends on the exact parameter values.