Two-phase Shear Instability: Waves, Fingers, and Drops
We examine the development of instability for a shear flow made up of two distinct immiscible fluids, taking into account their disparate densities, viscosities, and the possibility of tension acting on the interface that separates them. Linear theory leads to a pair of coupled Orr-Sommerfeld equations supplemented by the required matching conditions at the interface. The most unstable mode found here is believed to explain the nature of the instability essential to breakup at its onset. In addition, we find a second mode, which can be most unstable in certain situations of interest. Direct numerical simulations are performed for a range of parameter values. At early times, the simulations reveal the linear and nonlinear amplitude growth, verifying the applicability and accuracy of the numerical method over a range of density and viscosity ratios. At later times, the simulations show the development of elongated structures and the subsequent breakup of the heavier fluid into drops.
waves hydrodynamics two-phase flow droplets atomization