Internal instability of thin liquid sheets

Abstract

Linear stability analysis of an inviscid liquid sheet with different velocity profiles across its thickness is reported. The velocity profiles for which there is a progressive increase or decrease in velocities between the two interfaces are demonstrated to be inherently unstable even in the absence of the destabilizing aerodynamic shear at the liquid-gas interfaces. Compared to a flat velocity profile, a linear or a parabolic profile, symmetric at the center line of the sheet reduced both the maximum growth rate and the wavelength range over which the waves grow. The convective acceleration from the velocity gradient is found to stabilize longer waves while the growth of shorter waves is hampered by the combined effect of the surface tension and a decrease in the interface velocity between gas and liquid media. The wave forms are dominantly sinuous for symmetric velocity profiles; however, with larger velocity gradients the dilatational modes are observed. The inherent instability of liquid sheets with a progressive change in velocities between the interfaces is seen to arise from the differential convective acceleration at the two interfaces in the plane of reference of the liquid sheets.