Linear instability of viscoelastic planar liquid sheets in the presence of gas velocity oscillations

The linear temporal instability of a viscoelastic liquid sheet has been studied here, in the presence of gas velocity oscillations. The Floquet theory was applied to solve this problem. More than one unstable region appeared and these regions were divided into the Kelvin–Helmholtz (K–H) and the parametric unstable regions. In the K–H unstable region, the disturbance grew in the form of travelling waves; but in the parametric unstable regions, the disturbance was in the form of standing waves. An increase in oscillation amplitude contributed to the growth of instability in both regions, due to the stronger hydrodynamic force and parametric resonance, respectively; and the parametric unstable regions were more sensitive to the increased amplitude. The main effect of the oscillation frequency was to change the location of the parametric unstable regions. A viscoelastic liquid sheet can behave with greater stability than its Newtonian counterpart in all unstable regions; however, zero shear viscosity, stress relaxation time, and deformation retardation time all affect the parametric regions more dramatically than the K–H unstable regions. The parametric unstable region is more sensitive to viscous dissipation than the K–H unstable regions, resulting in a shift in the leading role between the different unstable regions. The competition between the K–H and parametric unstable regions is discussed in detail here.