Nonlinear dual-mode instability of viscoelastic planar liquid sheet in two inviscid gas streams of equal velocities

Abstract

The weakly nonlinear instability of viscoelastic planar liquid sheet subjected to simultaneous linear sinuous and varicose perturbations (i.e., dual-mode) has been studied. In the analysis of temporal instability, we considered the case where both sides of the sheet have an inviscid gas moving at the same velocities. The solutions of second-order interfacial perturbation instability were derived based on the perturbation technique, followed by a parametric study. The impact of different disturbance modes on the instability of the upper and lower interfaces was studied under different initial phase differences. When the linear sinuous and varicose modes start with equal initial amplitudes, the influence of the first harmonic of the sinuous mode is notably significant due to its relatively large amplitude. We also checked the influences from several parameters, like elasticity number, time constant ratio on the instability of the sheet under a fixed gas–liquid velocity difference. The results demonstrate that elasticity number has a non-monotonic dual effect on the instability of the sheet: Within a lower range of elasticity numbers, the instability of the sheet is suppressed; Conversely, the instability is enhanced at higher elasticity numbers. Furthermore, under the condition of maintaining a fixed gas–liquid velocity difference, increasing the gas–liquid velocity ratio leads to a decrease in the maximum linear growth rate of perturbations, thereby suppressing the instability of the sheet. However, it has no significant effect on the amplitude of second-order perturbations and the breakup profile of the sheet.