Abstract
This study investigates the energy budget of a viscoelastic planar liquid sheet in the presence of gas velocity oscillations. The energy budget is studied in different unstable regions, and the results are very different from those obtained for steady basic flow. The work done by surface tension and aerodynamic forces is periodic, leading to the growth of standing waves on liquid sheets. The positive work done by aerodynamic forces is the main cause of the instability, as for steady basic flow. However, treating the negative work of the surface tension as an increment in the surface energy is an effective means of determining the instability mechanisms. The unsteady basic flow causes the rate of change in the work done by viscosity and elasticity to vary periodically. An increase in elasticity and a decrease in deformation retardation promote the instability by increasing the work done by the gas medium, with reduced dissipation only as a secondary factor. This effect is more significant in parametric unstable regions than in the Kelvin–Helmholtz unstable region.
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