Effects of unrelaxed stress tension on the weakly nonlinear instability of viscoelastic sheets

The effects of unrelaxed stress tension on the instability of viscoelastic sheets have been investigated through a weakly nonlinear temporal analysis. The surrounding gas is inviscid, incompressible, and stationary. The Oldroyd-B model is applied to describe the rheologic properties of the viscoelastic fluids, which is appropriate for highly elastic "Boger fluids" the high elasticity makes rational the assumption of constant unrelaxed tension. The analytical expression of the second-order amplitude and the dispersion relation have been obtained and solved numerically. Results show that increasing residual tension not only significantly suppresses the instability but also affects elasticity (viscosity) from enhancement (stabilization) to inhibition (destabilization). This may provide a qualitative explanation for the complex influences of elasticity observed in experiments. An energy budget has also been performed to explain the trend of the linear temporal growth rate versus the variation of parameters.