Instability of a confined viscoelastic liquid sheet in a viscous gas medium

A linear analysis method was used to investigate the instability behavior of a viscoelastic liquid sheet moving through a viscous gas bounded by two horizontal parallel flat plates. The liquid sheet velocity profile was taken into account. The result showed that the velocity gradient of viscoelastic liquid sheets was greater than that of the corresponding Newtonian sheets. The effects of time-constant, elasticity number, and the ratio of distance between the liquid sheet and flat plate to liquid sheet thickness on the velocity profiles of viscoelastic liquid sheets were also investigated. The relationship between temporal growth rate and the wave number was obtained using linear stability analysis and solved using the Chebyshev spectral collocation method. The rheological parameters and flow parameters were tested for their influence on the instability of the viscoelastic liquid sheets. It is concluded that disturbances grow faster on viscoelastic liquid sheets than on Newtonian sheets with identical zero shear viscosity. Increasing the momentum flux ratio, elasticity number, Weber number, and liquid Reynolds number accelerated the breakup of the viscoelastic liquid sheet, while increasing the time constant, ratio of the distance between the liquid sheet, and the flat plate to the liquid sheet thickness had the opposite effect.