Linear Stability Analysis of Viscoelastic Liquid Sheet in Presence of Moving Gas Medium

A linear analysis of sinuous instabilities in a two-dimensional planar viscoelastic sheet subjected to two inviscid gas streams of equal non-zero velocities is performed. The rheological model of the viscoelastic sheet is considered to be corotational Jeffrey’s model. Perturbation technique is employed to obtain the linear governing equation and boundary conditions. Solution of the first-order dispersion equation yields the maximum growth rate and corresponding dominant wave number. Parametric investigation of the effects of elasticity number and time constant ratio is performed for different gas-to-liquid velocity ratios. Linear analysis predicts that elasticity number enhances the maximum growth rate. On the contrary, time constant ratio is observed to dampen the maximum growth rate. Hence, elasticity number and time constant ratio exhibit a destabilizing and stabilizing effect on the liquid sheet, respectively