Coupling effect of Kelvin–Helmholtz, Rayleigh–Taylor, and parametric instabilities on a viscoelastic liquid sheet with heat and mass transfer

This study investigates the coupling effects of Kelvin–Helmholtz, Rayleigh–Taylor, and parametric instabilities at the gas–liquid interface, considering the heat and mass transfer. In the model constructed in this paper, the liquid phase contacts the upper wall at a relatively low temperature, while the gas phase contacts the lower wall at a higher temperature. Evaporation from the liquid–gas interface into the gas phase is used to represent heat and mass transfer, and the gas layer supports the liquid to represent the Leidenfrost phenomenon. The liquid is treated as a non-Newtonian fluid governed by the Oldroyd-B model [J. G. Oldroyd, “On the formulation of rheological equations of state,” Proc. R. Soc. London, Ser. A: Math. Phys. Sci. 200, 523–541 (1950)], with no initial velocity, whereas the gas is inviscid and flows with a certain initial velocity. A dispersion equation is derived and solved using the Floquet theory to explore the effects of various nondimensional parameters on the instability. The results indicate that the increase in acceleration amplitude and gas–liquid density ratio suppresses Rayleigh–Taylor instability. The increase in heat and mass transfer initially suppresses both Kelvin–Helmholtz and parametric instabilities. However, once heat and mass transfer surpass a critical value, it begins to promote instability. The critical points differ for Kelvin–Helmholtz and parametric instabilities, and both decrease with increasing Weber number. The critical value is also influenced by other parameters. Increasing Bond number increases the critical value for Kelvin–Helmholtz instability, making it harder for transition to occur. Conversely, increasing the acceleration amplitude decreases the critical value. In the parametric unstable region, increasing the Bond number decreases the critical value, while increasing the acceleration amplitude increases it.