Temporal Instability of a Power-Law Planar Liquid Sheet

A linear stability analysis has been carried out to reveal the atomization mechanism of a power-law planar liquid sheet. The dispersion equation that governs the symmetric instability of a power-law liquid sheet is obtained by considering the gas boundary-layer thickness and the velocity profile of power-law liquid sheet. The dispersion equation is worked out by numerical solution to test the effects of the physical properties and flow parameters of liquid on the stability of a liquid sheet. Regarding the effects of rheological parameters, it is found that there is a critical value of consistency coefficient K above which increasing K will make the liquid sheet unstable, and below which the effect of K is opposite. A larger flow index number n makes the instability of the power-law liquid sheet damped. As the gas boundary-layer thickness, liquid sheet thickness, and surface tension increase, the disturbance wave growth rate will decrease and the instability will be damped. It is the gas-to-liquid relative velocity that governs the instability of the liquid sheet. A larger liquid density, viscosity, and density of ambient air can accelerate the growth of symmetric disturbance waves.