Stability of an annular power-law liquid sheet

Abstract

Because of the mathematical difficulties dealing with the nonlinear viscous stress term in momentum equation for power-law liquid, the study of stability analysis of a power-law liquid sheet has been lacking. In the present study, a temporal stability analysis has been carried out for an annular power-law liquid sheet exposed to both inner and outer-gas streams, by integrating the governing equations for the power-law liquid sheet. The dimensionless dispersion equation that governs the instability of liquid sheet is obtained by considering the velocity profile of liquid sheet. It is found that the instability of liquid sheet can be enhanced by independently increasing either the outer gas stream velocity, or the inner gas stream velocity. The liquid sheet is more unstable when both inner and outer gas streams are applied. To promote the instability of annular liquid sheet, a gas stream applied to the outer interface is more effective than when applied to the inner surface. The effects of rheological parameters on the instability of the liquid sheet are actually determined by the relative velocity across the gas–liquid interfaces. The surface tension, liquid sheet thickness, and outer surface radius of annular liquid sheet have been tested for their influence on the instability of annular power-law liquid sheet.