Instability analysis of a power law liquid jet

Abstract

The temporal instability of a power law liquid jet injected into a static inviscid gas medium is investigated theoretically for axisymmetric disturbances. The corresponding dispersion relation between the growth rate and the wavenumber of disturbed waves is derived after using a linear approximation. It is available for both shear-thinning and shear-thickening liquids. The effects of several dimensionless parameters including the generalized Reynolds number, the Weber number, the density ratio of gas to liquid and the power law exponent, on the instability of the jet are studied. The results reveal that the jet breakup can be classified into Rayleigh Mode and Taylor Mode. And the instability characteristics are different for different modes and power law exponents. For Rayleigh Mode, surface tension promotes the breakup of the jet and the liquid viscosity prevents the jet from breaking up; for Taylor Mode, both surface tension and the viscosity prevent the jets from breaking up, while the interaction between the gas and the liquid significantly promotes the breakup process. Moreover a liquid jet with a smaller power law exponent is easier to disintegrate.