Improved modeling of free power-law liquid sheets by weighted-residual approximations

The linear temporal instability of planar power-law liquid sheets surrounded by viscous gas medium is investigated theoretically for symmetric disturbances. The linear stability analysis is improved by method of the weighted residual approach using an appropriate projection basis, instead of the traditional Kármán's momentum integral method which is known to make the resulting model inaccurate near the stability threshold. Two different ways are used to deal with linear stability analysis with the existence of the viscous gas medium: inviscid gas pressure approximation and spectral collocation method. A system of two equations in relation to the film thickness h and the local flow rate q is obtained through the first way and then the first-order dispersion equation is deduced. The results are analyzed to investigate how the power-law index, consistency coefficient, gas boundary-layer thickness and other rheological parameters affect the atomization mechanism of planar power-law sheets. Meanwhile, comparisons of the results obtained by the two ways have been made to verify rationality of the inviscid gas pressure approximation. Furthermore, the competition between the power-law characteristic property and aerodynamic instability on sheet instability has been examined. Finally, the theoretical calculations have been compared with previous experimental results and show relatively good agreement.