On the breakup of viscous liquid sheets by dual-mode linear analysis

The breakup of plane viscous liquid sheets moving in a gas stream has been studied. A dual-mode linear stability analysis has been tarried out under the combined influence of sinuous and varicose modes of disturbances at the two liquid-gas interfaces. The effect of various parameters, such as the Reynolds number, Weber number, density ratio, velocity ratio, and the phase angle between the two modes, on the breakup characteristics of the liquid sheets has been investigated. At wavelengths corresponding to the dominant wavelengths for either the sinuous or the varicose mode, the breakup of the liquid sheet occurs at full-wavelength intervals, but the breakup point shifts between the half- and the full-wavelength when the respective dominant wavelengths corresponding to the sinuous and the varicose modes are applied simultaneously. The breakup time decreases as the proportion of the varicose mode is increased in the initial disturbance imposed on the liquid sheets. The breakup length (or time) decreases with an increase in the Reynolds number, Weber number, density ratio, and velocity ratio, The sheet profiles change for different values of Weber number, density ratio, velocity ratio, and the phase angle between the two modes. Comparison with experimental results shows that the present analysis is able to match the interface profile close to the nozzle exit, but not further downstream where nonlinear effects are predominant.