3-DIMENSIONAL INSTABILITY OF VISCOUS-LIQUID SHEETS

The instability of a viscous liquid sheet issued in an inviscid gas me dium is investigated. The dispersion relations between the growth rate and wave number of both symmetric and antisymmetric disturbances are derived and solved numerically. The effects of Weber number, gas-to-li quid density ratio, and Ohnesorge number on the growth rates of two- a nd three-dimensional disturbances are studied. It is observed that at low Weber number, two-dimensional disturbances always dominate the ins tability of symmetric and antisymmetric waves. When the Weber number i s high, long-wave three-dimensional symmetric disturbances have a high er growth rate than their two-dimensional counterparts, while the oppo site is hue for antisymmetric disturbance. For short waves, both two- and three-dimensional disturbances grow at approximately the same rate . Increasing the gas-to-liquid density ratio or decreasing the Ohnesor ge number enhances the departure in the growth rates of two- and three -dimensional symmetric disturbances of long wavelength. Both the maxim um growth rate and the dominant wave number increase with Weber number and density ratio but decrease with Ohnesorge number.