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.