Linear stability theory is applied to study the breakup process of an
annular viscous liquid jet exposed to both inner and outer gas streams
of unequal velocities. The absolute liquid and gas velocities are con
sidered in this temporal instability analysis. It is round that not on
ly the velocity difference across each interface, but also the absolut
e velocity of each fluid is important for the jet instability, althoug
h the effect of absolute velocity is secondary compared with that of r
elative velocity. A high-velocity coflowing gas stream is found to sig
nificantly-improve atomization performance, A high-velocity gas inside
of the annular liquid jet promotes the jet breakup process more than
the gas of equivalent velocity outside of the jet. For equal liquid an
d gas velocities, surface tension, liquid, and gas density exhibit eff
ects on wave growth rates different from those when a velocity discont
inuity is present across interfaces. However, the viscous damping effe
ct on jet instability always exists for the cases with and without vel
ocity differences at high Weber numbers. The liquid inertia, density r
atio, and high gas velocity all contribute to better atomization perfo
rmance, whereas surface tension and liquid viscosity increase the resu
lting droplet size.