Most unstable waves of a stagnant planar liquid film blown by a high speedviscous gas with a Blasius velocity profile

The linear most unstable waves generated on the surface of a stagnant plana r liquid (gasoline) film with infinite thickness, blown by a high speed vis cous gas (air) with a Blasius velocity profile, are computed and analyzed. The free-stream velocity of the gas ranges from 30 m/s to 50 m/s, which is typical of high speed atomization problems. The Reynolds number based on th e local thickness of the boundary-layer lies between 200 and 2500. The nume rical computation shows that the dimensional wavelength of the most unstabl e wave is a power function of the boundary-layer thickness (or Reynolds num ber) with a power close to 3/4, while the growth rate is inversely proporti onal to the boundary-layer thickness. When reducing the boundary-layer thic kness, the viscous results approach the inviscid results. This result shows that, under the present parameter range, the gas viscosity would have a se condary role on the atomization speed and important influence on the drople t size.