Investigation of the instability of a moving liquid film

The stability of a thin layer of liquid moving in still air is studied theoretically with the object of throwing light on the break-up of films during atomization. It is found that instability occurs if W = T /ρ 1 U 2 h < 1 and that the wavelength for maximum growth factor, for W « 1, is λ = (4π T /ρ 2 U 2 ) where ρ 1 is the liquid density, ρ 2 is the air density, U is the film velocity, 2 h is the film thickness and T is the surface tension of the liquid. Comparison with experimental data shows fair agreement with the observed wavelengths.