Instability of a Moving Cylindrical Liquid Sheet

Abstract

The instability of a cylindrical liquid sheet of finite thickness moving with a uniform velocity in still air is studied theoretically with the aim of throwing light on the break-up of films during atomization. It is shown that instability occurs for an axisymmetric disturbance when its wavelength exceeds the outer circumference of the sheet. For small values of the Weber number W(= T/ρa U2 ra ) a sheet of given thickness tends to become unstable for disturbances of large wavelengths although it is completely stabilized when W < 2.5 (approx.). The maximum growth rate for instability increases with W for fixed value of the sheet thickness. For fixed W, it is found that λ̄m (the wavelength corresponding to maximum growth rate) increases rather slowly with increase in the sheet thickness. The value of λ̄m decays rapidly from a high value as Weber number increases for a fixed sheet thickness. Further as W → ∞, λ̄m approaches asymptotically the value 10 (approx.) which agrees with the corresponding value due to Rayleigh in his study of the capillary instability of a jet.