This paper extends the Rayleigh theory to study the interface instability of axisymmetric gas-liquid flows. The dispersion equations of cylindrical liquid sheets were derived and numerical solutions were obtained. Two families of instability curves were found; one for symmetric disturbances and the other for antisymmetric disturbances. Two limiting cases can be recovered from derived dispersion equations. The equation recovers the Rayleigh instability of round jets for symmetric disturbances and recovers the hollow jet or submerged jet instability for antisymmetric disturbances. Effects due to ambient fluid density and ambient fluid velocity on liquid-sheet instabilities were examined. Nomenclature a = inner jet radius, m b = outer jet radius, m D = density ratio between the gas and liquid, p g /p 7 0 , /i = modified Bessel functions of the first kind of order 0 and 1, respectively K 0 , ^ = modified Bessel functions of the second kind of order 0 and 1, respectively k = disturbance wave number, ZTT/X, 1/m L -characteristic length P -mean pressure p = pressure fluctuation due to disturbances p = instantaneous pressure r = coordinate in radial direction t = time, s U -mean velocity of the liquid phase, m/s Uj = relative velocity with respect to the coordinate moving with the liquid phase (y = a, b) u = disturbance velocity, m/s u ~ instantaneous velocity, m/s We = Weber number, p£/ 2 /cr z = coordinate in axial direction a = disturbance growth rate, rad/s y = parameter of Bessel functions, kr, where r = a or b y l = parameter of Bessel functions, /r, where P = k 2 + a/v and r = a or b r\ = disturbance expression, Re [T\ O cxp(ikz r\ 0 = initial amplitude of disturbance X = wavelength of disturbance, m | JL = liquid-phase dynamic viscosity v -liquid-phase kinematic viscosity, jx/p p = liquid-phase density, kg/m 3 a = interface surface tension, N/m T = initial disturbance amplitude ratio o) = dimensionless disturbance growth, a/ 4-at)] a -quantity of the fluid inside the liquid sheet b = quantity of the fluid outside the liquid sheet g = gas phase r = radial component z = axial component
