Instabilities of a cylindrical liquid sheet in the presence of two gaseous flows

The instabilities in a cylindrical liquid sheet caused by the presence of axial and azimuthal velocity components of two gaseous flows are analyzed. The static pressure is formulated at the cylinder, outside the liquid cylinder, and within the liquid cylinder, noting that the velocity is dependent on the radial distance outward. Limiting conditions are defined for the interior and exterior flows, and perturbation waves (monochromatic) are formulated for each flow. Attention is also given to kinematic coupling between the three flows, to pressure discontinuities across the interfaces, and to pulsation of the flow. The formulations are applied to a cylindrical sheet whose thickness is small compared to the radius. It is found that small azimuthal velocity differences at the liquid sheet lead to disintegration of the sheet due to axisymmetric disturbances.