Equilibrium shape and stability of a liquid cylinder in cross flow at low Weber numbers

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Abstract
The cross-section shape and stability of a liquid cylinder moving perpendicularly to its axis in a gaseous medium is studied. Such liquid cylinders are formed during the break-up process of thin, rapidly moving liquid sheets, appearing in spray and atomization processes. The equilibrium shape is affected mainly by two factors: the dynamic-pressure distribution in the gas flow and the surface tension on the liquid boundary. The former tends to distort the liquid cross-section into an oval shape while the latter tends to restore the circular cross-section. A series expansion for the shape of the cylinder cross-section was determined by assuming incompressible potential flow, neglecting the effects of body forces and internal circulation in the liquid. The stability analysis shows that in the range of low Weber numbers the cylinder break-up is due to the divergence of varicose perturbations. The wavenumber of the most rapidly growing perturbation, its rate of growth and the maximal wavenumber for which varicose instability occurs, are all found to decrease as the Weber number grows, owing to a pressure distribution caused by the varicose distortion, which tends to reduce these perturbations.

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