Atomization of a liquid jet

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Generation of ripples by wind blowing over a viscous fluid was investigated by G. I. Taylor [The Scientific Papers of G. I. Taylor (Cambridge U. P., Cambridge, 1963), Vol. 3, No. 25] with linear stability analysis. Taylor considered the case of temporally growing disturbances in a low density gas and applied his results to explain the process of atomization of a liquid jet injected into a low density gas. Taylor’s analysis is extended here to investigate the case of a spatially growing disturbance in a dense gas. Taylor showed that temporal disturbances of wavelength shorter than the capillary length are stable. The same is found for the spatial disturbances. Each type of disturbance possesses a maximum growth rate with a specific wavelength and frequency. The atomized droplet size corresponding to the maximum growth rate is shown in both theories to decrease inversely as the square of the jet velocity. While the maximum growth rate increases as the square root of the gas-to-liquid density ratio when A2 exceeds 1 for the temporal disturbances, the same dependence on the density ratio does not hold for spatial disturbances until A2 exceeds 100, where A2 is a flow parameter representing the ratio of surface force to the viscous force. When A2 exceeds 100 the growth rates predicted by two theories deviate significantly only at air pressure higher than 10 atm for most liquids at room temperature. However, for all parameters, the spray angle changes along the jet axis according to the spatial theory, but remains constant according to the temporal theory. It is shown that the viscous force in the liquid may be increased relative to the surface tension force to the point that no discernable spray angle may be observed in practice. Then an intact jet without atomization may result. It is shown that the onset of atomization is primarily caused by the pressure fluctuation which resonates the capillary waves. The results on the interfacial amplification rate suggest that a sufficiently large initial amplitude at the nozzle exit is essential for the onset of atomization.