A temporal stability analysis was carried out to model the atomization of a swirling viscous annular liquid sheet emanating from an air-blast atomizer subject to inner and outer inviscid swirling air streams. The dimensionless dispersion equation that governs the instability of a viscous annular liquid sheet under swirling air streams was obtained. Numerical solutions to the dispersion equation under a wide range of flow conditions were obtained to investigate the effect of the liquid and gas flow on the maximum growth rate and its corresponding unstable wave number. The theoretical behaviour predicted by the dispersion diagrams was compared with the experimental results obtained by the same authors in previous works from the atomization of alginate solution using an air-blast atomizer. It was found that the instability model proposed justify the experimental effects found for the atomization of the fluid and under the work range for alginate flow rate and viscosity and air flow rate. (C) 2007 Elsevier B.V. All rights reserved.