The occurrence of swarms of small bubbles in a variety of industrial systems enhances their performance. However, the effects that size polydispersity may produce on the stability of kinematic waves, the gain factor, mean bubble velocity, kinematic and dynamic wave velocities is, to our knowledge, not yet well established. We generalize the model by Biesheuvel and Gorissen  to incorporate size polydispersity of bubbles. We find that it enhances the stability of a bubble column by a factor of about $23\%$ as a function of frequency. In this way our model predicts effects that might be verified experimentally; however, this remain to be assessed. Our results reinforce the point of view advocated in this work in the sense that a description of a bubble column based on the concept of randomness of a bubble cloud and average properties of the fluid motion, may be a useful approach that has not been exploited in engineering systems. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 200647.35.+i Hydrodynamic waves, 47.55.Dz Drops and bubbles, 47.55.Kf Multiphase and particle-laden flows, 82.70.-y Disperse systems; complex fluids ,
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