PARTICLE MOTION IN RESONANCE TUBES

Small particle motions in standing or travelling acoustic waves are we ll known and extensively studied. Particle motion in weak shock waves has been studied much less, especially particle motion in periodic wea k shock waves which as yet has not been dealt with. The present study considers small particle motions caused by weak periodic shock waves i n resonance tubes filled with air. A simple mathematical model is deve loped for resonance gas oscillations under the influence of a vibratin g piston with a finite amplitude at the first acoustic resonance frequ ency. It is shown that a symmetrical sinusoidal piston motion generate s non-symmetric periodic shock waves. A model of particle motion in su ch a flow field is suggested. It is found that non-symmetric shock wav es cause particle drift from the middle cross-section toward the ends of the resonance tube. The velocity of particle drift is found to be o f the order of D-p rho(p)/T-r rho(g), where D-p is the particle diamet er, T-r the period of the resonance oscillation, rho(p) and rho(g) are the particle and gas density, respectively. At the same time, the vel ocity drift strongly depends on the ratio tau/T-r, where tau is the pa rticle relaxation time. Particle drift is vigorous when tau/T-r simila r to 1 and insignificant when tau/T-r much less than 1. Theoretical pr edictions of particle drift in resonance tubes are verified numericall y as well as experimentally. When the particle relaxation time is much smaller than period of the resonance oscillations particles perform o scillations around their equilibrium positions with amplitude of the o rder of D-p rho(p)/rho(g). It is shown that the difference in oscillat ion amplitude of particle of difference sizes explains coalescence of aerosol droplets observed in experiments of Temkin (1970). The importa nce of the phenomena for particle separation, coagulation and transpor t processes is discussed.