Particle motion in resonance tubes

Abstract

Small particle motions in standing or travelling acoustic waves are well known and extensively studied. Particle motion in weak shock waves has been studied much less, especially particle motion in periodic weak shock waves which as yet has not been dealt with. The present study considers small particle motions caused by weak periodic shock waves in resonance tubes filled with air. A simple mathematical model is developed for resonance gas oscillations under the influence of a vibrating piston with a finite amplitude at the first acoustic resonance frequency. It is shown that a symmetrical sinusoidal piston motion generates non-symmetric periodic shock waves. A model of particle motion in such a flow field is suggested. It is found that non-symmetric shock waves cause particle drift from the middle cross-section toward the ends of the resonance tube. The velocity of particle drift is found to be of the order of D p ρ p / T r ρ g , where D p is the particle diameter, T r the period of the resonance oscillation, ρ p and ρ g are the particle and gas density, respectively. At the same time, the velocity drift strongly depends on the ratio τ/ T r , where τ is the particle relaxation time. Particle drift is vigorous when τ/ T r ∼1 and insignificant when τ/ T r 1. Theoretical predictions of particle drift in resonance tubes are verified numerically as well as experimentally. When the particle relaxation time is much smaller than period of the resonance oscillations particles perform oscillations around their equilibrium positions with amplitude of the order of D p ρ p /ρ g . It is shown that the difference in oscillation amplitude of particle of difference sizes explains coalescence of aerosol droplets observed in experiments of Temkin (1970). The importance of the phenomena for particle separation, coagulation and transport processes is discussed.