Weak waves in multifractional liquids with bubbles

Abstract

The propagation of weak waves in multifractional mixtures of liquid with vapor-gas and gas bubbles of different sizes and different compositions with phase transitions is studied. The dispersed phase consists of N+M fractions having various gases in bubbles and different in the bubbles radii. Phase transitions accounted for N fractions. The total bubble volume concentration is small (less than 1%). The dispersion relation is derived and dispersion curves is built. Influence of the mass concentration is shown. It is shown that dispersion and dissipation of acoustic waves depends significantly on presence of different bubbles in fractions of the dispersed phase. 1. Introduction A propagation of acoustic waves in liquid with gas bubbles is studied intensively both theoretically and experimentally. Nigmatulin [1], Nakoryakov et al. [2], Temkin [3] considered various basic aspects of acoustics of multiphase flows. Hao and Prosperetti [4] obtained the results of study of the vapor bubble dynamics in liquid. Commander and Prosperetti [5] presented a model of the propagation of plane waves with small amplitude in a mixture of liquid and of gas bubbles. This model is adequate for the frequencies far from resonance at the volume content of a disperse phase of 1-2%. Nigmatulin et al. [6] showed the need of allowing for the effect of liquid compressibility for problems of acoustics of bubbly liquids. Shagapov [7] considered a problem of propagation of small disturbances in liquids with polydisperse bubbles. Nigmatulin et al. [8] studied the small radial oscillations of vapor-gas bubbles in liquid under the influence of an acoustic field. They showed that capillary effects and phase transitions lead to the new resonant frequency of small bubbles. This frequency is different from the Minnaert frequency. Vakhitova and Shagapov [9] investigated the propagation of small disturbances in two-component two-phase bubbling media with a three-temperature model. They found that heat and mass transfer rather than an interphase friction mainly determine dispersion. Gubaidullin and Nikiforov [10] obtained a dispersion relation describing a propagation of harmonic spherical and cylindrical disturbances in monodisperse mixture of liquid with the vapor-gas bubbles. They showed strong dependence of an attenuation of pulse waves on a vapor concentration in bubbles. The propagation of acoustic waves in a two-fractional mixture of liquid with bubbles is investigated in [11-13]. The propagation of sound waves in two-fractional liquids with polydisperse bubbles is investigated in [14-17]. A mathematical model of the propagation of sound waves in the two-fractional mixture of liquid with polydisperse vapor-gas and gas bubbles with phase transitions is shown in [18].

Reflection and Transmission of Acoustic Waves through the Layer of Multifractional Bubbly Liquid

“…A mathematical model of the propagation of sound waves in the two-fractional mixture of liquid with polydisperse vapor-gas and gas bubbles with phase transitions is shown in [14][15][16]. The propagation of acoustic waves in multifractional mixtures of liquid with gas and vapor-gas bubbles of different sizes and different compositions is studied in [17][18][19]. The problem of reflection of an acoustic wave from a two-layer medium containing a layer of bubble liquid is considered in [20][21][22].…”

Reflection of acoustic waves from the boundary or layer of two-phase medium

“…The problem of small disturbance propagation in a liquid with gas-vapor bubbles in some or another formulation was studied in [20][21][22][23][24][25][26][27][28][29][30][31][32][33].…”