Heat transfer effect on sound propagation in foam

Abstract

The influence of heat transfer on the propagation of acoustic disturbances in a gas–liquid foam of polyhedral structure is considered in this paper. The presence of quasiordered structure of microcapillaries (Plateau–Gibbs channels) results in the appearance of a hydrodynamic effect caused by liquid motion along the channels and due to the competition with the contribution of heat transfer in general wave dissipation. The interphase heat transfer process in a gas-filled foam is considered within the framework of a cell model. Liquid motion through the proposed channels depends on the radial dynamics of the foam cell and on the hydroconductivity of the foam defining a free liquid motion through the channels. The Rayleigh equation analog, which takes into account liquid motion through the channels of the foam and small moisture content, is obtained. The dispersion relation shows that the influence of surface tension can be ignored. The effects of added liquid mass and the viscous interphase mechanism in the frame of applicability of the suggested model are analyzed. It is concluded that the general influence on the evolution of the initial perturbation has been exerted by the heat transfer process between the carrying and dispersion phases and liquid motion through the channels. The attenuation decrement consists of two parts: thermal and viscous. The intensity is defined by the foam dispersion a0 (size of the foam cell). Where a0<a*0 the signal dissipation, to a marked degree, is caused by liquid motion, and it is possible to neglect heat transfer. When the thermal processes define the attenuation, the liquid motion can be ignored. The formula for the critical dispersion a*0 is obtained. For the water–air foam with volumetric water content α10=10−2, the critical dispersion is a*0=5×10−4 m. It is shown that the frequency range of validity of the suggested model can be divided into the two subranges. A brief review of the published experimental data on research of acoustic disturbances propagating in gas–liquid foam is presented. The experimental data analysis shows that the calculation of only heat exchange processes is insufficient for their interpretation. The comparison of experimental curves (obtained by Z. M. Orenbakh and G. A. Shushkov at the Institute of Northern Development) and calculated profiles for different parameters of gas–liquid foam is presented. It is shown that the calculation of liquid motion in the frames of the suggested model permits a more accurate description of the experimental results.