Model of nonlinear sound propagation in a foam

Model of process of low-frequency sound propagation in a gas-liquid foam is suggested. This model is obtained in assumption of an adiabatic variation of a glass bubble volume and in neglect of the interphase heat transfer. The analysis of the Rayleigh equation analogue for a foam takes into account different physical mechanisms affecting sound propagation in a foam: surface tension; liquid added mass effect, viscous deformed boundary accurences, liquid motion along the system of mutually constrained microcapillaries, i. e. Plato-Gibbs channels. The model assumptions concerning liquid motion include the following: dynamics of liquid transference in a channel is defined by the dependence of a bubble radius on time and degree of liquid free motion along the channel is the dominant effect. The nonlinear wave equation is obtained. It containes in the right part the third derivative of a variable square besides classic dissipative item. The equation can be reduced to the form of Burgers one with nonlinear dissipative right part. It is researched analytically including nonlinearity influence on the evolution of a different form initial profile (finite signal and disturbance in the form of Talor shock wave). It is shown that the presence of such kind of dissipative nonlinearity is connected with specific features of a gas-liquid foam.