Theory of liquids with vapor bubbles

In this paper, which consists of three major parts, the theory of bubbly liquids developed previously by the authors is extended to the case of a liquid containing spherical vapor bubbles. In the first part, the nonlinear equations of motion are derived by a variational procedure. The equations are then linearized. In the second part, a set of constitutive relations for vapor bubbles are developed which include the temperature distributions in both the spherical bubbles and in the surrounding liquid. Nonequilibrium evaporation and condensation processes are also included. In the third part, solutions for plane harmonic wave propagation are presented for water--steam and for liquid sodium--sodium vapor mixtures. The qualitative effects of condensation and evaporation on the propagation of waves through the mixture are discussed. It is found that the wave attenuation is greatly increased and the phase velocity is substantially decreased when phase transitions are included