Summary: We present first the general formulations of dynamical equations for two- phase fluids. We restrict the discussion to dynamic equations for bubbly liquids. Based on our knowledge about the motion of a single bubble in a liquid, we develop rationally the constitutive relations and the governing continuum equations for the bubbly liquids. Section IV is devoted to the topic of sound waves in bubbly liquids. Characteristic equations are derived, the subjects of “Dead Zone” and negative damping are discussed, and some comparisons with experimental results are made.
In Section V, we discuss the finite amplitude waves in bubbly liquids as well as the instability problem which is associated with the “ill- posed” nature of the fundamental equations. A Burgers-KdV type equation is derived and the instability is demonstrated to be the Kelvin-Helmholtz type. Steady flow problems are discussed in Section VI. There we also show the mechanisms of the shock transition. Finally in Section VI, the dynamics of a liquid containing vapor bubbles are presented. The effects of evaporation-condensation are explicitly taken into account and problems of wave propagation are discussed.