Brownian motion and reversible hydrodynamic equations of bubble liquid

A system of kinetic equations of bubble liquid is constructed by using the method of microscopic phase density. It is based on macroscopic equations of Voinov-Golovin, which describe bubbles of varying radii interacting in an incompressible liquid. An equation for a one-particle distribution function and an expression for the integral of collisions are obtained in terms of the values of simultaneous pairwise correlators. A system of reversible hydrodynamic equations of a single-velocity bubble liquid is constructed on the basis of the system of equations for the moments of the one-particle distribution function. The dispersion dependence of the phase sound speed is investigated. It is shown that hydrodynamic interactions of bubbles in the approximation of a self-consistent field splits the wave from the paper of Nakoryakov-Schreiber into two independent acoustic modes.