Equations of coupled radial and translational motions of a bubble in a weakly compressible liquid

Coupled equations of radial and translational motions of a spherical bubble, accounting to the first order for the compressibility of the surrounding liquid, are derived using an energy approach. It is shown that the compressibility corrections appear only in the radial equation, while the translational equation keeps the same form as in an incompressible liquid. However, if the radial equation is recast to the Keller-Miksis form, the translational term in this equation acquires a correction that is of importance in high-intensity fields.