- Recently, there has been a growing interest in the properties of bubbly liquids. This interest ranges from the propagation of sound waves in liquids to the properties of bubbly liquid metals for various technological applications. The dynamics of compressible bubbles in a liquid exhibit variations on two distinct time scales under various conditions. This behavior is caused by the natural volume oscillations of the bubbles, which are much faster than the motion of the liquid. As a result, the time step used in numerical calculations of bubbly flows is limited by the low period of the fast oscillations. This limitation can be removed by separating the flow variables into slow and fast components. By analytically finding the fast behavior and integrating over it, the time step can be significantly increased and is limited only by the much slower motion.