The speed of sound in a gas-vapour bubbly liquid

In addition to the vapour of the liquid, bubbles in cavitating flows usually contain also a certain amount of permanent gas that diffuses out of the liquid as they grow. This paper presents a simplified linear model for the propagation of monochromatic pressure waves in a bubbly liquid with these characteristics. Phase change effects are included in detail, while the gas is assumed to follow a polytropic law. It is shown that even a small amount of permanent gas can have a major effect on the behaviour of the system. Particular attention is paid to the low-frequency range, which is of special concern in flow cavitation. Numerical results for water and liquid oxygen illustrate the implications of the model.