An analytical model of gas content in fluids considering the distribution of bubble radius

Gas bubbles in liquid can change the properties of liquid, such as density, viscosity and compressibility. Therefore, to predict the liquid properties, it is essential to evaluate the gas content, which depends on the bubble radius and its size distribution. This paper presents an analytical model of gas content with consideration of the distribution of bubble radius. A steady state formula of bubble radius is presented based on force equilibrium of bubble interface. From the experimental data, the distribution of bubble radius is found to agree with the logarithmic normal distribution, so a corresponding distribution function is proposed. Then, both the gas content and the average bubble radius are derived from the distribution function. Specific tests are performed to validate the developed model particularly as concerns the change of bubble radius with respect to the fluid pressure. Combined with the steady state model of bubble radius, the presented analytical model allows an accurate prediction of gas content at different pressures, implying its potentials to describe the fluid properties in two-phase flows.