Kinetic energy and added mass of hydrodynamically interacting gas bubbles in liquid

By averaging the basic equations on microscale, expressions are derived for the effective added mass density and the kinetic energy density of a mixture of liquid and gas bubbles. Due to hydrodynamic interaction between the bubbles there appears to be a difference between the effective added mass density and the mass coefficient of the kinetic energy density due to relative motion of the phases. For spherical bubbles with velocities all equal, isotropic spatial distribution, gas fraction α and liquid density 1, the effective added mass density and the mass coefficient of the kinetic energy density (due to relative motion) are calculated. They are respectively 0.5α(1 + 3.324α)1 and 0.5α(1−0.676α)1 and show good agreement with results in the literature