Mechanistic pressure jump terms based on the system eigenvalues of two-fluid model for bubbly flow

Interfacial pressure jump terms based on the physics of phasic interface and bubble dynamics are introduced into the momentum equations of the two-fluid model for bubbly flow. The pressure discontinuity across the phasic interface due to the surface tension force is expresses as the function of fluid bulk moduli and bubble radius. The consequence is that we obtain from the system of equations the real eigenvalues representing the void-fraction propagation speed and the pressure wave speed in terms of the bubble diameter. Inversely, we obtain an analytic closure relation for the radius of bubbles in the bubbly flow by using the kinematic wave speed given empirically in the literature. It is remarkable to see that the present mechanistic model using this practical bubble radius can indeed represent both the mathematical well-posedness and the physical wave speeds in the bubbly flow