Effective Equations for Multiphase Flows—Waves in a Bubbly Liquid

This chapter elaborates various aspects of effective equations for multiphase flows. The subject of multiphase flow presents many practical and challenging engineering problems, such as sedimentation, flows in porous media, flows with additives, blood flows, and bubbly liquids. On the microscopic scale, the motion of the fluids and all of the interfaces are coupled. The motion of the gas is indirectly coupled to the dynamics of the other interfaces through the motion of the liquid outside the interfaces. A set of workable equations can be derived from the original set of complicated equations by a systematic and formal assymptotic analysis. The examples of the small microscopic to macroscopic scale ratio limit are presented. The coefficients in the equations are defined by the microscopic structure in the equilibrium state, and the global effect of the dynamics of the microscopic field appears only in the next-order equations for the macroscopic field. The equations of motion for each phase and interface are also described.