Bounding principles for two-phase flow systems

For two classes of multiphase flow problems, upper and lower bounding principles are constructed for the rate of dissipation of mechanical energy as the result of viscous forces both in the bulk fluid and in the phase interface. These principles are developed for simple classes of non-linear constitutive equations for the bulk stress tensor and for the surface stress tensor. The integral mechanical energy balance relates these bounds to quantities that are subject to direct experimental evaluation.