Criticism Of The Classical Mass Balance ForMultiphase Flow

Abstract

The key point in multiphase flows is that the phases have different velocities. Being velocity the space-time ratio, it is impossible that the phases spend the same time in traveling the same distance i.e., the length of the control volume. Hence, the time scale of any phase should be different from the other ones. As a main consecuence any of the phase velocities could be the global velocity of the multiphase flow. This important result is readily demonstrated following two equivalent procedures: the first one, based on the total mass conservation in the domain, uses new control volumes of variable length which follows any of the velocity fields present in the domain; the second way proposes the strict application of the classic Reynolds theorem but to a moving and deforming control volume. Whilst it is clearly shown that the classical mass balance expression for multiphase flow fails in the correct interpretation and application of the total derivative concept, this new point of view gives a coherent solution.