THE AVERAGED BERNOULLI EQUATION AND MACROSCOPIC EQUATIONS OF MOTION FOR THE POTENTIAL FLOW OF A 2-PHASE DISPERSION

A description of a uniform two-phase dispersion in a potential flow is developed in terms of a macroscopic (averaged) potential and the average velocity of each phase. Using analogues to electromagnetic theory, the constitutive laws are expressed in terms of either an effective conductivity of the matrix or its polarization (average dipole moment). Bernoulli's equation for the fluid is expressed in averaged form. The results are applied to three example problems. The equations of motion for the "two-fluid model" are derived using the hypothesis that the averaged Bernoulli equation is differentiable. The continuous phase is incompressible but the dispersed phase may be compressible. The results are compatible with Geurst's equations which were derived using variational methods.