Recent improvements of novel porous media formulation for multiphase flow conservation equation

In the derivation of time averaging of local volume averaged multiphase flow conservation equations presented in my book titled “Novel Porous Media Formulation for Multiphase Flow Conservation Equations” published by Cambridge University Press, September, 2011. The high-frequency fluctuation of all dependent variables were included except for the high frequency fluctuations of volume fraction, fluid–fluid interfacial area, and local averaging volume for the simplicity and lacking of pertinent experimental data on fluid–fluid interface. These equations are valid for use (1) for laminar flows by dropping out all high frequency terms in these derived equations; and (2) for weak turbulent flows allowing for neglecting of the high frequency fluctuations of volume fraction, fluid–fluid interfacial area and local averaging volume. The major contributions of this paper are (1) to include the high-frequency fluctuations of volume fraction, fluid–fluid interfacial area and local averaging volume, in the derivation for completeness and rigor, and to demonstrate flexibility of novel porous media formulation; (2) to incorporate the concept of a coherence component in turbulence and for simplification in deriving the time-volume averaged multiphase flow conservation equations; and (3) to include stationary, nonporous, and nonreactive internal structures. With these three improvements, a new set of multiphase flow conservation equations have been derived and presented here for the first time and they have greatly widened the range of applicability.