A Note on Mixture Density Using the Shannak Definition

In this study, a note on mixture density using the Shannak definition of the Froude number is presented (Shannak, B., 2009, “Dimensionless Numbers for Two-Phase and Multiphase Flow,” Proceedings of the International Conference on Applications and Design in Mechanical Engineering (ICADME), Penang, Malaysia, Oct. 11–13, 2009). From the definition of the two-phase Froude number, an expression of the two-phase density is obtained. The definition of the two-phase density can be used to compute the two-phase frictional pressure gradient using the homogeneous modeling approach in circular pipes, minichannels, and microchannels. We cannot have $gasdensity≤two-phasedensity≤liquiddensity$ for $0≤massquality≤1$⁠. Therefore, attention must be paid when using the obtained expression of the two-phase density in this note at any $x$ value.