A note on the mixture viscosity using the Shannak definition

Abstract

In this study, a note on the mixture viscosity using the Shannak definition is presented [Shannak, B. A., 2008. Frictional pressure drop of gas liquid two-phase flow in pipes. Nucl. Eng. Des. 238, 3277–3284]. From his definition of the two-phase Reynolds number (Re(2ph)), an expression of the two-phase viscosity (μ(2ph)) is obtained. This expression of the two-phase viscosity (μ(2ph)) satisfies the following important limiting conditions: i. at x=0, μ(2ph)=μf, and at x=1, μ(2ph)=μg. This definition of the two-phase viscosity (μ(2ph)) can be used to compute the two-phase frictional pressure gradient using the homogeneous modeling approach in circular pipes, minichannels and microchannels. By plotting μ(2ph)/μf versus x for air–water system at atmospheric conditions using the Shannak definition as well as the other most commonly used formulas of the two-phase viscosity (μ(2ph)) in gas–liquid two-phase flows such as McAdams et al. (1942), Cicchitti et al. (1960), and Awad and Muzychka (2008) (Definition 1, Definition 2, Definition 3, and Definition 4), it is clear that the Shannak definition of the two-phase viscosity gives μ(2ph)>μf at low x. This is impossible because we must have μg<μ(2ph)<μf for 0<x<1. Therefore, attention must be taken when using the Shannak definition of the two-phase viscosity at low x.