Questions about shear stress in official references

Hi everyone,

I am reading online resources: Theory Guide (1993) [ MFIX Documentation Theory Guide [Tech Note] (doe.gov)], Summary of MFIX Equations (2012) [ Microsoft Word - MFIXEquations2012-1.doc (doe.gov)] and Theoretical Review of the MFIX Fluid and Two-Fluid Models (2020) [ Theoretical Review of the MFIX Fluid and Two-Fluid Models (osti.gov)].

Q1: Are the conservations of momentum for gas and solid phases in the Theory Guide (1993) expressed in the Ishii formulation? Volume fraction is involved in the expression of stress tensor there while it is not included in the default formulation for Model A in MFIX.

① In the Theory Guide (1993)


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② In the Theoretical Review of the MFIX Fluid and Two-Fluid Models (2020)


Q2: The kinetic model for solid stress in the Theory Guide (1993) is different from the one in the Theoretical Review of the MFIX Fluid and Two-Fluid Models (2020). Which one is right?

① In the Theory Guide (1993)

② In the Theoretical Review of the MFIX Fluid and Two-Fluid Models (2020)