Resolving Unit Inconsistencies in Non-Newtonian Viscosity Calculations (Herschel-Bulkley Model)

There is  the inconsistency in units for non-Newtonian viscosity calculations in the Herschel-Bulkley model. The inconsistency arises because the model expresses shear stress (tau) in units of N/m^2 (Pascals), while the shear rate (gamma_dot) is in units of s^-1 (reciprocal seconds).

Here's the breakdown:

 * Shear stress (tau): N/m^2 (measures force per unit area)

 * Shear rate (gamma_dot): s^-1 (measures rate of deformation)

Kinematic viscosity (nu) has units of m^2/s, which combines units from both shear stress and shear rate. However, the Herschel-Bulkley model directly outputs kinematic viscosity below the yield stress threshold, while it calculates a dynamic viscosity (eta) above the threshold (eta = nu * rho, where rho is density).

The solution you propose is indeed correct:

 * tau0 and k parameters should be pre-divided by density (rho). This ensures that the units cancel out correctly and the final result is kinematic viscosity (m^2/s) as expected.

The documentation oversight you identified is a common issue. Many resources don't explicitly mention this pre-division because it's assumed as a standard practice in computational rheology.

Here's a recommendation:

 * Before implementing the model, consult the OpenFOAM user guide or community forums for confirmation.

 * Look for examples or tutorials on implementing the Herschel-Bulkley model in OpenFOAM to see how others handle the units.

 * If the documentation remains unclear, consider contacting the OpenFOAM developers for clarification.