We know that the LBE is non-dimensional. If I want to introduce the Carreau model in LBM, what are the ways to make the prescribed dimensional model into non-dimensional form, especially when the zero and infinite shear-rate viscosities are expressed in Pa s. Some references to this will be of great help. Also how to take care of the Carreau number.
Attached figure is from https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/numerical-simulation-of-flow-of-a-shearthinning-carreau-fluid-over-a-transversely-oscillating-cylinder/70BA8A4937C5A0531EF5B1175CEE4E7D
A fascinating project. There are many optional models for non-Newtonian fluids apart from Carreau, all need data on the fluid. The more complex models need data for the temperature effects on the parameters in the model. The values at zero shear rate and infinite shear rate are in the same unit as the viscosity (i.e. Pa.s) which is normally used unless you are using a different set of units from SI.
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