For water and air, viscosity is a material constant. For many fluids processed in industry it is not: viscosity depends on how fast the fluid is being sheared.
The main behaviours
Shear-thinning (pseudoplastic). Viscosity falls as shear rate rises. The most common class: polymer solutions, paint, ketchup, blood. The fluid is thin near an impeller blade and thick at the tank wall — and that is precisely why dead zones form.
Shear-thickening (dilatant). The opposite. Seen in dense suspensions; dangerous for pumping equipment.
With a yield stress (Bingham). Does not flow at all below a certain stress and behaves as a solid. Toothpaste, drilling mud, fresh concrete. Restarting a Bingham fluid stopped in a pipeline requires far higher pressure than steady flow — and that is the condition that sets the design.
Modelling
Viscosity is defined by a model curve (power law, Carreau, Herschel-Bulkley). Two things need care in the choice:
The shear rate range. The model coefficients are valid over the range in which the rheometer measurement was made. If the shear rates in the analysis fall outside that range, the model is being extrapolated — a power law gives infinite viscosity at low shear rates, which is not physical.
The numerical treatment of yield stress. In the zero-shear region the viscosity goes to infinity; solvers clip this with an upper bound, and the value of that bound affects the result. It should be reported.
Regime
Because of the high apparent viscosity these flows are usually laminar. Leaving the turbulence model switched on produces mixing that does not exist and exaggerates mixing time and heat transfer. Computing the Reynolds number with the local viscosity and confirming the regime is the first step. See the stirred tank note.
References
- Ferziger, J. H., Perić, M. & Street, R. L. (2020). Computational Methods for Fluid Dynamics, 4th ed. Springer. DOI: 10.1007/978-3-319-99693-6
- Ergun, S. (1952). Fluid flow through packed columns. Chemical Engineering Progress, 48(2), 89–94.