For a non-Newtonian fluid, the dynamic viscosity is assumed to be a function of the shear rate:
where m and
n are scalars that can be set to arbitrary values. For
n > 1, the power law describes a shear thickening (dilatant) fluid. For
n < 1, it describes a shear thinning (pseudoplastic) fluid. A value of
n equal to one gives the expression for a
Newtonian fluid.
Equation 3-19 predicts an infinite viscosity at zero shear rate for
n < 1. This is however never the case physically. Instead, most fluids have a constant viscosity for shear rates smaller than 10
-2 s
-1 (
Ref. 19). Since infinite viscosity also makes models using
Equation 3-19 difficult to solve, COMSOL Multiphysics implements the power law model as
where λ is a parameter with the unit of time,
μ0 is the zero shear rate viscosity,
μinf is the infinite shear-rate viscosity, and
n is a dimensionless parameter. This expression is able to describe the viscosity for most stationary polymer flows.