# 2.10. Viscosity Models¶

A number of different viscosity models are available.

The …

## 2.10.2. Arrhenius¶

For free energies involing a compositional order parameter $$\phi$$ one can define a local viscosity following a relation owing to Arrhenius:

$\eta(\mathbf{r}) = \eta_{-}^{(1-\phi/\phi^\star)/2} \eta_{+}^{(1+\phi/\phi^\star)/2}.$

For example for a symmetric binary fluid with $$\phi^\star = \pm (-A/B)^{1/2}$$, $$\eta_+$$ is the viscosity when the composition is $$\phi = +\phi^\star$$ and $$\eta_-$$ is the viscosity when $$\phi = -\phi^\star$$.

This may be specified in the input file via

viscosity_model                  arrhenius
viscosity_arrhenius_eta_plus     0.1
viscosity_arrhenius_eta_minus    0.5
viscoisty_arrhenius_phistar      1.0


Values for $$\eta_+$$ and $$\eta_-$$ must be specified, and set the shear viscosity in the corresponding phases. If the value for $$\phi^\star$$ is omitted, it will default to that specified by the free energy parameters $$(-A/B)^{1/2}$$. However, one is free to choose a $$\phi^\star$$ for the viscosity model independently of the value that would be computed from the free energy parameters.

The values of $$\eta_+$$ and $$\eta_-$$ override any Newtonian viscosity that may also be specified in the input. The local bulk viscosity is computed via

$\eta_\nu (\mathbf{r}) = (\eta_\nu/\eta) \eta (\mathbf{r})$

where $$\eta$$ and $$\eta_\nu$$ are the fixed Newtonian shear and bulk viscosities, respectively.