Carreau-Yasuda equation¶

Summary¶

Fit the complex viscosity with the Carreau-Yasuda equation.

• Function
$\eta^*(\omega) = \eta_\infty + (\eta_0-\eta_\infty)\left( 1 + (\lambda\omega)^a \right)^{(n-1)/a}$
• Parameters
• $$\eta_0$$: Viscosity at zero shear rate.

• $$\eta_\infty$$: Viscosity at infinite shear rate.

• $$\lambda$$: Relaxation time.

• $$n$$: Power law index.

• $$a$$: Dimensionless parameter (2 in most cases)

Description¶

Fit of the complex viscosity to the phenomenological Carreau-Yasuda equation. The equation used in the fit is:

$\eta^*(\omega) = \eta_\infty + (\eta_0-\eta_\infty)\left( 1 + (\lambda\omega)^a \right)^{(n-1)/a}$

In the equation, $$a$$ is a dimensionless parameter that describes the transition from the zero-shear rate region to the power law region. It frequently takes the value 2. In some experimental data, it is safe to assume that $$\eta_\infty$$ is equal to zero.

Warning

The fit only makes sense when applied using the logstar view (logarithm of the complex viscosity). The logarithm is needed, due to the wide range of viscosity values.

Warning

The theory can only be applied to one file per data set. If more than one file is active in the current data set, the theory will be applied to the first one in the list of active files.