Plastic Viscosity

The plastic viscosity options enable you to model liquid viscosity. You can specify the type of viscosity model and the type of temperature dependence model that you want to use.

You can define the following types of plastic viscosity and temperature dependence:

Cross Model + Arrhenius: Cross model for viscosity with the Arrhenius model for temperature dependence.
Cross Model + WLF: Cross model for viscosity with the Williams-Landel-Ferry (WLF) model for temperature dependence.
Campus Carreau + WLF: Campus Carreau model for viscosity with the WLF model for temperature dependence.
Macosko: Viscosity model for thermoset materials.

This page discusses:

Cross Model + Arrhenius
Cross Model + WLF
Campus Carreau + WLF
Macosko Model

Cross Model + Arrhenius

The Cross model of viscosity can be expressed as:

η = \frac{η_{0}}{1 + {(η_{0} \dot{γ} / τ^{*})}^{1 - n}},

where

\dot{γ}

is the shear rate, and

η_{0}

is the zero shear rate viscosity at temperature

T

You can introduce the Arrenhius model of temperature dependence into the viscosity specification by using the following expression:

η_{0} (\dot{γ}, T, P) = B \exp (T_{b} / T) \exp (β P)

where

B

is expressed in terms of force time per area;

T_{b}

is a temperature value in degrees K;

τ^{*}

is expressed in terms of degrees K area per force;

n

is a dimensionless constant; and

β

is expressed in terms of force.

Cross Model + WLF

The Cross model of plastic viscosity can be expressed as:

η = \frac{η_{0}}{1 + {(η_{0} \dot{γ} / τ^{*})}^{1 - n}},

where

\dot{γ}

is the shear rate, and

η_{0}

is the zero shear rate viscosity at temperature

T

The Williams-Landel-Ferry equation (or WLF equation) introduces temperature dependence into the viscosity model:

η_{0} (\dot{γ}, T, P) = D_{1} \exp [- A_{1} (T - T^{*}) / (A_{2} + T - T^{*})] f o r T \geq T^{*}, η_{0} (\dot{γ}, T, P) = \infty f o r T \geq T^{*}

where

T^{*} = D_{2} + D_{3} P,

and

A_{2} = {\tilde{A}}_{2} + D_{3} P .

$D_{1}$ is expressed in terms of force time per area; $D_{2}$ is a temperature value in degrees K; $D_{3}$ is a temperature value in degrees K area per force; $A_{1}$ is a dimensionless constant; ${\tilde{A}}_{2}$ is a temperature value in degrees K; $τ^{*}$ is expressed in terms of force per area; and $n$ is a dimensionless constant.

Campus Carreau + WLF

The Campus Carreau-WLF viscosity can be expressed as:

η (T, \dot{γ}) = \frac{K_{1} η_{0}}{{[1 + (K_{2} \dot{γ} η_{0})]}^{K_{3}}}, \log_{10} (η_{0}) = \frac{8.86 (K_{4} - K_{5})}{101.6 + K_{4} - K_{5}} - \frac{8.86 (T - K_{5})}{101.6 + T - K_{5}}, f o r T \geq K_{5} \log_{10} (η_{0}) = \infty f o r T < K_{5}

where

K_{1}

is expressed in terms of force time per area;

K_{2}

is expressed in time;

K_{3}

is a dimensionless constant; and

K_{4}

and

K_{5}

are temperature values in degrees C.

Macosko Model

The Macosko Model viscosity can be expressed as:

η (T, γ, α) = η' (T, γ) (\frac{α_{g}}{α_{g} - α}),

η (T, γ, α) = \infty

with

η' (T, γ) = (\frac{η_{0} (T)}{1 + {(η_{0} \dot{γ} / τ^{*})}^{1 - n}}),

η_{0} (T) = B \exp (T_{b} / T),

where $α$ is the conversion; and $n$ , $τ^{*}$ , $C_{1}$ , $C_{2}$ , $B$ , $T_{b}$ , and $T_{b}$ are material parameters.