Plastic Viscosity

The Cross model of viscosity can be expressed as:

where $\dot{\gamma }$ is the shear rate, and ${\eta }_0$ 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:

where $B$ is expressed in terms of force time per area; $T_b$ is a temperature value in degrees K; ${\tau }^{*}$ is expressed in terms of degrees K area per force; $n$ is a dimensionless constant; and $\beta$ is expressed in terms of force.

The Cross model of plastic viscosity can be expressed as:

where $\dot{\gamma }$ is the shear rate, and ${\eta }_0$ is the zero shear rate viscosity at temperature $T$ .

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

where $T^{*}=D_2+D_{3}P,$ and $A_2={\tilde{A}}_2+D_{3}P\mathrm{.}$

$D_1$ 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; ${\tau }^{*}$ is expressed in terms of force per area; and $n$ is a dimensionless constant.

The Campus Carreau-WLF viscosity can be expressed as:

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.

The Macosko Model viscosity can be expressed as:

with

where $\alpha$ is the conversion; and $n$ , ${\tau }^{*}$ , $C_1$ , $C_2$ , $B$ , $T_b$ , and $T_b$ are material parameters.