Chemorheological Models
Polymer melts are usually non-Newtonian fluids. For the inelastic non-Newtonian models, it is possible to define an apparent viscosity from a generalized Newtonian relationship between the deviatoric stress tensor and the strain-rate tensor
where is the shear rate.
For the thermosets, the apparent viscosity depends both on the temperature and the degree of cure. The viscosity of the polymer decreases with the temperature. On the other hand, the raising temperature will increase the reaction rate, thus leading to increase in the conversion and viscosity
The Castro–Macosko model is often used to describe the changes of the apparent viscosity with degree of conversion
(9-2)
where is the conversion at which the viscosity of the melt grows drastically and c1 and c2 are the model parameters.
Another often used model is a percolation model is
(9-3)
where p is the percolation exponent.
Power law and Cross non-Newtonian inelastic models are available in the Curing Reaction interface to specify the shear-rate dependence.
Power Law
The Power law model prescribes
(9-4)
where m, n are scalars that can be set to arbitrary values and denotes a reference shear rate where is a lower limit for the evaluation of the shear rate magnitude. The temperature and conversion dependent Power law viscosity becomes
(9-5)
Cross Model
Combining the Cross model for shear-rate dependence and thermal effects gives
(9-6)
where τtr is the critical stress, μ0 is the zero shear rate viscosity, μ is the infinite shear-rate viscosity, and n is a dimensionless parameter.
Thermal Effects
Several models are available to describe the temperature dependence.
Arrhenius
One commonly used thermal function is defined by the Arrhenius equation:
where Q denotes the activation energy, R is the universal gas constant, and T and T0 are the temperature and reference temperature, respectively.
Williams-Landel-Ferry
Williams-Landel-Ferry model is defined as
(9-7)
where C1WLF and C2WLF are model constants, and TWLF is the reference temperature.
Exponential
Exponential model is defined as
(9-8)
where b denotes a temperature sensitivity, and T0 is the reference temperature.
Viscosity factor calculated using Equation 9-2 or Equation 9-3 can be used together with the non-Newtonian inelastic models included in the fluid flow interfaces. The models are defined in the fluid flow interfaces and provide a complete model for the apparent viscosity that is temperature and shear-rate dependent.