POLYFLOW - What can be said about the CEF (Criminale-Ericksen-Filbey) model?
Let us D and T respectively denote the rate-of-deformation tensor and the extra-stress tensor. The constitutive equation of the CEF fluid model can be written as follows:
T = 2.eta.D - psi1.dD/dt + 4.psi2.D.D
In this equation, eta is the shear viscosity, psi1 and psi2 are material coefficients. In the CEF equation, eta, psi1 and psi2 are general functions of the generalised shear rate. The quantity dD/dt is actually the upper-convected derivative of D.
Shear properties are dictated by the coefficient eta. "Viscoelasticity" is dictated by the coefficient psi1. The model does not predict relaxation: then the flow stops, D=0, and the stress vanish.
For a possible flow simulation, next to velocity and pressure, one should also calculate D as an additional unknown field. This is required by the upper-convected derivative that appears in the constitutive equation. As a consequence, the model involves an additional tensor field; by comparison, the light viscoelastic model ScaFTen in POLYFLOW involves only one additional scalar unknown.
4. In the book by C.W. Macosko, "Rheology, principle, measurements and applications" (Wiley 1994), one reads the following on page 148:
"Although the resulting equation, called the Criminale-Ericksen-Filbey equation (1958), is valid for any steady shearing flow, it cannot be expected to predict steady extensional viscosities or the stresses in any flow besides steady simple shear. More seriously, neither the second-order-fluid equation nor the Criminale-Ericksen-Filbey equation can predict time-dependent viscoelastic phenomena such as stress growth or stress relaxation."