Viscometric approach - the CEF model

The practical and computational complications encountered in obtaining solutions for the described differential or integral viscoelastic equations sometimes justifies using a heuristic approach based on an equation proposed by Criminale, Ericksen and Filbey (1958) to model polymer flows. Similar to the generalized Newtonian approach, under steady-state viscometric flow conditions components of the extra stress in the (CEF) model are given a.s explicit relationships in terms of the components of the rate of deformation tensor. However, in the (CEF) model stress components are corrected to take into account the influence of normal stresses in non-Newtonian flow behaviour. For example, in a two-dimensional planar coordinate system the components of extra stress in the (CEF) model are written as 

Vectors, Tensors and the Basic Equations of Fluid Mechanics, Dover Publications, New York. 

Bernstein, B., Kearslcy, E.A. and Zapaa, L., 1963. A study of stress relaxation with finite strain. Trans. Soc. Rheol. 7, 391-410. 

Armstrong, R.C. and Hassager, O., 1977. Dynamics of Polymeric Fluids, Vol 1 Fluid Mechanics, Wiley, New Yoi k. 

Stewart, W.E, and Lightfoot, E.M., 1960. Transport Phenomena, Wiley, New York. 

---