Rheological modeling of both shear-thickening and thinning behaviors through constitutive equations

On the consistent modeling of shear-thickening polymer solutions

“…( 5) is identical to the one obtained using the fluidity methodology. In particular, when a ¼ 0 and h ¼ 1 (Hookean dumbbells), we obtain the BMP model; when a ¼ 0, we obtain the f-FENE model; 24 and when h ¼ 1, we obtain the f-Giesekus model. 24 As such, our approach provides the proper evolution equation when both anisotropic and finite extensibility effects are concurrently considered.…”

“…In particular, when a ¼ 0 and h ¼ 1 (Hookean dumbbells), we obtain the BMP model; when a ¼ 0, we obtain the f-FENE model; 24 and when h ¼ 1, we obtain the f-Giesekus model. 24 As such, our approach provides the proper evolution equation when both anisotropic and finite extensibility effects are concurrently considered. Altogether, our present NET approach explicitly and unequivocally states that the BMP model, 19 as well as its generalizations, 21,22,24 is not thermodynamically admissible unless additional terms, concerning the function f k ð Þ in Eqs.…”

“…It is important to elaborate as to how the new constitutive model for STPSs, as derived here in the context of the generalized bracket formalism of NET, compares with previously proposed models using the fluidity methodology. 19,21,22,24 To do this, we first write down the evolution equation of the polymer stress tensor by using Eq. (2) in Eq.…”

“…Note that the evolution equation is not independent of the conformation tensor. According to the fluidity methodology, 19,21,22,24 the relaxation time is given as…”

“…However, in these generalized BMP models, kinetic parameters rely empirically on the second invariants of the deformation rate and shear stress tensors. More recently, Tamano et al 24 coupled the Giesekus and FENE-P models with Fredrickson's kinetic equation; the use of the anisotropic Giesekus parameter in the former allowed for the prediction of a nonvanishing second normal stress coefficient. Both normal stress coefficients have been predicted to shear thicken followed by a shear thinning behavior.…”