Papanastasiou integral equation

A.C.Papanastasiou, L.E.Scriven, C.W.Macosko, An integral constitutive equation for mixed flows viscoelastic characterization, J. Rheol. 21 (1983), 387-410. 

It should be pointed out that the improvement of convergence might also be related to realistic preditions of shear and elongational viscosities by the Phan-Thien Tanner model, when compared to the Upper Convected Maxwell, Oldroyd-B and White-Metzner models. Satisfactory munerical results were also obtained with multi-mode integral constitutive equations using a spectnun of relaxation times [7, 17, 20-27], such as the K-BKZ model in the form introduced by Papanastasiou et al. [19]. 

As an example of a popular viscoelastic constitutive equation used in the past 25 years, vhich possesses enough degree of complexity so as to capture as accurately as possible the complex nature of polymeric liquids, we present here the K-BKZ integral constitutive equation with multiple relaxation times proposed by Papanastasiou et al. [27] and further modified by Luo and Tanner [28]. This is often referred to in the literature as K-BKZ/PSM model (from the initials of Papanastasiou, Scriven, Macosko) and is vritten as... 

Papanastasiou, A.C., Scriven, LE., and Macosko, C.W. (1983) An integral constitutive equation for mixed flows rheological characterization. 

Alaie, S.M. and Papanastasiou, T.C. (1993) Modeling of non-isothermal film blowing with integral constitutive equations. Int. Polym. Proc., 8, 51—65. 

Alaie, S. M. and T. C. Papanastasiou. 1993. Modeling of Non-isotheimal Film Blowing with Integral Constitutive Equations. Intern. Polym. Proc., 8(1), 51-65. 

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