Papanastasiou

Therefore the viscoelastic extra stress acting on a fluid particle is found via an integral in terms of velocities and velocity gradients evalua ted upstream along the streamline passing through its current position. This expression is used by Papanastasiou et al. (1987) to develop a finite element scheme for viscoelastic flow modelling. 

Papanastasiou et al. (1992) suggested that in order to generate realistic solutions for Navier-Stokes equations the exit conditions should be kept free (i.e. no outflow conditions should be imposed). In this approach application of Green s theorem to the equations corresponding to the exit boundary nodes is avoided. This is eqvrivalent to imposing no exit conditions if elements with... 

A. Papanastasiou-Diamandi, T. K. Christopoulos, and E. P. Diamandis, Ultrasensitive thyrotropin immunoassay based on enzymatically amplified time-resolved fluorescence with a terbium chelate, Clin. Chem. 38, 545-548 (1992). 

G. Papanastasiou and I. Ziogas, Simultaneous Determination of Equivalence Volumes and Acid Dissociation Constants from Potentiometric Titration Data, Talanta 1995,42, 827. 

Petraki CD, Gregorakis AK, Papanastasiou PA, Karavana VN, Luo LY, Diamandis EP. Immunohistochemical localization of human kallikreins 6, 10 and 13 in benign and malignant prostatic tissues. Prostat CancerProstatic Dis 2003 6 223-227. 

For example, Figs. 2.43 and 2.44 present the measured [55] viscosity and first normal stress difference data, respectively, for three blow molding grade high density polyethylenes along with a fit obtained from the Papanastasiou-Scriven-Macosko [59] form of the K-BKZ equation. A memory function with a relaxation spectrum of 8 relaxation times was used. 

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]. 

In equation (42), the quantities j denote the vailues of the function / or those of its derivative / jj and / z. The details of the basis functions, the quantities j and the nodes of an element have been presented elsewhere [26], The first and second derivatives of the mapping function / can be obtained from derivatives of the basis fimctions. To compute the pressiure p and tensor components, the four nodal values at points A, B, C and D of each element are chosen as unknowns. Their derivatives are evaluated by using finite-difference formulae. In Fig 14 we present computed streamlines for 4/1 and 8/1 axisymmetric contractions, and the computed shear stress along the computed streamlines, for a K-BKZ fluid of the form given by Papanastasiou et al [19]. 

N Papadopoulos, C Hasiotis, G Kokkinidis, G Papanastasiou. J Electroanal Chem. 308 83, 1991. 

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