Phan Thien-Tanner fluid model

Solution of the flow equations has been based on the application of the implicit 0 time-stepping/continuous penalty scheme (Chapter 4, Section 5) at a separate step from the constitutive equation. The constitutive model used in this example has been the Phan-Thien/Tanner equation for viscoelastic fluids given as Equation (1.27) in Chapter 1. Details of the finite element solution of this equation are published elsewhere and not repeated here (Hou and Nassehi, 2001). The predicted normal stress profiles along the line AB (see Figure 5.12) at five successive time steps are. shown in Figure 5.13. The predicted pattern is expected to be repeated throughout the entire domain. 

Figure 9.7. Steady shear and normal stress data at 170 °C for two polyethylenes (a) low-density Resin 10 and (b) high-density Resin 22. The lines are the fit to the Phan-Thien/Tanner model, discussed below. Reprinted with permission from Tsang and Dealy, /. Non-Newtonian Fluid Mech., 9, 203 (1981). Copyright Elsevier.

Figure 9.13. Comparison of the Phan-Thien/Tanner model to the extensional data of Meissner. Reprinted with permission from Phan-Thien and Tanner, J. Non-Newtonian Fluid Mech.,...

Phan-Thien N, Fan XJ, Tanner RI, Zheng R (2002) Folgar-Tucker constant for a fiber suspension in a Newtonian fluid. J Non-Newtonian Fluid Mech 103 251-260 Phan-Thien N, Fan XJ, Zheng R (2000) A numerical simulation of suspension flow using a constitutive model based on anisotropic interparticle interactions. Rheol Acta 39 122-130 Phan-Thien N, Graham AL (1991) A new constitutive model for fiber suspensions flow past a sphere. Rheol Acta 30 44-57... 

Phan-Thien N, Pham DC (2000) Differential multiphase models for polydispersed spheroidal inclusions thermal conductivity and effective viscosity. Int J Eng. Sci 38 73-88 Phan-Thien N, Tanner RI (1977) A new constitutive equation derived from network theory. J Non-Newtonian Fluid Mech 2 353-365... 

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