Viscoelastic flow through fibrous media using the CONNFFESSIT approach

Journal of Rheology

Volumn 42, Issue 3, 1998, Pages 477-491

  Hua, C C ^a,c   Schieber, J D ^b  

^a University of Houston   (United States)

^b Illinois Institute of Technology   (United States)

^c NATIONAL CHUNG CHENG UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000137599     PISSN: 01486055     EISSN: None     Source Type: Journal    
DOI: 10.1122/1.550960     Document Type: Article

References (30)

1. Bernstein, B., D. S. Malkus, and E. T. Olsen, "A finite element for incompressible plane flows of fluids with memory," Int. J. Num. Methods Fluids 5, 43-70 (1985).
2. Bird, R. B., C. F. Curtiss, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids. Vol 2: Kinetic Theory, 2nd ed. (Wiley-Interscience, New York, 1987).
3. Bird, R. B., W. E. Stewart, and E. N. Lightfoot, Transport Phenomena (Wiley, New York, 1960).
4. Brown, E. F. and W. R. Burghardt, "First and second normal stress difference relaxation in reversing double-step strain flows," J. Rheol. 40, 37-54 (1996).
5. Chmielewski, C. and K. Jayaraman, "The effect of polymer extensibility on crossflow of polymer solutions through cylinder arrays," J. Rheol. 36, 1105-1126 (1992).
6. Chmielewski, C. and K. Jayaraman, "Elastic instability in crossflow of polymer solutions through periodic arrays of cylinders," J. Non-Newtonian Fluid Mech. 48, 285-301 (1993).
7. de Gennes, P. G., "Reptation of a polymer chain in the presence of fixed obstacles," J. Chem. Phys. 55, 572-579 (1971).
8. Doi, M., "Stress relaxation of polymeric liquids after double-step strain," J. Polym. Sci., Polym. Phys. Ed. 18, 1891-1901 (1980).
9. Doi, M. and S. F. Edwards, "Dynamics of concentrated polymer systems part 1. Brownian motions in the equilibrium state," J. Chem. Soc. Faraday Trans. II 74, 1789-1800 (1978a).
10. Doi, M. and S. F. Edwards, "Dynamics of concentrated polymer systems part 2. Molecular motion under flow," J. Chem. Soc. Faraday Trans. II, 74, 1802-1817 (1978b).
11. Doi, M. and S. F. Edwards, "Dynamics of concentrated polymer systems part 3. The constitutive equation," J. Chem. Soc. Faraday Trans. II 74, 1818-1832 (1978c).
12. Doi, M. and S. F. Edwards, The Theory of Polymer Dynamics (Clarendon, Oxford, 1986).
13. Feigl, K., M. Laso, and H. C. Öttinger, "CONNFFESSIT approach for solving a two-dimensional viscoelastic fluid problem," Macromolecules 28, 3261-3274 (1995).
14. Guenette, R. and M. Fortin, "A new mixed finite element method for computing viscoelastic flows," J. Non-Newtonian Fluid Mech. 60, 27-52 (1995).
15. Hua, C. C., J. D. Schieber, and N. C. Andrews, "A constant-contour-length reptation model without independent alignment or consistent averaging approximations for chain retraction," Rheol. Acta. 36, 544-554 (1997).
16. Hulsen, M. A., A. P. G. van Heel, and B. H. A. A. van den Brule, "Simulation of viscoelastic flows using Brownian configuration fields," J. Non-Newtonian Fluid Mech. 70, 79-101 (1997).
17. Khomami, B., K. K. Talwar, and H. K. Ganpule, "A comparative study of higher- and lower-order finite element techniques for computation of viscoelastic flows," J. Rheol. 38, 255-289 (1994).
18. Laso, M. and H. C. Öttinger, "Calculation of viscoelastic flow using molecular models: the CONNFFESSIT approach," J. Non-Newtonian Fluid Mech. 47, 1-20 (1993).
19. Laso, M., M. Picasso, and H. C. Öttinger, "Two-dimensional, time-dependent viscoelastic flow calculations using CONNFFESSIT," AICHE J. 43, 877-892 (1997).
20. Nagtegaal, J., D. M. Parks, and J. R. Rice, "On numerically accurate finite element solutions in the fully plastic range," Comput. Methods Appl. Mech. Eng. 4, 153-177 (1974).
21. Osaki, K., S. Kimura, and M. Kurata, "Relaxation of shear and normal stresses in double-step shear deformations for a polystyrene solution. A test of the Doi-Edwards theory for polymer rheology," J. Rheol. 25, 549-562 (1981).
22. Öttinger, H. C., "Computer simulation of reptation theories I. Doi-Edwards and Curtiss-Bird models," J. Chem. Phys. 91, 6455-6462 (1989).
23. Petruccione, F. and P. Biller, "A numerical stochastic approach to network theories of polymeric fluids," J. Chem. Phys. 89, 577-582 (1988).
24. Skartsis, L., B. Khomami, and J. L. Kardos, "Polymeric flow through fibrous media," J. Rheol. 36, 589-620 (1992).
25. Souvaliotis, A. and A. N. Beris, "Applications of domain decomposition spectral collocation methods in viscoelastic flows through model porous media," J. Rheol. 36, 1417-1453 (1992).
26. Talwar, K. K. and B. Khomami, "Applications of higher order finite element methods to viscoelastic flow in porous media," J. Rheol. 36, 1377-1416 (1992).
27. Talwar, K. K. and B. Khomami, "Flow of viscoelastic fluids past periodic square arrays of cylinders: Inertial and shear thinning viscosity and elasticity effects," J. Non-Newtonian Fluid Mech. 57, 177-202 (1995).
28. Venerus, D. C. and H. Kahvand, "Normal stress relaxation in reversing double-step strain flows," J. Rheol. 38, 1297-1315 (1994).
29. Viriyayuthakorn, M. and B. Caswell, "Finite element simulation of viscoelastic flow," J. Non-Newtonian Fluid Mech. 6, 245-267 (1980).
30. Vossoughi, S. and F. A. Seyer, "Pressure drop for flow of polymer solution in a model porous medium," Can. J. Chem. Eng. 52, 666-669 (1974).