Perturbation solution of Poiseuille flow of a weakly compressible Oldroyd-B fluid

Journal of Non-Newtonian Fluid Mechanics

Volumn 166, Issue 1-2, 2011, Pages 73-92

  Housiadas, Kostas D ^a   Georgiou, Georgios C ^b  

^a UNIVERSITY OF THE AEGEAN   (Greece)

^b UNIVERSITY OF CYPRUS   (Cyprus)

Author keywords

Compressibility; Flow curve; Normal stress difference; Oldroyd B fluid; Perturbation solution; Poiseuille flow

Indexed keywords

FLOW CURVES; NORMAL STRESS DIFFERENCE; OLDROYD-B FLUID; PERTURBATION SOLUTIONS; POISEUILLE FLOW;

ASPECT RATIO; DIFFERENTIAL EQUATIONS; EQUATIONS OF STATE; FLUIDS;

COMPRESSIBILITY;

EID: 78650179888     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2010.10.007     Document Type: Article

References (27)

1. Hatzikiriakos S.G., Dealy J.M. Role of slip and fracture in the oscillating flow of HDPE in a capillary. J. Rheol. 1992, 36:845-884.
2. Keshtiban I.J., Belblidia F., Webster M.F. Computation of incompressible and weakly-compressible viscoelastic liquids flow: finite element/volume schemes. J. Non-Newtonian Fluid Mech. 2005, 126:123-143.
3. Vinay G., Wachs A., Frigaard I. Numerical simulation of weakly compressible Bingham flows: the restart of pipeline flows of waxy crude oils. J. Non-Newtonian Fluid Mech. 2006, 136:93-105.
4. Guillopé C., Hakim A., Talhouk R. Existence of steady flows of slightly compressible viscoelastic fluids of White-Metzner type around an obstacle. Commun. Pure Appl. Anal. 2005, 4:23-43.
5. Taliadorou E., Georgiou G., Alexandrou A.N. A two-dimensional numerical study of the stick-slip extrusion instability. J. Non-Newtonian Fluid Mech. 2007, 146:30-44.
6. Georgiou G.C., Crochet M.J. Compressible viscous flow in slits with slip at the wall. J. Rheol. 1994, 38:639-654.
7. Taliadorou E., Georgiou G.C., Mitsoulis E. Numerical simulation of the extrusion of strongly compressible Newtonian liquids. Rheol. Acta 2008, 47:49-62.
8. Hatzikiriakos S.G., Dealy J.M. Start-up pressure gradients in a capillary rheometer. Polym. Eng. Sci. 1994, 34:493-499.
9. Ranganathan M., Mackley M.R., Spitteler P.H.J. The application of the multipass rheometer to time-dependent capillary flow measurements of a polyethylene melt. J. Rheol. 1999, 43:443-451.
10. Valério V., Carvalho M.S., Tomei C. Efficient computation of the spectrum of viscoelastic flows. J. Comp. Phys. 2009, 228:1172-1187.
11. Georgiou G. The time-dependent, compressible Poiseuille and extrudate-swell flows of a Carreau fluid with slip at the wall. J. Non-Newtonian Fluid Mech. 2003, 109:93-114.
12. Valette R., Mackley M.R., Hernandez Fernandez del Castillo G. Matching time dependent pressure driven flows with a Rolie Poly numerical simulation. J. Non-Newtonian Fluid Mech. 2006, 136:118-125.
13. Mitsoulis E., Delgadillo-Velazquez O., Hatzikiriakos S.G. Transient capillary-rheometry: compressibility effects. J. Non-Newtonian Fluid Mech. 2007, 145:102-108.
14. Taliadorou E., Georgiou G.C., Moulitsas I. Weakly compressible Poiseuille flows of a Herschel-Bulkley fluid. J. Non-Newtonian Fluid Mech. 2009, 158:162-169.
15. Keshtiban I.J., Belblidia F., Webster M.F. Numerical simulation of compressible viscoelastic liquids. J. Non-Newtonian Fluid Mech. 2004, 122:131-146.
16. Brujan E.A. A first-order model for bubble dynamics in a compressible viscoelastic fluid. J. Non-Newtonian Fluid Mech. 1999, 84:83-103.
17. Belblidia F., Keshtiban I.J., Webster M.F. Stabilised computations for viscoelastic flows under compressible considerations. J. Non-Newtonian Fluid Mech. 2006, 134:56-76.
18. Puangkird B., Belblidia F., Webster M.F. Numerical simulation of viscoelastic fluids in cross-slot devices. J. Non-Newtonian Fluid Mech. 2009, 162:1-20.
19. Edwards B.J., Beris A.N. Remarks concerning compressible viscoelastic fluid models. J. Non-Newtonian Fluid Mech. 1990, 36:411-417.
20. Matusu-Necasova S., Sequeira A., Videman J.H. Existence of classical solutions for compressible viscoelastic fluids of Oldroyd type past an obstacle. Math. Methods Appl. Sci. 1999, 22:449-460.
21. Taliadorou E.G., Neophytou M., Georgiou G.C. Perturbation solutions of Poiseuille flows of weakly compressible Newtonian liquids. J. Non-Newtonian Fluid Mech. 2009, 158:162-169.
22. Joseph S., Joseph L., Georgiou G.C. Perturbation solution of the compressible annular Poiseuille flow of a viscous fluid. J. Non-Newtonian Fluid Mech. 2010, 165:676-680.
23. Venerus D.C. Laminar capillary flow of compressible viscous fluids. J. Fluid Mech. 2006, 555:59-80.
24. Venerus D.C., Bugajsky D.J. Compressible laminar flow in a channel. Phys. Fluids 2010, 22:046101.
25. Wolfram Research, Inc. Mathematica Edition: Version 7.0 2008, Wolfram Research, Inc., Champaign, Illinois.
26. Poinsot T., Lele S. Boundary conditions for direct simulations of compressible viscous flows. J. Comp. Phys. 1992, 101:104-129.
27. Schwartz L.W. A perturbation solution for compressible viscous channel flows. J. Eng. Math. 1987, 21:69-86.