Viscoelastic Poiseuille flows with total normal stress dependent, nonlinear Navier slip at the wall

Physics of Fluids

Volumn 25, Issue 4, 2013, Pages

  Housiadas, Kostas D ^a  

^a UNIVERSITY OF THE AEGEAN   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

CAPILLARY FLOW; ROAD CONSTRUCTION; SHEAR STRESS; SPECTRUM ANALYSIS;

DIMENSIONLESS NUMBER; EXPONENTIAL DECAYS; EXPONENTIAL DEPENDENCE; ISOTROPIC PRESSURE; PERTURBATION SERIES; REGULAR PERTURBATIONS; SKIN-FRICTION FACTORS; VIS-COELASTIC FLUIDS;

VISCOELASTICITY;

EID: 84877672763     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4799157     Document Type: Article

References (37)

1. Barnes H.A. A review of the slip (wall depletion) of polymer solutions, emulsions and particle suspensions in viscometers: Its cause, character, and cure. J. Non-Newtonian Fluid Mech. 1995, 56:221-251. 10.1016/0377-0257(94)01282-M
2. Denn M.M. Extrusion instabilities and wall slip. Annu. Rev. Fluid Mech. 2001, 33:265-287. 10.1146/annurev.fluid.33.1.265
3. Denn M.M. Polymer Melt Processing 2008, 199-216. (Cambridge University Press, New York), Chap. 12, pp.
4. Sochi T. Slip at fluid-solid interface. Polym. Rev. 2011, 51:309-340. 10.1080/15583724.2011.615961
5. Hatzikiriakos S.G. Wall slip of molten polymers. Prog. Polym. Sci. 2012, 37:624-643. 10.1016/j.progpolymsci.2011.09.004
6. Buscall R. Letter to the editor: Wall slip in dispersion rheometry. J. Rheol. 2010, 54:1177-1183. 10.1122/1.3495981
7. Schowalter W.R. The behavior of complex fluids at solid boundaries. J. Non-Newtonian Fluid Mech. 1988, 29:25-36. 10.1016/0377-0257(88)85048-1
8. Navier C.L. M. N. Memoire sur les lois du mouvement des fluides. Mem. Acad. Roy. Sci. Inst. Fr. 1827, 6:389-440
9. Maxwell J.C. On stresses in rarified gases arising from inequalities of temperature. Philos. Trans. R. Soc. London 1879, 170:231-256. 10.1098/rstl.1879.0067
10. Lau H.C. Schowalter W.R. A model of adhesive failure of viscoelastic fluids during flow. J. Rheol. 1986, 30:193-206. 10.1122/1.549888
11. Hill D.A. Hasegawa T. Denn M.M. On the apparent relation between the adhesive failure and melt fracture. J. Rheol. 1990, 34:891-918. 10.1122/1.550105
12. Hatzikiriakos S.G. Dealy J.M. Wall slip of molten high density polyethylenes. II. Capillary rheometer studies. J. Rheol. 1992, 36:703-741. 10.1122/1.550313
13. Hatzikiriakos S.G. Mitsoulis E. Slip effects in tapered dies. Polym. Eng. Sci. 2009, 49:1960-1969. 10.1002/pen.21430
14. Ferras L.L. Nobrega J.M. Pinho F.T. Analytical solutions for Newtonian and inelastic non-Newtonian flows with wall slip. J. Non-Newtonian Fluid Mech. 2012, 175-176:76-88. 10.1016/j.jnnfm.2012.03.004
15. Ferras L.L. Nobrega J.M. Pinho F.T. Analytical solutions for channels flows of Phan-Thien-Tanner and Giesekus fluids under slip. J. Non-Newtonian Fluid Mech. 2012, 171-172:97-105. 10.1016/j.jnnfm.2012.01.009
16. Ansari M. Hatzikiriakos S.G. Mitsoulis E. Slip effects in HDPE flows. J. Non-Newtonian Fluid Mech. 2012, 167-168:18-29. 10.1016/j.jnnfm.2011.09.007
17. Kalyon D.M. Malik M. Axial laminar flow of viscoplastic fluids in a concentric annulus subject to wall sip. Rheol. Acta 2012, 51:805-820. 10.1007/s00397-012-0641-y
18. Person T.J. Denn M.M. The effect of die materials and pressure-dependent slip on the extrusion of linear low-density polyethylene. J. Rheol. 1997, 41:249-265. 10.1122/1.550877
19. Kalika D. Denn M.M. Wall slip and extrudate distortion in linear low-density polyethylene. J. Rheol. 1987, 31:815-834. 10.1122/1.549942
20. Vinogradov G.V. Ivanova L.L. Wall slippage and elastic turbulence of polymers in the rubbery state. Rheol. Acta 1968, 7:243-254. 10.1007/BF01985785
21. White J.L. Han M.H. Nakajima N. Brzoskowski R. The influence of materials of construction on biconical rotor and capillary measurements of shear viscosity of rubber and its compounds and considerations of slippage. J. Rheol. 1991, 35:167-189. 10.1122/1.550226
22. Kumar K.A. Graham D. Effect of pressure-dependent slip on flow curve multiplicity. Rheol. Acta 1998, 37:245-255. 10.1007/s003970050112
23. Rao I.J. Rajagopal K.J. The effect of the slip boundary condition on the flow of fluids in a channel. Acta Mech. 1999, 135:113-126. 10.1007/BF01305747
24. Tang H.S. Kalyon D.M. Unsteady circular tube flow of compressible polymeric liquids subject to pressure-dependent wall slip. J. Rheol. 2008, 52:507-525. 10.1122/1.2837104
25. Tang H.S. Kalyon D.M. Time-dependent tube flow of compressible suspensions subject to pressure-dependent wall slip: Ramifications on development of flow instabilities. J. Rheol. 2008, 52:1069-1090. 10.1122/1.2955508
26. Ramos J.I. Asymptotic analysis of channel flows with slip lengths that depend on the pressure. Appl. Math. Comput. 2007, 188:1310-1318. 10.1016/j.amc.2006.11.002
27. Panaseti P. Housiadas K.D. Georgiou G.C. Newtonian Poiseuille flows with pressure dependent wall slip. J. Rheol. 2013, 57:315-332. 10.1122/1.4769823
28. Knudsen M. The Kinetic Theory of Gases 1950, 3rd ed. (Methuen, London).
29. Bird R.B. Armstrong R.C. Hassanger O. Dynamics of Polymeric Liquids. Vol. 1. Fluid Mechanics 1987, and 2nd ed. (Wiley, New York).
30. Munstedt H. Schmidt M. Wassner E. Stick and slip phenomena during extrusion of polyethylene melts as investigated by laser-Doppler velocimetry. J. Rheol. 2000, 44:413-427. 10.1122/1.551092
31. Ramamurthy A.V. Wall slip in viscous fluids and influence of materials of construction. J. Rheol. 1986, 30:337-3357. 10.1122/1.549852
32. Hatzikiriakos S.G. Dealy J.M. Wall slip of molten high density polyethylene. I. Sliding plate rheometer studies. J. Rheol. 1991, 35:497-523. 10.1122/1.550178
33. Hatzikiriakos S.G. Stewart C.W. Dealy J.M. Effect of surface coatings on wall slip of LLDPE. Int. Polym. Process. 1993, 8:30-35
34. Stewart C.W. Wall slip in the extrusion of linear polyolefins. J. Rheol. 1993, 37:499-513. 10.1122/1.550456
35. Poyiadji S. Georgiou G.C. Kaouri K. Housiadas K.D. Perturbation solutions of weakly compressible Newtonian Poiseuille flows with Navier slip at the wall. Rheol. Acta 2012, 51:497-510. 10.1007/s00397-012-0618-x
36. See supplementary material at E-PHFLE6-25-013304 for the perturbation solution up to third order in e{open}.
37. Lauga E. Cossu C. A note on the stability of slip channel flows. Phys. Fluids 2005, 17:088106. 10.1063/1.2032267