Perturbation solutions of weakly compressible Newtonian Poiseuille flows with Navier slip at the wall

Rheologica Acta

Volumn 51, Issue 6, 2012, Pages 497-510

  Poyiadji, Stella ^a   Georgiou, Georgios C ^a   Kaouri, Katerina ^b   Housiadas, Kostas D ^c  

^a UNIVERSITY OF CYPRUS   (Cyprus)

^b Intercollege Limassol ^*  (Cyprus)

^c UNIVERSITY OF THE AEGEAN   (Greece)

Author keywords

Compressibility; Darcy friction factor; Newtonian flow; Perturbation solution; Poiseuille flow; Slip

Indexed keywords

EID: 84861640006     PISSN: 00354511     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00397-012-0618-x     Document Type: Article

References (30)

1. Arkilic EB, Schmidt MA (1997) Gaseous slip flow in long microchannels. J MEMS 6: 167-178.
2. Beskok A, Karniadakis GE (1999) Simulation of heat and momentum transfer in complex micro-geometries. J Thermophys Heat Transfer 8: 355-377.
3. Denn MM (2001) Extrusion instabilities and wall slip. Ann Rev Fluid Mech 33: 265-287.
4. Dubbeldam JLA, Molenaar J (2003) Dynamics of the spurt instability in polymer extrusion. J Non-Newton Fluid Mech 112: 217-235.
5. Felderhof BU, Ooms G (2011) Flow of a viscous compressible fluid produced in a circular tube by an impulsive point source. J Fluid Mech 668: 100-112.
6. Georgiou G (2005) Stick-slip instability. Chapter 7. In: Hatzikiriakos SG, Migler K (eds) Polymer processing instabilities: control and understanding. Mercel Dekker, Inc., pp 161-206.
7. Georgiou GC, Crochet MJ (1994) Compressible viscous flow in slits with slip at the wall. J Rheol 38: 639-654.
8. Guaily A, Cheluget E, Lee K, Epstein M (2011) A new hyperbolic model and an experimental study for the flow of polymer melts in multi-pass rheometer. Comp Fluids 44: 258-266.
9. Hatzikiriakos SG (2012) Wall slip of molten polymers. Progr Polym Sci 37: 624-643.
10. Hatzikiriakos SG, Dealy JM (1992) Role of slip and fracture in the oscillating flow of a HDPE in a capillary. J Rheol 36: 845-884.
11. Hatzikiriakos SG, Dealy JM (1994) Start-up pressure transients in a capillary rheometer. Polym Eng Sci 34: 493-499.
12. Hatzikiriakos SG, Migler K (2005) Polymer processing instabilities: control and understanding. Mercel Dekker, New York.
13. Housiadas K, Georgiou GC (2011) Perturbation solution of Poiseuille flow of a weakly compressible Oldroyd-B fluid. J Non-Newton Fluid Mech 166: 73-92.
14. Housiadas KD, Georgiou GC, Mamoutos IG (2012) Laminar axisymmetric flow of a weakly compressible viscoelastic fluid. Rheol Acta doi: 10. 1007/s00397-011-0610-x.
15. Kohl MJ, Abdel-Khalik SI, Jeter SM, Sadowski DL (2005) An experimental investigation of microchannel flow with internal pressure measurements. Int J Heat Mass Transfer 48: 1518-1533.
16. Mitsoulis E, Hatzikiriakos SG (2009) Steady flow simulations of compressible PTFE paste extrusion under severe wall slip. J Non-Newton Fluid Mech 157: 26-33.
17. Piau JM, El Kissi N (1994) Measurement and modelling of friction in polymer melts during macroscopic slip at the wall. J Non-Newton Fluid Mech 54: 121-142.
18. Poyiadji S (2012) Flows of fluids with pressure-dependent material properties. PhD Thesis, University of Cyprus.
19. Qin FH, Sun DJ, Yin XY (2007) Perturbation analysis on gas flow in a straight microchannel. Phys Fluids 19: 027103.
20. Stone HA, Stroock AD, Ajdari A (2004) Engineering flows in small devices: microfluidics toward a lab-on-a-chip. Annu Rev Fluid Mech 36: 381-411.
21. Taliadorou E, Georgiou E, Alexandrou AN (2007) A two-dimensional numerical study of the stick-slip extrusion instability. J Non-Newton Fluid Mech 146: 30-44.
22. Taliadorou E, Georgiou GC, Mitsoulis E (2008) Numerical simulation of the extrusion of strongly compressible Newtonian liquids. Rheol Acta 47: 49-62.
23. Taliadorou E, Neophytou M, Georgiou GC (2009) Perturbation solutions of Poiseuille flows of weakly compressible Newtonian liquids. J Non-Newton Fluid Mech 158: 162-169.
24. Tang HS, Kalyon DM (2008a) Unsteady circular tube flow of compressible polymeric liquids subject to pressure-dependent wall slip. J Rheol 52: 507-525.
25. Tang HS, Kalyon DM (2008b) Time-dependent tube flow of compressible suspensions subject to pressure-dependent wall slip: ramifications on development of flow instabilities. J Rheol 52: 1069-1090.
26. Venerus DC (2006) Laminar capillary flow of compressible viscous fluids. J Fluid Mech 555: 59-80.
27. Venerus DC, Bugajsky DJ 2010 Laminar flow in a channel. Phys Fluids 22: 046101.
28. Vinay G, Wachs A, Frigaard I (2006) Numerical simulation of weakly compressible Bingham flows: the restart of pipeline flows of waxy crude oils. J Non-Newton Fluid Mech 136: 93-105.
29. Wachs A, Vinay G, Frigaard I (2009) A 1. 5D numerical model for the start up of weakly compressible flow of a viscoplastic and thixotropic fluid in pipelines. J Non-Newton Fluid Mech 159: 81-94.
30. Zhang TT, Jia L, Wang ZC, Li CW (2009) Slip flow characteristics of compressible gaseous in microchannels. Energy Conv Manage 50: 1676-1682.