Stability of Thixotropic Fluids in Pipe Flow

Document Type : Article

Authors

Center of Excellence in Design and Optimization of Energy Systems (CEDOES), School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

Abstract

Linear stability of a thixotropic fluid obeying the Moore model is investigated in pipe flow using a temporal stability analysis in which infinitesimally-small perturbations, represented by normal modes, are superimposed on the base flow and their evolution in time is monitored in order to detect the onset of instability. An eigenvalue problem is obtained which is solved numerically using the pseudo-spectral Chebyshev-based collocation method. The neutral instability curve is plotted as a function of the thixotropy number of the Moore model. Based on the results obtained in this work, it is concluded that the thixotropic behavior of the Moore fluid has a destabilizing effect on pipe flow

Keywords


References
1. Mewis, J. Thixotropy-a general review", Int. J. of Non-Newt. Fluid Mech., 6, pp. 1-20 (1979).
2. Barnes, H.A. Thixotropy-a review", Int. J. of Non- Newt. Fluid Mech., 70(1-2), pp. 1-33 (1997).
3. Mewis, J. and Wagner, N.J. Thixotropy", Adv. Colloid and Interface Sci, 147/148, pp. 214-227 (2009).
4. Chandrasekhar, S., Hydrodynamic and Hydromagnetic
Stability, Oxford University Press, London (1961).
5. Drazin, P.G. and Reid, W.H., Hydrodynamic Stability,
2nd edition. Camb. Univ. Press, Cambridge (2004).
6. Pearson, J.R.A. and Tardy, P.M.J. Models for
ow
of non-Newtonian and complex
uids through porous
media", Int. J. of Non-Newt. Fluid Mech., 102, pp.
447-473 (2002).
7. Ebrahimi, B., Taghavi, S.M., and Sadeghy, K. Twophase
viscous ngering of immiscible thixotropic
uids:
A numerical study", Int. J. of Non-Newt. Fluid Mech.,
218, pp. 40-52 (2015).
8. Pourjafar, M., Chaparian, E., and Sadeghy, K.
Taylor-Couette instability of thixotropic
uids", Meccanica,
50, pp. 1451-1465 (2015).
9. Wygnanski, I. and Champagne, F. On transition in
a pipe. Part 1. The origin of pu s and slugs and the

ow in a turbulent slug", J. of Fluid Mechanics, 59,
pp. 281-335 (1973).
10. Leite, R.J. An experimental investigation of the
stability of Poiseuille
ow", J. of Fluid Mechanics, 5,
pp. 81-96 (1959).
11. Eliahou, S., Tumin, A., and Wygnanski, I. Laminarturbulent
transition in Poiseuille pipe
ow subjected
to periodic perturbation emanating from the wall", J.
of Fluid Mechanics, 361, pp. 333-349 (1998).
12. Darbyshire, A. and Mullin, T. Transition to turbulence
in constant-mass-
ux pipe
ow", J. of Fluid
Mechanics, 289, pp. 83-114 (1995).
13. Garg , V. and Rouleau, W. Linear spatial stability of
pipe Poiseuille
ow", J. of Fluid Mechanics, 54, pp.
113-127 (1972).
14. Stuart, J. Instability and transition in pipes and channels",
Transition and Turbulence, pp. 77-94 (1981).
15. Zikanov, O.Y. On the instability of pipe poiseuille

ow", Physics of Fluids (1994-present), 8, pp. 2923-
2932 (1996).
16. Guzel, B., Frigaard, I., and Martinez, D. Predicting
laminar-turbulent transition in Poiseuille pipe
ow for
non-Newtonian
uids", Chemical Engineering Science,
64, pp. 254-264 (2009).
17. Nouar, C. and Frigaard, I. Nonlinear stability of
Poiseuille
ow of a Bingham
uid: theoretical results
and comparison with phenomenological criteria", Int.
J. of Non-Newt. Fluid Mech., 100, pp. 127-149 (2001).
18. Frigaard, I., Howison, S., and Sobey, I. On the
stability of Poiseuille
ow of a Bingham
uid", J. of
Fluid Mechanics, 263, pp. 133-150 (1994).
19. Frigaard, I. On the stability of shear
ows of suspensions",
7th International Congress on Rheology,
August 3-8, Monterey, California (2008).
20. Macosko, C.W., Rheology: Principles, Measurements
and Applications, 1st edition, Wiley VCH (1994).
21. Moore, F. The rheology of ceramic slips and bodies",
Trans. Br. Ceram. Soc., 58, p. 470 (1959).
22. Cheng, D.C.H. and Evans, F. Phenomenological characterization
of the rheological behavior of inelastic
reversible thixotropic and antithixotropic
uids", Br.
J. Appl. Phys., 16(11), pp. 1599-1617 (1965).
23. Billingham, J. and Ferguson, J.W.J. Laminar, unidirectional
flow of a thixotropic
uid in a circular pipe",
Int. J. of Non-Newt. Fluid Mech., 47, pp. 21-55 (1993).
24. Nahavandian, M.H. Instability of thixotropic
frluids in pipe flow", MSc Thesis, University of Tehran (2015).
25. Whittington, R. and Ashton, E. Instability in pipe flow", Nature, 162, pp. 997-998 (1948).