Stability of the flow of a viscoelastic fluid past a deformable surface in the low Reynolds number limit

Physics of Fluids

Volumn 19, Issue 10, 2007, Pages

  Chokshi, Paresh ^a   Kumaran, V ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTITUTIVE MODELS; ELASTIC MODULI; NONLINEAR ANALYSIS; POLYMER SOLUTIONS; REYNOLDS NUMBER; SHEAR DEFORMATION; SURFACE TENSION; VISCOELASTICITY;

COUETTE FLOW; VISCOUS DISSIPATION; WEISSENBERG NUMBER;

NON NEWTONIAN FLOW;

CONSTITUTIVE MODELS; ELASTIC MODULI; NON NEWTONIAN FLOW; NONLINEAR ANALYSIS; POLYMER SOLUTIONS; REYNOLDS NUMBER; SHEAR DEFORMATION; SURFACE TENSION; VISCOELASTICITY;

EID: 35748956752     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2798069     Document Type: Article

References (26)

1. M. O. Kramer, "Boundary-layer stabilisation by distributed damping," J. Aeronaut. Sci. JASCAR0095-9812 24, 458 (1957).
2. P. Krindel and A. Silberberg, "Flow through gel-walled tubes," J. Colloid Interface Sci. JCISA50021-979710.1016/0021-9797(79)90219-4 71, 39 (1979).
3. V. Kumaran, G. H. Fredrickson, and P. Pincus, "Flow induced instability of the interface between a fluid and a gel at low Reynolds number," J. Phys. II JPAHER1155-431210.1051/jp2:1994173 4, 893 (1994).
4. V. Kumaran, "Stability of the viscous flow of a fluid through a flexible tube," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112095002886 294, 259 (1995).
5. V. Kumaran, "Stability of an inviscid flow through a flexible tube," J. Fluid Mech. JFLSA70022-112010.1017/S0022112096007434 320, 1 (1996).
6. V. Kumaran, "Stability of fluid flow through a flexible tube at intermediate Reynolds number," J. Fluid Mech. JFLSA70022-112010.1017/S0022112097008033 357, 123 (1998).
7. V. Kumaran, "Stability of wall modes in a flexible tube," J. Fluid Mech. JFLSA70022-112010.1017/S002211209700832X 362, 1 (1998).
8. V. Gkanis and S. Kumar, "Instability of creeping Couette flow past a neo-Hookean solid," Phys. Fluids PHFLE61070-663110.1063/1.1605952 15, 2864 (2003).
9. L. E. Malvern, Introduction to the Mechanics of a Continuous Medium (Prentice-Hall, Englewood Cliffs, NJ, 1969).
10. V. Gkanis and S. Kumar, "Stability of pressure-driven creeping flows in channels lined with a nonlinear elastic solid," J. Fluid Mech. JFLSA70022-112010.1017/S0022112004002472 524, 357 (2005).
11. V. Kumaran and R. Muralikrishnan, "Spontaneous growth of fluctuations in the viscous flow of a fluid past a soft interface," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.84.3310 84, 3310 (2000).
12. R. Muralikrishnan and V. Kumaran, "Experimental study of the instability of the viscous flow past a flexible surface," Phys. Fluids PHFLE61070-663110.1063/1.1427923 14, 775 (2002).
13. V. A. Gorodtsov and A. I. Leonov, "On a linear instability of a plane parallel Couette flow of viscoelastic fluid," J. Appl. Math. Mech.JAMMAR0021-892810.1016/0021-8928(67)90156-6 31, 310 (1967).
14. Y. Renardy, "Stability of the interface in two-layer Couette flow of the upper convected Maxwell liquids," J. Non-Newtonian Fluid Mech. JNFMDI0377-025710.1016/0377-0257(88)80012-0 28, 99 (1988).
15. H. J. Wilson, M. Renardy, and Y. Renardy, "Structure of the spectrum in zero Reynolds number shear flow of the UCM and Oldroyd-B liquids," J. Non-Newtonian Fluid Mech. JNFMDI0377-025710.1016/ S0377-0257(98)00087-1 80, 251 (1999).
16. V. Shankar and S. Kumar, "Instability of viscoelastic plane Couette flow past a deformable wall," J. Non-Newtonian Fluid Mech. JNFMDI0377-025710.1016/j.jnnfm.2003.10.003 116, 371 (2004).
17. P. Chokshi and V. Kumaran, "Stability of the viscous flow of a polymeric fluid past a flexible surface," Phys. Fluids PHFLE61070-663110.1063/1.2711149 19, 034102 (2007).
18. J. T. Stuart, "On the non-linear mechanics of wave disturbances in stable and unstable parallel flows. Part 1: The basic behavior in plane Poiseuille flow," J. Fluid Mech. JFLSA70022-112010.1017/ S002211206000116X 9, 353 (1960).
19. J. Watson, "On the non-linear mechanics of wave disturbances in stable and unstable parallel flows. Part 2: The development of a solution for plane Poiseuille and for plane Couette flow," J. Fluid Mech.JFLSA70022-112010.1017/S0022112060001171 9, 371 (1960).
20. V. Shankar and V. Kumaran, "Weakly nonlinear stability of viscous flow past a flexible surface," J. Fluid Mech.JFLSA70022-112010.1017/ S0022112001003615 434, 337 (2001).
21. M. D. Eggert and S. Kumar, "Observations of instability, hysteresis, and oscillation in low-Reynolds number flow past polymer gels," J. Colloid Interface Sci.JCISA50021-979710.1016/ j.jcis.2004.05.043 278, 234 (2004).
22. N. Phan-Thien, "Squeezing flow of a viscoelastic solid," J. Non-Newtonian Fluid Mech. JNFMDI0377-025710.1016/S0377-0257(00)00175-0 95, 343 (2000).
23. J. M. Rotenberry and P. G. Saffman, "Effect of compliant boundaries on weakly nonlinear shear waves in channel flow," SIAM J. Appl. Math. SMJMAP0036-139910.1137/0150023 50, 361 (1990).
24. L. Srivatsan and V. Kumaran, "Flow induced instability of the interface between a fluid and a gel," J. Phys. II JPAHER1155-431210.1051/jp2:1997164 7, 947 (1997).
25. V. Shankar, "Linear and weakly nonlinear stability of fluid flow through flexible tubes and channels," Ph.D. thesis, Indian Institute of Science, Bangalore (2000).
26. R. M. Thaokar and V. Kumaran, "Stability of fluid flow past a membrane," J. Fluid Mech. JFLSA70022-112010.1017/S0022112002001751 472, 29 (2002).