Electrically driven convection in a thin annular film undergoing circular Couette flow

Physics of Fluids

Volumn 11, Issue 12, 1999, Pages 3613-3628

  Daya, Zahir A ^a   Deyirmenjian, V B ^a   Morris, Stephen W ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001721584     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.870226     Document Type: Article

References (46)

1. Z. A. Daya, V. B. Deyirmenjian, S. W. Morris, and J. R. de Bruyn, "Annular electroconvection with shear," Phys. Rev. Lett. 80, 964 (1998).
2. Z. A. Daya, S. W. Morris, and J. R. de Bruyn, "Electroconvection in a suspended fluid film: A linear stability analysis," Phys. Rev. E 55, 2682 (1997).
3. V. B. Deyirmenjian, Z. A. Daya, and S. W. Morris, "Weakly nonlinear analysis of electroconvection in a suspended fluid film," Phys. Rev. E 56, 1706 (1997).
4. M. C. Cross and P. C. Hohenberg, "Pattern formation outside of equilibrium," Rev. Mod. Phys. 65, 851 (1993).
5. D. Fulze, "Developments in controlled experiments on larger scale geophysical problems," Adv. Geophys. 7, 1 (1961), P. Hignett, A. A. White, R. D. Carter, W. D. N. Jackson, and R. M. Small, "A comparison of laboratory measurements and numerical simulations of baroclinic wave flows in a rotating cylindrical annulus," Q. J. R. Meteorol. Soc. 111, 131 (1985).
6. D. Fulze, "Developments in controlled experiments on larger scale geophysical problems," Adv. Geophys. 7, 1 (1961), P. Hignett, A. A. White, R. D. Carter, W. D. N. Jackson, and R. M. Small, "A comparison of laboratory measurements and numerical simulations of baroclinic wave flows in a rotating cylindrical annulus," Q. J. R. Meteorol. Soc. 111, 131 (1985).
7. A. Alonso, M. Net, and E. Knobloch, "On the transition to columnar convection," Phys. Fluids 7, 935 (1995).
8. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Clarendon, Oxford, 1961).
9. H. F. Goldstein, E. Knobloch, I. Mercader, and M. Net, "Convection in a rotating cylinder. Part 1. Linear theory for moderate Prandtl numbers," J. Fluid Mech. 248, 583 (1993); "Convection in a rotating cylinder. Part 1. Linear theory for low Prandtl numbers," ibid. 262, 293 (1994).
10. H. F. Goldstein, E. Knobloch, I. Mercader, and M. Net, "Convection in a rotating cylinder. Part 1. Linear theory for moderate Prandtl numbers," J. Fluid Mech. 248, 583 (1993); "Convection in a rotating cylinder. Part 1. Linear theory for low Prandtl numbers," ibid. 262, 293 (1994).
11. F. Zhong, R. E. Ecke, and V. Steinberg, "Rotating Rayleigh-Bénard convection: Asymmetric modes and vortex states," J. Fluid Mech. 249, 135 (1993), "Asymmetric modes and the transition to vortex structures in rotating Rayleigh-Bénard convection," Phys. Rev. Lett. 67, 2473 (1991); R. E. Ecke, F. Zhong, and E. Knobloch, "Hopf bifurcation with broken reflection symmetry in rotating Rayleigh-Bénard convection," Europhys. Lett. 19, 177 (1992).
12. F. Zhong, R. E. Ecke, and V. Steinberg, "Rotating Rayleigh-Bénard convection: Asymmetric modes and vortex states," J. Fluid Mech. 249, 135 (1993), "Asymmetric modes and the transition to vortex structures in rotating Rayleigh-Bénard convection," Phys. Rev. Lett. 67, 2473 (1991); R. E. Ecke, F. Zhong, and E. Knobloch, "Hopf bifurcation with broken reflection symmetry in rotating Rayleigh-Bénard convection," Europhys. Lett. 19, 177 (1992).
13. F. Zhong, R. E. Ecke, and V. Steinberg, "Rotating Rayleigh-Bénard convection: Asymmetric modes and vortex states," J. Fluid Mech. 249, 135 (1993), "Asymmetric modes and the transition to vortex structures in rotating Rayleigh-Bénard convection," Phys. Rev. Lett. 67, 2473 (1991); R. E. Ecke, F. Zhong, and E. Knobloch, "Hopf bifurcation with broken reflection symmetry in rotating Rayleigh-Bénard convection," Europhys. Lett. 19, 177 (1992).
14. E. Knobloch, "Bifurcations in rotating systems," in Lectures on Solar and Planetary Dynamos, edited by M. R. E. Proctor and A. D. Gilbert (Cambridge University Press, New York, 1994), p. 331.
15. S. P. Trainoff, "Rayleigh-Bénard Convection in the Presence of a Weak Lateral Flow," Ph.D. thesis, University of California, Santa Barbara, 1997 (unpublished); H. W. Muller, M. Tveitereid, and S. Trainoff, "Rayleigh-Bénard problem with imposed weak through-flow: Two coupled Ginzburg-Landau equations," Phys. Rev. E 48, 263 (1993).
16. S. P. Trainoff, "Rayleigh-Bénard Convection in the Presence of a Weak Lateral Flow," Ph.D. thesis, University of California, Santa Barbara, 1997 (unpublished); H. W. Muller, M. Tveitereid, and S. Trainoff, "Rayleigh-Bénard problem with imposed weak through-flow: Two coupled Ginzburg-Landau equations," Phys. Rev. E 48, 263 (1993).
17. K. Fujimura and R. E. Kelly, "Stability of unstably stratified shear flow between parallel plates," Fluid Dyn. Res. 2, 281 (1988).
18. S. W. Morris, J. R. de Bruyn, and A. D. May, "Electroconvection and pattern formation in a suspended smectic film," Phys. Rev. Lett. 65, 2378 (1990).
19. S. W. Morris, J. R. de Bruyn, and A. D. May, "Patterns at the onset of electroconvection in freely suspended smectic films," J. Stat. Phys. 64, 1025 (1991).
20. S. W. Morris, J. R. de Bruyn, and A. D. May, "Velocity and current measurements in electroconvecting smectic films," Phys. Rev. A 44, 8146 (1991).
21. S. S. Mao, J. R. de Bruyn, and S. W. Morris, "Electroconvection patterns in smectic films at and above onset," Physica A 239, 189 (1997).
22. S. S. Mao, J. R. de Bruyn, Z. A. Daya, and S. W. Morris, "Boundary-induced wavelength selection in a one-dimensional pattern-forming system," Phys. Rev. E 54, R1048 (1996).
23. K. L. Babcock, G. Ahlers, and D. S. Cannell, "Noise amplification in open Taylor-Couette flow," Phys. Rev. E 50, 3670 (1994).
24. N. Agrait and A. Castellanos, "Linear instability analysis for the super-position of weak unipolar injection and cylindrical couette flow," PhysicoChem. Hydrodynamics 10, 181 (1988).
25. P. G. Drazin and W. H. Reid, Hydrodynamic Stability (Cambridge University Press, Cambridge, 1989).
26. X-I. Wu, B. Martin, H. Kellay, and W. I. Goldburg, "Hydrodynamic convection in a two-dimensional Couette cell," Phys. Rev. Lett. 75, 236 (1995).
27. A. T. Pérez and A. Castellanos, "Role of charge diffusion in finite-amplitude electroconvection," Phys. Rev. A 40, 5844 (1989); J. R. Melcher, Continuum Electromechanics (MIT, Cambridge, MA, 1981); N. J. Felici, "La conduction électrique dans les liquides diélectrique. Phénomènes d'instabilité et de transport: Mécanismes chimiques et hydrodynamiques," J. Phys. (Paris) Colloq. 37, C1 (1976).
28. A. T. Pérez and A. Castellanos, "Role of charge diffusion in finite-amplitude electroconvection," Phys. Rev. A 40, 5844 (1989); J. R. Melcher, Continuum Electromechanics (MIT, Cambridge, MA, 1981); N. J. Felici, "La conduction électrique dans les liquides diélectrique. Phénomènes d'instabilité et de transport: Mécanismes chimiques et hydrodynamiques," J. Phys. (Paris) Colloq. 37, C1 (1976).
29. A. T. Pérez and A. Castellanos, "Role of charge diffusion in finite-amplitude electroconvection," Phys. Rev. A 40, 5844 (1989); J. R. Melcher, Continuum Electromechanics (MIT, Cambridge, MA, 1981); N. J. Felici, "La conduction électrique dans les liquides diélectrique. Phénomènes d'instabilité et de transport: Mécanismes chimiques et hydrodynamiques," J. Phys. (Paris) Colloq. 37, C1 (1976).
30. Pattern Formation in Liquid Crystals, edited by A. Buka and L. Kramer (Springer, Berlin, 1995).
31. S. Faetti, L. Fronzoni, and P. Rolla, "Static and dynamic behavior of the vortex-electrohydrodynamic instability in freely suspended layers of nematic liquid crystal," J. Chem. Phys. 79, 5054 (1983).
32. A. Becker, S. Ried, R. Stannarius, and H. Stegemeyer, "Electroconvection in smectic C liquid crystal films visualized by optical anisotropy," Europhys. Lett. 39, 257 (1997).
33. S. Ried, H. Pleiner, W. Zimmermann, and H. R. Brand, "Electroconvective instabilities in SmC* liquid crystal films," Phys. Rev. E 53, 6101 (1996).
34. In Ref. 26, the charge density is eliminated using the Maxwell equation, so that the surface charges that we consider here are not included. The film is treated as if it were unbounded in the z direction.
35. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 2, Special Functions (Gordon and Breach, New York, 1992), p. 207.
36. I. S. Gradshetyn and I. M. Ryzhik, Integrals, Series and Products (Academic, New York, 1980), p. 666.
37. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge University Press, Cambridge, 1992).
38. c =91.84.
39. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Clarendon, Oxford, 1993).
40. To control the nature of the ionic species in the liquid crystal, octylcyanobiphenyl (8CB), was doped with tetracyanoquinodimethane (TCNQ).
41. D. Avsec and M. Luntz, "Tourbillons électroconvectifs," C. R. Acad. Sci. (Paris) 203, 1140 (1936).
42. W. V. R. Malkus and G. Veronis, "Surface electroconvection," Phys. Fluids 4, 13 (1961).
43. D. Dash and X.L. Wu, "A shear-induced instability in freely suspended smectic-A liquid crystal films," Phys. Rev. Lett. 79, 1483 (1997).
44. The drift in conductivity was typically 2% over the course of a run, and is due to electrochemical reactions between the liquid crystal and the electrodes. See S. Barret, F. Gaspard, R. Herino, and F. Mondon, "Dynamic scattering in nematic liquid crystals under dc conditions. 1. Basic electrochemical analysis," J. Appl. Phys. 47, 2375 (1976).
45. D. A. Dunmur, M. R. Manterfield, W. H. Miller, and J. K. Dunleavy, "The dielectric and optical properties of the homologous series of cyanoalkyl-biphenyl liquid crystals," Mol. Cryst. Liq. Cryst. 46, 127 (1978).
46. F. H. Busse, "Thermal instabilities in rapidly rotating systems," J. Fluid Mech. 44, 441 (1970).