Abstract
We report the results of experiments on electrically driven convection that occurs in a thin, freely suspended film of smectic A liquid crystal when an electric field is applied in the plane of the film. Convection in a vortex pattern is found above a well-defined critical voltage. The film behaves as a two-dimensional isotropic liquid: neither its thickness nor the director field are modified by the flow. We present measurements of the critical voltage at the onset of convection in two experimental configurations—one which allows the injection of charges into the film from the electrodes, and one which does not. When injection is present, the critical voltage for the onset of flow increases monotonically with increasing frequency of applied field. With no injection, there is no instability at DC and the critical voltage diverges there. The nature of the flow pattern observed at onset changes with frequency. Below a certain frequency the film flows in vortices that extend over the width of the film; above this frequency the flow is confined to two lines of smaller vortices localized along the electrodes. We present a simple discussion of the mechanisms which drive the convection.
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References
G. Ahlers, inLectures in the Sciences of Complexity, D. Stein, ed. (Addison-Wesley, Reading, Massachusetts, 1989).
F. Busse, inHydrodynamic Instabilities and the Onset of Turbulence, H. L. Swinney and J. P. Gollub, eds. (Springer, Berlin, 1984).
R. C. DiPrima and H. L. Swinney, inHydrodynamic Instabilities and the Onset of Turbulence, H. L. Swinney and J. P. Gollub, eds. (Springer, Berlin, 1984).
I. Rehberg, B. Winkler, M. de la Torre Juarez, S. Rasenat, and W. Schöpf, inFestkörperprobleme/Advances in Solid State Physics, U. Rössler, ed. (Vieweg, Braunschweig, 1989).
E. Dubois-Violette, P. G. de Gennes, and O. Parodi,J. Phys. (Paris)32:305 (1971).
P. G. de Gennes,The Physics of Liquid Crystals (Clarendon Press, Oxford, 1979).
L. M. Blinov,Electro-Optical and Magneto-Optical Properties of Liquid Crystals (Wiley, New York, 1983).
W. Helfrich,J. Chem. Phys. 51:4092 (1969).
E. Bodenschatz, W. Zimmermann, and L. Kramer,J. Phys. (Paris)49:1875 (1988).
S. W. Morris, J. R. de Bruyn, and A. D. May, inNonlinear Evolution of Spatio-Temporal Structures in Dissipative Continuous Systems, F. Busse and L. Kramer, eds. (Plenum Press, New York, 1990).
S. W. Morris, J. R. de Bruyn, and A. D. May,Phys. Rev. Lett. 65:2378 (1990).
A. J. Leadbetter, J. C. Frost, J. P. Gaughan, G. W. Gray, and A. Mosly,J. Phys. (Paris)40:375 (1979).
L. Léger and A. Martinet,J. Phys. (Paris)37:C3–89 (1976).
R. G. Horn and M. Kléman,Ann. Phys. 3:229 (1978).
G. Friedel,Ann. Phys. (Paris)18:273 (1922).
R. Pindak and D. Moncton,Phys. Today 35(5):57 (1982).
D. A. Dunmur, M. R. Manterfield, W. H. Miller, and J. K. Dunleavy,Mol. Cryst. Liq. Cryst. 46:127 (1978).
S. Faetti, L. Fronzoni, and P. A. Rolla,J. Phys. (Paris)40:C3–497 (1979).
S. Faetti, L. Fronzoni, and P. A. Rolla,J. Chem. Phys. 79:1427 (1983).
S. Faetti, L. Fronzoni, and P. A. Rolla,J. Chem. Phys. 79:5054 (1983).
N. Felici,Rev. Gen. Elect. 78:717 (1969);J. Phys. (Paris)37:C1–117 (1976).
J. M. Schnieder and P. K. Watson,Phys. Fluids 18:1948 (1970).
P. Atten and R. Moreau,J. Mécanique 11:471 (1972).
J. C. Lacroix, P. Atten, and E. J. Hopfinger,J. Fluid Mech. 69:539 (1975).
J. C. Lacroix and P. Atten,C. R. Acad. Sci. 278A:689 (1974);J. Electrostatics 5:453 (1978).
P. Atten and J. C. Lacroix,J. Mécanique 18:469 (1979);J. Electrostatics 5:439 (1978).
R. J. Turnbull,J. Phys. D 6:1746 (1973).
R. Bruinsma and S. Alexander,J. Chem. Phys. 92:3074 (1990).
P. Atten, B. Malraison, and S. Ali Kani,J. Electrostatics 12:477 (1982).
M. I. Barnik, L. M. Blinov, S. A. Pikin, and A. N. Trufanov,Sov. Phys. JETP 45:396 (1977).
R. Cocco, F. Gaspard, and R. Herino,J. Chim. Phys. 76:383 (1979).
R. Foster,Organic Charge Transfer Complexes (Academic Press, New York, 1969).
M. Born and E. Wolf,Principles of Optics (Pergamon Press, New York, 1980).
C. Rosenblatt and N. Amer,Appl. Phys. Lett. 36:432 (1980).
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Morris, S.W., de Bruyn, J.R. & May, A.D. Patterns at the onset of electroconvection in freely suspended smectic films. J Stat Phys 64, 1025–1043 (1991). https://doi.org/10.1007/BF01048812
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DOI: https://doi.org/10.1007/BF01048812