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Capillary Instabilities in a Thin Nematic Liquid Crystalline Fiber Embedded in a Viscous Matrix

Published online by Cambridge University Press:  15 March 2011

Ae-Gyeong Cheong  and
Alejandro D. Rey
Ae-Gyeong Cheong
Affiliation:
Department of Chemical Engineering, McGill University, 3610 University Street, Montreal, Quebec, Canada H3A 2B2
Alejandro D. Rey
Affiliation:
Department of Chemical Engineering, McGill University, 3610 University Street, Montreal, Quebec, Canada H3A 2B2
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Abstract

Linear stability analysis of capillary instabilities in a thin nematic liquid crystalline cylindrical fiber embedded in an immiscible viscous matrix is performed by formulating and solving the governing nemato-capillary equations, that include the effect of interfacial viscous shear forces due to flow in the viscous matrix. A representative axial nematic orientation texture is studied. The surface disturbance is expressed in normal modes, which include the azimuthal wavenumber m to take into account non-axisymmetric modes. Capillary instabilities in nematic fibers reflect the anisotropic nature of liquid crystals, including the orientation contribution to the surface elasticity and surface bending stresses. Surface gradients of bending stresses provide additional anisotropic contributions to the capillary pressure that may renormalize the classical displacement and curvature forces that exist in any fluid fiber. The exact nature (stabilizing and destabilizing) and magnitude of the renormalization of the displacement and curvature forces depend on the nematic orientation and the anisotropic contribution to the surface energy, and accordingly capillary instabilities may be axisymmetric or non-axisymmetric, with finite or unbounded wavelengths. Thus, the classical fiber-to-droplet transformation is one of several possible instability pathways while others include surface fibrillation. The contribution of the viscosity ratio to the capillary instabilities of a thin nematic fiber in a viscous matrix is analyzed by two parameters, the fiber and matrix Ohnesorge numbers, which represent the ratio between viscous and surface forces in each phase. The capillary instabilities of a thin nematic fiber in a viscous matrix are suppressed by increasing either the fiber or matrix Ohnesorge number, but estimated droplet sizes after fiber breakup in axisymmetric instabilities decrease with increasing matrix Ohnesorge number.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 709: Symposium CC – Advances in Liquid Crystalline Materials and Technologies , 2001 , CC5.16.1
Copyright
Copyright © Materials Research Society 2002

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References

REFERENCES

[1] Edwards, D. A., Brenner, H., and Wasan, D. T., Interfacial Transport Processes and Rheology (Butterworths, MA, 1989).Google Scholar
[2] Levich, V. G., Physicochemical Hydrodynamics (Prentice-Hall, Englewood Cliffs, NJ, 1962).Google Scholar
[3] Pozrikidis, C., Introduction to Theoretical and Computational Fluid Dynamics (Oxford University Press, New York, 1997).Google Scholar
[4] Gennes, P. G. de and Prost, J., The Physics of Liquid Crystals (Oxford University Press, London, 1993).Google Scholar
[5] Ehrentraut, H. and Hess, S., Phys. Rev. E 51, 2203 (1995).Google Scholar
[6] Larson, R. G., The Structure and Rheology of Complex Fluids (Oxford University Press, New York, 1999).Google Scholar
[7] Sonin, A. A., The Surface Physics of Liquid Crystals (Gordon and Breach Publishers, Amsterdam, 1995).Google Scholar
[8] Yokoyama, H., Handbook of Liquid Crystal Research, edited by Collins, P. J. and Patel, J. S. (Oxford University Press, New York, 1997).Google Scholar
[9] Rey, A. D., J. Phys. II France 7, 1001 (1997).Google Scholar
[10] Rey, A. D., Ind. Engin. Chem. Res. 36, 1114 (1997).Google Scholar
[11] Rey, A. D., Phys. Rev. E 61, 1540 (2000).Google Scholar
[12] Tomotika, S., Proc. R. Soc. A150, 322 (1935).Google Scholar
[13] Kinoshita, C. M., Teng, H., and Masutani, S. M., Int. J. Multiphase Flow 20, 523 (1994).Google Scholar
[14] Kitamura, Y., Mishima, H., and Takahashi, T., Can. J. Chem. Eng. 60, 273 (1982).Google Scholar
[15] Chandrasekhar, S., Liquid Crystals (Cambridge University Press, Cambridge, 1992).Google Scholar
[16] Cheong, A., Rey, A. D., and Mather, P. T., Phys. Rev. E 64, 041701 (2001).Google Scholar