Theory of surface excess Miesowicz viscosities of planar nematic liquid crystal-isotropic fluid interfaces |
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Authors: | AD Rey |
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Institution: | (1) Department of Chemical Engineering, McGill University, 3610 University Street, Montreal, Quebec, Canada H3A 2B2, CA |
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Abstract: | An expression for the surface excess stress tensor for planar compressible interfaces between rod-like nematic liquid crystals
and isotropic viscous fluids is derived using the classical surface excess theory formalism, adapted to capture the intrinsic
anisotropy of the nematic orientational ordering. A required step in the theory is to find the actual stress tensor in the
three-dimensional interfacial region, which is obtained by a decomposition of the kinematic fields (rate of deformation tensor
and director Jaumann derivative) into tangential, normal, and mixed components with respect to the interface. The viscosity
coefficients appearing in the surface excess stress tensor are expressed in terms of interfacial and bulk viscosities for
planar, constant orientation, flows. The expressions are used to define the three fundamental surface excess Miesowicz shear
viscosities, in analogy with the three bulk Miesowicz shear viscosities. The ordering in the magnitudes of the surface excess
Miesowicz shear viscosities is shown to depend on the magnitude of the surface scalar nematic order parameter relative to
that of the adjoining bulk nematic phase. When the surface scalar order parameter is greater than in the bulk, the classical
ordering in terms of magnitudes of the three bulk Miesowicz shear viscosities is recovered. On the other hand, when the surface
scalar order parameter is smaller than in the bulk, the classical ordering in terms of magnitudes of the three viscosities
does not hold, and inequality transitions are predicted as the surface scalar order parameter increases towards the bulk value.
Received 5 July 1999 and Received in final form 16 November 1999 |
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