Eur. Phys. J. E 2, 169-179
Theory of surface excess Miesowicz viscosities of planar nematic liquid crystal-isotropic fluid interfaces
A.D. Rey
Department of Chemical Engineering, McGill University,
3610 University Street, Montreal, Quebec, Canada H3A 2B2
inaf@musicb.mcgill.ca
Received 5 July 1999 and Received in final form 16 November 1999
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.
PACS
61.30.Cz Theory and models of liquid crystal structure
-
68.10.Et Interface elasticity, viscosity, and viscoelasticity
- 68.10.Cr Surface energy (surface tension,
interface tension, angle of contact, etc.)
Copyright EDP Sciences, Società Italiana di Fisica, Springer-Verlag
