Theory of surface excess Miesowicz viscosities of planar nematic liquid crystal-isotropic fluid interfaces

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.