DOI: 10.1140/epje/i2002-10083-3
Temperature effects on capillary instabilities in a thin nematic liquid crystalline fiber embedded in a viscous matrix
A.-G. Cheong and A.D. ReyDepartment of Chemical Engineering, McGill University, 3610 University Street, Montreal, Quebec, Canada H3A 2B2 alejandro.rey@mcgill.ca
(Received 15 April 2002 and Received in final form 3 October 2002 / Published online: 23 December 2002)
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 temperature on the
nematic ordering as well as the effect of the nematic orientation. A
representative axial nematic orientation texture with the planar easy axis
at the fiber surface is studied. The surface disturbance is expressed in
normal modes, which include the azimuthal wave number
m to take into
account non-axisymmetric modes. Capillary instabilities in nematic fibers
reflect the anisotropic nature of liquid crystals, such as the ordering and
orientation contributions to the surface elasticity and surface normal and
bending stresses. Surface gradients of normal and 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 ordering and orientation, i.e. the anisotropic
contribution to the surface energy, and accordingly capillary instabilities
may be axisymmetric or non-axisymmetric. In addition, when the interface
curvature effects are accounted for as contributions of the work of
interfacial bending and torsion to the total energy of the system, the
higher-order bending moment contribution to the surface stress tensor is
critical in stabilizing the fiber instabilities. For the planar easy axis,
the nematic ordering contribution to the surface energy, which renormalizes
the effect of the fiber shape,
plays a crucial role to determine the instability
mechanisms. Moreover, the unstable modes, which are most likely observed,
can be driven by the dependence of surface energy on the surface area.
Low-ordering fibers display the classical axisymmetric mode, since the surface
energy decreases by decreasing the surface area. Decreasing temperature gives
rise to the encounter with a local maximum or to monotonic increase of the
characteristic length of the axisymmetric mode. Meanwhile, in the presence
of high surface ordering, non-axisymmetric finite wavelength instabilities
emerge, with higher modes growing faster since the surface energy decreases
by increasing the surface area. As temperature decreases, the pitches
of the chiral microstructures become smaller. However, this non-axisymmetric
instability mechanism can be regulated by taking account of the surface
bending moment, which contains higher order variations in the interface
curvatures. More and more non-axisymmetric modes emerge as temperature
decreases, but, at constant temperature, only a finite number of
non-axisymmetric modes are unstable and a single fastest growing mode
emerges with lower and higher unstable modes growing slower. For nematic
fibers, the classical fiber-to-droplet transformation is one of several
possible instability pathways, while others include chiral microstructures.
The capillary instabilities' growth rate of a thin nematic fiber in a
viscous matrix is suppressed by increasing either the fiber or matrix
viscosity, but the estimated droplet sizes after fiber breakup in axisymmetric
instabilities decrease with increasing the matrix viscosity.
61.30.Hn - Surface phenomena: alignment, anchoring, anchoring transitions, surface-induced layering, surface-induced ordering, wetting, prewetting transitions, and wetting transitions.
68.03.Kn - Dynamics (capillary waves).
68.03.Cd - Surface tension and related phenomena.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2002
