Capillary Instabilities in a Thin Nematic Liquid Crystalline Fiber Embedded in a Viscous Matrix
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Capillary Instabilities in a Thin Nematic Liquid Crystalline Fiber Embedded in a Viscous Matrix Ae-Gyeong Cheong* and Alejandro D. Rey Department of Chemical Engineering, McGill University, 3610 University Street, Montreal, Quebec, Canada H3A 2B2 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. INTRODUCTION A question of fundamental importance in capillary instabilities of thin fibers is the geometric character of the modes that arise when driven by surface tension forces. In isotropic fluid fibers, the fiber-to-droplet transformation is well understood and known as the fiber Rayleigh instability [1, 2, 3]. In this case, displacement capillary forces drive the fiber break-up, while curvature dependent forces resist the instability. Since in these materials surface tension is isotropic, only axisymmetric mode emerges, eventually generating spherical droplets. On the other hand, an essential characteristic of nematic liquid crystals is mechanical anisotropy [4]. The anisotropies in the viscoelastic bulk properties of nematic liquid crystal are well understood theoretically [5, 6] and experimentally [4], and the anisotropies in the surface elastic propert
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