ANISOTROPIC MICROSTRUCTURE-INDUCED REDUCTION OF THE RAYLEIGH INSTABILITY FOR LIQUID-CRYSTALLINE POLYMERS

We analyze a macroscopic 3D model for flows of liquid crystalline poly mers (LCPs), deduced from Doi-type [3,4] kinetic equations. The Doi mo del accounts for rigid-rod microstructure, which introduces elastic re laxation and polymer-induced viscosity in addition to a Newtonian solv ent viscosity, thus capturing all effects contained in standard isotro pic viscoelastic models for Maxwell and Oldroyd B fluids. The rod-like microstructure further introduces anisotropic effects in the form of drag on the rods, together with a short-range, Maier-Saupe intermolecu lar potential, whose critical points vary with LCP concentration and y ield stable isotropic (at low density) and nematic (at high density) e quilibrium phases. From this single model, we compare various physical mechanisms for reducing the capillary instability of inviscid cylindr ical jets: solvent viscosity as studied by Rayleigh and Chandrasekhar; isotropic viscoelasticity, both with and without Newtonian solvent vi scosity; anisotropic polymer friction; and finally, the nematic, highl y aligned prolate phase at high LCP density. Realistic parameter value s for LCPs correspond to a regime in which the LCP capillary number (p olymer bulk free energy relative to surface tension) is above an ident ified critical value; in such regimes, the unstable growth rates of th e isotropic and nematic phases are lowered arbitrarily close to zero i f the molecular drag is sufficiently anisotropic even in the absence o f solvent viscosity. In low capillary number regimes, where surface te nsion dominates LCP bulk free energy, the LCP growth rates are sandwic hed below the inviscid Rayleigh curve and above an explicit positive l ower bound. (C) 1998 Elsevier Science B.V.