The role of microstructure in taming the Rayleigh capillary instability ofcylindrical jets

It is observed both in nature and in technological processes that filaments with anisotropic molecular-scale structure are less susceptible to breakup due to capillary instability than homogeneous, isotropic fluids in similar filament flows. Here we provide rigorous evidence that the strong coupling of microstructure to the hydrodynamics of cylindrical axisymmetric free su rface filaments, indeed fundamentally alters the linearized stability of cy lindrical jets. We extend Rayleigh's classical inviscid analysis of cylindr ical jets to the three-dimensional (3D), macroscopic flow-orientation equat ions derived from the Doi kinetic theory for liquid crystalline polymers (L CPs). These equations assume rigid rod-like molecules and incorporate LCP e ffects of molecular relaxation, anisotropic drag, polymer kinetic energy, L CP density, and an intermolecular potential which couple orientation dynami cs to standard free surface fluid equations. Depending on the LCP density, there are between one and three flow-independent orientation equilibria whi ch persist in a constant-velocity, cylindrical free surface flow: an isotro pic phase exists at all concentrations, whereas two anisotropic phases exis t at sufficiently high LCP density. These equilibrium LCP cylindrical jets have two independent sources of instability, hydrodynamic and orientational , each identified within the coupled flow/orientation free surface equation s. For this paper we restrict to equilibria free of orientational instabili ties. All streamwise perturbations of wavelength greater than the jet circu mference are unstable to capillary instability; only the strength of the in stability and most dominant wavelength are affected by LCP microstructure. The degree to which microstructure reduces the capillary instability depend s on two critical scaling parameters: an LCP capillary number C alpha(1cp) (a ratio of LCP-induced surface stress to interfacial capillary stress); an d the anisotropic drag/friction parameter sigma. The most striking result i s: for sufficiently large C alpha(1cp) and highly anisotropic drag (sigma s imilar to 0) the capillary growthrate can be uniformly lowered, arbitrarily close to zero. For sufficiently small C alpha(1cp), all capillary-dominate d growthrates are reduced, but are bounded below in terms of an explicit, s harp estimate and bounded above by the Rayleigh formula. The upshot is: inv iscid LCP jets are predicted to yield bigger drops which form on longer tim escales than an inviscid isotropic fluid with the same surface tension. Cop yright (C) 1998 Elsevier Science B.V.