Modes of dispersion of viscoelastic fluids in flow

Abstract

It is shown that when a viscoelastic mixture of molten polymers is extruded, “alloy” composites are produced as a result of the formation of two distinct modes of dispersion: stratification or droplet-fiber formation. Important parameters responsible for these effects are: particle size, interfacial tension, and differences in the viscoelastic properties of the two phases. The formation of polymer spheres, ribbons, or fibers in a matrix can be predicted on the basis of a new theory which has been confirmed experimentally and provides a route to composites of controlled structure and properties. Explicit expressions are derived for the interfacial tension between two phases α and β in flow: γαβ=γ 0αβ+ 1 6 α α[( σ 2) α−( σ 2) β] and γαβ=γ 0αβ+ 1 6 α β[( σ 2) α−( σ 2) β] where γ ij is the interfacial tension of a droplet of fluid i in matrix j; γ ij 0 the interfacial tension in absence of flow; a i , the droplet radius; and ( σ 2) i the second normal stress function of fluid i which depends on molecular weight, molecular weight distribution, and shear stress. Since γ ij ≥ 0 for droplet formation to be possible, these equations predict that when ( σ 2) α > ( σ 2) β , phase α will always form droplets/fibers in phase β. Droplet formation of phase β in phase α will be possible only when α β ≤ 6γ αβ 0/[( σ 2) α − ( σ 2) β] , a quantity of the order of 1-0.1 μ for polymer melts. If the phase dimension of phase β, therefore, is larger than 1 μ, as may be accomplished by incomplete mixing, phase β does not form droplets but stratifies. A further consequence is that in the submicron region, phase a will form single droplets; droplet formation of phase β leads to composite droplets, i.e., droplets of β containing smaller droplets of α. Differences in viscosity, shear rate, extrusion temperature, and residence time in the capillary influence only the homogeneity of the dispersion and not the mode of dispersion.