Shear viscosity of a molten short fibers composite

Abstract

At a molten state, short fibers composites are generally modeled as non Brownian anisotropic viscous fluids [3, 4, 8, 7]. A micromechanical approach enables in simple cases to evaluate the rheological parameters as a function of the fiber’s volumic rate and shape factor. However even in these cases where the fibers are in a semi-dilute or in a dilute state, a simple test as a steady shear viscosimeter test is in fact subject nowadays to different interpretations. In particular there is a sort of paradox if we assume for example that the system is described with a slender bodies approximation [8, 4], if one neglects the Brownian motion, a solution for which the fibers are locally aligned along the velocity field is theoretically possible. It can be shown in this case, that the shear viscosity would be less than that of a spherical particles suspension with the same volumic rate of fibers. This result is well known and is usually analyzed in noting that a slight desorientation of the fibers can give rise to a great increase in the shear viscosity. For this reason some authors [6] propose to model the rotation of the fibers with a Brownian diffusion constant which vanishes at zero shear rates and which intends to give a phenomenological modeling of the fibers-fibers interaction. This modeling has shown its efficiency but requires to measure this diffusion constant C _I with respect to the volumic rate and to the fibers aspect ratio. In this presentation we show that this misalignment can be also modeled in considering a large but finite shape factor of the particle. In this case, since early papers of Mason or Hinch, it is known that if their is no interactions between the particles, their is generally no steady solution in shear flows. However in assuming that the time averaging along a trajectory is equal to the local ensemble averaging, we calculate analytically the misalignment and thus the shear viscosity. If we compare this expression to the one computed with the interaction coefficient C _I , we find a way to evaluate C _I .