Towards the use of
probability distribution function to describe the flow of fiber suspensions
Julien Férec and Gilles Ausias
Université Bretagne Sud, France
Abstract
This talk will focus on describing the flow of
fiber suspensions since this kind of flow is largely encountered in
manufacturing processes, for instance. The performances of these composites are
directly related to the microstructure of the fibers that controls their
mechanical and physical properties, such as stiffness, strength, electrical and
thermal conductivities. After presenting some experimental rheological
observations for commercial and model systems, we then provide some basic
theoretical background on the modeling of fiber suspension in Newtonian and
non-Newtonian matrices. Usually, closure approximations are required to well
pose the problem in terms of moment-tensor equations. The use of tensors is
efficient and convenient, but they have three main drawbacks. The first one is
the loss of physics, the second one is the need to use a closure approximation
and the third is the inability to simply develop models to describe
non-Newtonian suspending fluid behaviors. Therefore, our recent developments,
in considering non-Newtonian suspending fluids for instance, motivate us to
directly use the probability distribution function in order to overcome these
issues. Hence, we show some flows of fiber suspensions in 2D planar geometries
(a parallel plate channel and a planar 4:1 contraction) and in 2D axisymmetric
geometries (a circular pipe, a center-gated disk and the die swell). This talk
aims to show the possibility of using the probability distribution function in
the future to develop more physical modeling, such as the flow of
non-homogeneous systems or the flow of semi-flexible fiber suspensions.
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