Microstructuture-rheology relationship in flexible fiber suspensions – FIBFLEX

This project focuses on the link between microstructure and rheology for flexible fiber suspensions using experimental, numerical, and theoretical studies. The flows of these complex systems are encountered in industrial, biological and natural fields. If the mechanical behavior of rigid fibers suspensions is fairly well established, that of systems involving flexible fibers is known much less. Thus, we wish to understand and characterize the role of fiber flexibility on the rheological behavior of the suspension using several approaches. The first will consist of carrying out rheological experiments with a wide-gap Couette geometry coupled with a visualization system made of laser sheets. Matching the refractive index of fibers and the suspending fluid, these experiments will make it possible to examine the fiber orientation and fiber curvature distributions, as well as the correlation function of the mutual positions of the fibers. On the other hand, a counter-rotating cylindrical Couette geometry device will be used to observe quasi-static but sheared structures providing fiber/cluster dynamics at longer timescales. Based on these two visualization techniques, our ambition is to tackle semi-dilute to concentrated regimes. To better understanding the microstructure-rheology relationships for flexible fiber suspensions with flow-induced anisotropy, a cross-shear experiment will be performed. It consists of measuring both the steady viscosity and the transient response of the viscosity under shear rotation in order to provide information on the tensorial viscosity (longitudinal and orthogonal shear viscosities). For a deeper understanding of the flow-induced anisotropy, we will study extensional flow in the gravity stretched suspension jet. In parallel, a second approach concerns the use of a digital rheometer to study the evolution of flexible fibers in viscometric flows. This consists of a 3D finite element calculation code capable of processing volumetric objects immersed in a fluid via a level-set method. The use of anisotropic remeshing techniques will make it possible to investigate more concentrated systems. This numerical framework has been succeeded in recovering the well-known Jeffery kinematics of a single rigid fiber in a Newtonian fluid under unconfined and homogeneous compression flow. This numerical rheometer will help in understanding the dynamics of a single flexible fiber, of two interacting flexible fibers and of a population of deformable fibers thank to massively parallel finite element computations. Computational time optimization will also be explored based on artificial intelligence. Finally, the third approach will concern mesoscopic scale modeling of the flexible fiber dynamics and macroscopic rheological properties using the kinetic theory. Indeed, a bead-rod system will be used to model to the particle dynamics by introducing a bending potential. To cover the multitude of particles constituting a flexible fiber suspension, an orientation distribution function, describing the probability of finding particles whose connectors have a certain orientation in space at a given instant, will be introduced. Based on this function, a tensorial equation for predicting 3D flexible fiber microstructures in complex flows will be derived, where special attentions will be devoted to a tackle the closure problem. These three approaches are complementary and will allow us to better understand the link between fiber microstructure and rheological properties in order to propose a relevant constitutive equation resulting from these observations, as well as tractable semi-empirical models and simulation routines for industrial applications related to forming of fiber-reinforced composites.