Contact-Free Simulations of Rigid Particle Suspensions Using Boundary Integral Equations

In many composite materials, rigid fibers are distributed throughout the material to tune the mechanical, thermal, and electric properties of the composite. The orientation and distribution of the fibers play a critical role in the properties of the composite. Many composites are processed as a liquid molten suspension of fibers and then solidified, holding the fibers in place. Once the fiber orientations are known, theoretical models exist that can predict properties of the composite.Modeling the suspended fibers in the liquid state is important because their ultimate configuration depends strongly on the flow history during the molten processing. Continuum models, such as the Folgar-Tucker model, predict the evolution of the fibers’ orientation in a fluid. These models are limited in several ways. First, they require empirical constants and closure relations that must be determined a priori, either by experiments or detailed computer simulations. Second, they assume that all the fibers are slender bodies of uniform length. Lastly, these methods break down for concentrated suspensions. For these reasons, it is desirable in certain situations to model the movement of individual fibers explicitly. This dissertation builds upon recent advances in boundary integral equations to develop a robust, accurate, and stable method that simulates fibers of arbitrary shape in a planar flow. In any method that explicitly models the individual fiber motion, care must be taken to ensure numerical errors do not cause the fibers to overlap. To maintain fiber separation, a repulsion force and torque are added when required. This repulsion force is free of tuning parameters and is determined by solving a sequence of linear complementarity problems to ensure that the configuration does not have any overlap between fibers. Numerical experiments demonstrate the stability of the method for concentrated suspensions.