Suspensions of fibers in viscoelastic fluids: Rheology

Abstract

Suspensions of fibers in polymeric fluids are regarded as two-component fluids. One component (the fibers) is a rigid body fluid; the second component (polymeric fluid) is a fluid composed of dumbbells. States of the suspension are chosen to be characterized by overall momentum field, configuration space distribution functions of fibers and macromolecules (or alternatively fields of conformation tensors of fibers and macromolecules), and the field of angular momentum (in the body-fixed coordinate system) of the fibers. The time evolution equations (that include expressions for the stress tensor) for these fields are formulated by following Hamiltonian modeling (GENERIC). In the process of solving the governing equations a simplified set of governing equations is derived. This simplified set of equations extends Jeffery’s equations describing suspensions in simple fluids to equations describing suspensions in polymeric fluids. The time evolution and the corresponding expression for the stress tensor are discussed for both distribution functions and conformation tensors.