A revisit of Jeffery‘s equation - modelling fiber suspensions with Smoothed Particle Hydrodynamics

Simulating fiber suspensions is a challenging task and of special interest for discontinuous reinforced plastics, because their properties depend on fiber orientation and fiber length after processing. Since the first description of a single suspended rigid ellipsoidal body by Jeffery almost hundred years ago, two research communities established in this field: The first one models macroscopic flow of fiber suspensions based on phenomenological extensions to Jeffery’s equation and the second one considers the deformation of flexible fibers for a given flow. However, most of them consider one-way coupling, i.e. the fluid only deforms fibers and not vice versa, due to difficulties with mesh based approaches for deforming domains.
An alternative description of flexible fiber suspensions can be achieved by employing Smoothed Particle Hydrodynamics (SPH), which is a Lagrangian method highly suited for fluid-structure interactions. Therefore, the first approach to model fibers with SPH-particle bead chains by Yang et al. was extended with surface traction and contact formulations in this work. The implemented method was validated for quasi-rigid fibers against Jeffery’s equation, experimental observations and other numerical results. ... mehrThen, multi fiber suspensions were modelled and potential applications for the improvement of phenomenological models are demonstrated, which may help building a bridge from single fiber models to the commercially attractive macroscopic models.