Elastohydrodynamics of Finite-Thickness Filaments: Boundary Conditions and Modeling Approaches

The dynamics of flexible filaments in viscous flows are central to many problems in fluid mechanics, from biological propulsion to industrial processes. For highly slender filaments, slender body theory provides a powerful modeling framework. However, as the aspect ratio decreases, its assumptions break down, and discrete approaches become more appropriate. In such cases, bead-based models offer an alternative that captures both elasticity and hydrodynamic interactions with greater fidelity. In this work, we study the elastohydrodynamics of filaments modeled as chains of beads connected by springs, allowing for both extensibility and bending stiffness. Bending is represented through a harmonic potential based on dihedral angles between adjacent bead triplets, and non-bonded interactions are modeled using Lennard-Jones potentials. To incorporate long-range viscous interactions, we use the Rotne-Prager-Yamakawa (RPY) approximation. A key focus of our study is the implementation and interpretation of boundary conditions in such discrete filament models, particularly in the finite-length regime where edge effects play a significant role.