An integral model based on slender body theory, with applications to curved rigid fibers

Abstract

We propose a novel integral model describing the motion of curved slender fibers in viscous flow, and develop a numerical method for simulating dynamics of rigid fibers. The model is derived from nonlocal slender body theory (SBT), which approximates flow near the fiber using singular solutions of the Stokes equations integrated along the fiber centerline. In contrast to other models based on (singular) SBT, our model yields a smooth integral kernel which incorporates the (possibly varying) fiber radius naturally. The integral operator is provably negative definite in a non-physical idealized geometry, as expected from PDE theory. This is numerically verified in physically relevant geometries. We propose a convergent numerical method for solving the integral equation and discuss its convergence and stability. The accuracy of the model and method is verified against known models for ellipsoids. Finally, a fast algorithm for computing dynamics of rigid fibers with complex geometries is developed.

References in corpus (11)

• The hydrodynamics of swimming microorganisms
• Comparative hydrodynamics of bacterial polymorphism
• A boundary element regularised Stokeslet method applied to cilia and flagella-driven flow
• Regularized Stokeslet segments
• An integral-based spectral method for inextensible slender fibers in Stokes flow
• Filament mechanics in a half-space via regularised Stokeslet segments
• Theoretical justification and error analysis for slender body theory with free ends
• An error bound for the slender body approximation of a thin, rigid fiber sedimenting in Stokes flow
• Accurate evaluation of integrals in slender-body formulations for fibers in viscous flow
• A slender body model for thin rigid fibers: validation and comparisons
• Accuracy of slender body theory in approximating force exerted by thin fiber on viscous fluid