Efficient Implementation of Elastohydrodynamics via Integral Operators

Abstract

The dynamics of geometrically non-linear flexible filaments play an important role in a host of biological processes, from flagella-driven cell transport to the polymeric structure of complex fluids. Such problems have historically been computationally expensive due to numerical stiffness associated with the inextensibility constraint, as well as the often non-trivial boundary conditions on the governing high-order PDEs. Formulating the problem for the evolving shape of a filament via an integral equation in the tangent angle has recently been found to greatly alleviate this numerical stiffness. The contribution of the present manuscript is to enable the simulation of non-local interactions of multiple filaments in a computationally efficient manner using the method of regularized stokeslets within this framework. The proposed method is benchmarked against a non-local bead and link model, and recent code utilizing a local drag velocity law. Systems of multiple filaments (1) in a background fluid flow, (2) under a constant body force, and (3) undergoing active self-motility are modeled efficiently. Buckling instabilities are analyzed by examining the evolving filament curvature, as well as by coarse-graining the body frame tangent angles using a Chebyshev approximation for various choices of the relevant non-dimensional parameters. From these experiments, insight is gained into how filament-filament interactions can promote buckling, and further reveal the complex fluid dynamics resulting from arrays of these interacting fibers. By examining active moment-driven filaments, we investigate the speed of worm- and sperm-like swimmers for different governing parameters. The MATLAB(R) implementation is made available as an open-source library, enabling flexible extension for alternate discretizations and different surrounding flows.

37 pages, 17 figures

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Cited by in corpus (11)

• An integral-based spectral method for inextensible slender fibers in Stokes flow
• Filament mechanics in a half-space via regularised Stokeslet segments
• Efficient simulation of filament elastohydrodynamics in three dimensions
• Doing more with less: the flagellar end piece enhances the propulsive effectiveness of human spermatozoa
• Slender Phoretic Theory of chemically active filaments
• The 3D coarse-graining formulation of interacting elastohydrodynamic filaments and multi-body microhydrodynamics
• Well-posedness and applications of classical elastohydrodynamics for a swimming filament
• Passively parallel regularized stokeslets
• Regularised non-uniform segments and efficient no-slip elastohydrodynamics
• Scaling law for a buckled elastic filament in a shear flow
• Instability and self-propulsion of flexible autophoretic filaments