In swimming microorganisms and the cell cytoskeleton, inextensible fibers resist bending and twisting, and interact with the surrounding fluid to cause or resist large-scale fluid motion. In this paper, we develop a novel numerical method for the simulation of cylindrical fibers by extending our previous work on inextensible bending fibers [Maxian et al., Phys. Rev. Fluids 6 (1), 014102] to fibers with twist elasticity. In our "Euler" model, twist is a scalar function that measures the deviation of the fiber cross section relative to a twist-free frame, the fiber exerts only torque parallel to the centerline on the fluid, and the perpendicular components of the rotational fluid velocity are discarded in favor of the translational velocity. In the first part of this paper, we justify this model by comparing it to another commonly-used "Kirchhoff" formulation where the fiber exerts both perpendicular and parallel torque on the fluid, and the perpendicular angular fluid velocity is required to be consistent with the translational fluid velocity. We then develop a spectral numerical method for the hydrodynamics of the Euler model. We define hydrodynamic mobility operators using integrals of the Rotne-Prager-Yamakawa tensor, and evaluate these integrals through a novel slender-body quadrature, which requires on the order of 10 points along the fiber to obtain several digits of accuracy. We demonstrate that this choice of mobility removes the unphysical negative eigenvalues in the translation-translation mobility associated with asymptotic slender body theories, and ensures strong convergence of the fiber velocity and weak convergence of the fiber constraint forces. We pair the spatial discretization with a semi-implicit temporal integrator to confirm the negligible contribution of twist elasticity to the relaxation dynamics of a bent fiber and study the instability of a twirling fiber.
翻译:在游泳微生物和细胞细胞细胞变色素中, 伸展性纤维会抵制弯曲和扭动, 并与周围的流体互动, 导致或抵制大规模流体运动。 在本文中, 我们开发了一种新型数字方法, 用于模拟圆心纤维。 通过扩展我们以前关于不可伸展性弯曲纤维的工作[Maxian 等人, Phys. Rev. Fliids 6, 014.102] 至具有扭曲弹性的纤维。 在我们的“ 变动” 模型中, 扭曲性纤维是一个测量纤维跨部分相对于扭曲性机能框架的偏差, 以测量纤维变异性变异性, 纤维只能与流体的中线平行, 而旋转流体纤维的直角性纤维变异异性成分被丢弃。 在本文的第一部分, 我们用另一种常用的“ 变异性变异性变异性变异性 ”, 我们用这种变异性变异性变异性变异性变异性变异性, 我们用这种变异性变异性变异性变异性变异性变异性变性变性变异性变性变体的流体, 的流变性变性变异性变异性变性变性变性变性变性变性变性变性变性变性变性变体, 我们性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变体, 的变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性变性