Integral-based spectral method for inextensible slender fibers in Stokes flow

Every animal cell is filled with a cytoskeleton, dynamic gel made of inextensible fibers, such as microtubules, actin and intermediate filaments, all suspended in viscous fluid. Numerical simulation this challenging because the fiber aspect ratios can be large $10^4$. We describe new method for rapidly computing dynamics slender filaments periodically-sheared Stokes flow. The are governed by nonlocal body theory which we partially reformulate terms Rotne-Prager-Yamakawa hydrodynamic tensor. To enforce inextensibility, parameterize space motions strictly confine to manifold configurations. do this, introduce set Lagrange multipliers tensile force densities on impose constraint no virtual work an $L^2$ weak sense. augment approach spectral discretization local operators linear number unknowns gives improved spatial accuracy over approaches based solving line tension equation. For dynamics, develop second-order semi-implicit temporal integrator requires at most few evaluations hydrodynamics block diagonal solves per time step. After demonstrating robustness our through numerical examples, apply formulation permanently cross-linked mesh background oscillatory shear observe characteristic frequency network transitions from quasi-static, primarily elastic behavior dynamic, behavior. find that increases modulus much 25%, even semi-dilute suspensions.