(or please see here for the abstract in pdf with figures and references. )
Every animal cell is filled with a cytoskeleton, a dynamic gel made of inextensible filaments / bio-polymers, such as microtubules, actin filaments, and intermediate filaments, all suspended in a viscous fluid. Similar suspensions of elastic filaments or polymers are widely used in materials processing. Numerical simulation of such gels is challenging because the filament aspect ratios are very large.
We have recently developed new methods for rapidly computing the dynamics of non-Brownian and Brownian inextensible slender filaments in periodically-sheared Stokes flow. We apply our formulation to a permanently and dynamically cross-linked actin mesh in a background oscillatory shear flow. We find that nonlocal hydrodynamics can change the visco-elastic moduli by as much as 40% at certain frequencies, especially in partially bundled networks.
I will focus on accounting for bending thermal fluctuations of the filaments by first establishing a mathematical formulation and numerical methods for simulating the dynamics of stiff but not rigid Brownian fibers in Stokes flow. I will emphasize open questions for the community such as whether there is a continuum limit of the Brownian contribution to the stress tensor from the filaments.
This work is supported in part by the U.S. National Science Foundation under grant DMS-2052515.
References:
[1] O. Maxian et al, Integral-based spectral method for inextensible slender fibers in Stokes flow,. Phys. Rev. Fluids, 6:014102, 2021
[2] O. Maxian et al,. Hydrodynamics of a twisting, bending, inextensible fiber in Stokes flow, Phys. Rev. Fluids, 7:074101, 2022
[3] O. Maxian et al, Interplay between Brownian motion and cross-linking controls bundling dynamics in actin networks, Biophysical J., 121:1230–1245, 2022.
[4] O. Maxian et al., Bending fluctuations in semiflexible, inextensible, slender filaments in Stokes flow: towards a spectral discretization, ArXiv:2301.11123, submitted to J. Chem. Phys., 2023.