Hydrodynamics of a twisting, bending, inextensible fiber in Stokes flow

Maxian, Ondrej; Sprinkle, Brennan; Peskin, Charles S.; Donev, Aleksandar

doi:10.1103/physrevfluids.7.074101

Cited by 13 publications

(24 citation statements)

References 59 publications

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“…Numerical evidence suggests that, unlike traditional SBT, our asymptotic formula keeps the eigenvalues of the mobility above zero (Maxian et al. 2022, § 4.4.1).…”

Section: Slender Body Theory From Regularized Singularitiesmentioning

confidence: 99%

“…solving the Stokes equations (Maxian et al. 2022, § 2.1) and . The translational and parallel rotational velocity of the fibre centreline are then given by convolving the pointwise velocity and half-vorticity once more with the regularized delta function, This yields a mobility that is guaranteed to be symmetric positive definite (Kallemov et al.…”

Section: Slender Body Theory From Regularized Singularitiesmentioning

confidence: 99%

“…Here we only consider the parallel component of rotational velocity, since, for unshearable filaments, the other components can be derived from the translational velocity (Maxian et al. 2022, § 2).…”

Section: Slender Body Theory From Regularized Singularitiesmentioning

confidence: 99%

“…In a companion paper (Maxian et al. 2022), we develop efficient quadrature schemes to evaluate the integrals to numerical, rather than asymptotic, precision. The RPY kernels change their form when the distance between the spheres is less than , i.e.…”

Section: Slender Body Theory From Regularized Singularitiesmentioning

confidence: 99%

“…(2014) and Maxian et al. (2022), has applications in the motion of bacterial flagella (Chen & Berg 2000; Yuan et al. 2010) and supercoiling during DNA transcription (Liu & Wang 1987).…”

Section: Introductionmentioning

confidence: 99%

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Slender body theories for rotating filaments

Maxian

Donev

2022

J. Fluid Mech.

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Slender fibres are ubiquitous in biology, physics and engineering, with prominent examples including bacterial flagella and cytoskeletal fibres. In this setting, slender body theories (SBTs), which give the resistance on the fibre asymptotically in its slenderness $\epsilon$ , are useful tools for both analysis and computations. However, a difficulty arises when accounting for twist and cross-sectional rotation: because the angular velocity of a filament can vary depending on the order of magnitude of the applied torque, asymptotic theories must give accurate results for rotational dynamics over a range of angular velocities. In this paper, we first survey the challenges in applying existing SBTs, which are based on either singularity or full boundary integral representations, to rotating filaments, showing in particular that they fail to consistently treat rotation–translation coupling in curved filaments. We then provide an alternative approach which approximates the three-dimensional dynamics via a one-dimensional line integral of Rotne–Prager–Yamakawa regularized singularities. While unable to accurately resolve the flow field near the filament, this approach gives a grand mobility with symmetric rotation–translation and translation–rotation coupling, making it applicable to a broad range of angular velocities. To restore fidelity to the three-dimensional filament geometry, we use our regularized singularity model to inform a simple empirical equation which relates the mean force and torque along the filament centreline to the translational and rotational velocity of the cross-section. The single unknown coefficient in the model is estimated numerically from three-dimensional boundary integral calculations on a rotating, curved filament.

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“…Numerical evidence suggests that, unlike traditional SBT, our asymptotic formula keeps the eigenvalues of the mobility above zero (Maxian et al. 2022, § 4.4.1).…”

Section: Slender Body Theory From Regularized Singularitiesmentioning

confidence: 99%

Section: Slender Body Theory From Regularized Singularitiesmentioning

confidence: 99%

Section: Slender Body Theory From Regularized Singularitiesmentioning

confidence: 99%

Section: Slender Body Theory From Regularized Singularitiesmentioning

confidence: 99%

“…(2014) and Maxian et al. (2022), has applications in the motion of bacterial flagella (Chen & Berg 2000; Yuan et al. 2010) and supercoiling during DNA transcription (Liu & Wang 1987).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations