The motion of long slender bodies in a viscous fluid Part 1. General theory

Cox, R. G.

doi:10.1017/s002211207000215x

Cited by 677 publications

(590 citation statements)

References 12 publications

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“…One option is to assume that there are no hydrodynamic interactions among fibers and use slender body theory, when the aspect ratio of the fibers is high enough. Cox 42 solved this problem and found the drag coefficients parallel ͑C 11 ͒ and perpendicular ͑C 22 and C 33 ͒ to the fiber axis to be C 11 = 2 l ln͑2e͒ − 0.806 85 , ͑11͒…”

Section: Volume-averaging Methodsmentioning

confidence: 99%

“…The formulation of this model requires a correlation to provide the drag coefficients for flows parallel and perpendicular to a fiber. Such correlations exist for the case of a long isolated fiber 42 and for spatially periodic arrays of fibers, 14,15 but not for the general case of a random fiber network. Therefore, these equations provide only an approximation.…”

Section: F Umentioning

confidence: 97%

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Permeability calculations in three-dimensional isotropic and oriented fiber networks

et al. 2008

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Hydraulic permeabilities of fiber networks are of interest for many applications and have been studied extensively. There is little work, however, on permeability calculations in three-dimensional random networks. Computational power is now sufficient to calculate permeabilities directly by constructing artificial fiber networks and simulating flow through them. Even with today's high-performance computers, however, such an approach would be infeasible for large simulations. It is therefore necessary to develop a correlation based on fiber volume fraction, radius, and orientation, preferably by incorporating previous studies on isotropic or structured networks. In this work, the direct calculations were performed, using the finite element method, on networks with varying degrees of orientation, and combinations of results for flows parallel and perpendicular to a single fiber or an array thereof, using a volume-averaging theory, were compared to the detailed analysis. The detailed model agreed well with existing analytical solutions for square arrays of fibers up to fiber volume fractions of 46% for parallel flow and 33% for transverse flow. Permeability calculations were then performed for isotropic and oriented fiber networks within the fiber volume fraction range of 0.3%-15%. When drag coefficients for spatially periodic arrays were used, the results of the volume-averaging method agreed well with the direct finite element calculations. On the contrary, the use of drag coefficients for isolated fibers overpredicted the permeability for the volume fraction range that was employed. We concluded that a weighted combination of drag coefficients for spatially periodic arrays of fibers could be used as a good approximation for fiber networks, which further implies that the effect of the fiber volume fraction and orientation on the permeability of fiber networks are more important than the effect of local network structure.

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Section: Volume-averaging Methodsmentioning

confidence: 99%

Section: F Umentioning

confidence: 97%

Permeability calculations in three-dimensional isotropic and oriented fiber networks

et al. 2008

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“…Machin [75] and Brokaw [22,21,23] investigated the propagation of spermatozoa bending waves in sinusoidal and nonsinusoidal form for free swimming organisms. Batchelor [2] and Cox [28] developed a slender body theory (SBT) for Stokes flow. Lighthill [70,71] developed an alternative slender body theory, to be described later, and suggested more advanced modifications of the resistive force coefficients of Gray and Hancock.…”

Section: Introductionmentioning

confidence: 99%

A 3D Motile Rod-Shaped Monotrichous Bacterial Model

Hsu

Dillon

2009

Bull. Math. Biol.

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We introduce a 3D model for a motile rod-shaped bacterial cell with a single polar flagellum which is based on the configuration of a monotrichous type of bacteria such as Pseudomonas aeruginosa. The structure of the model bacterial cell consists of a cylindrical body together with the flagellar forces produced by the rotation of a helical flagellum. The rod-shaped cell body is composed of a set of immersed boundary points and elastic links. The helical flagellum is assumed to be rigid and modeled as a set of discrete points along the helical flagellum and flagellar hook. A set of flagellar forces are applied along this helical curve as the flagellum rotates. An additional set of torque balance forces are applied on the cell body to induce counter-rotation of the body and provide torque balance. The three dimensional Navier-Stokes equations for incompressible fluid are used to described the fluid dynamics of the coupled fluid-microorganism system using Peskin's immersed boundary method. A study of numerical convergence is presented along with simulations of a single cell and the interaction of two model cells.

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“…We now consider the slender limit ϵ ≪ 1 using inner-outer asymptotic expansions. 16 The "outer" region, with r fixed as ϵ → 0, describes transport on the longitudinal scale, where the particle appears as a zero-thickness line segment of length 2. The "inner" region, where r = O(ϵ) as ϵ → 0, describes transport on the cross-sectional scale, where the particle appears as an infinite cylinder of a quasi-uniform radius.…”

mentioning

confidence: 99%

Osmotic self-propulsion of slender particles

Schnitzer

Yariv

2015

Physics of Fluids

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We consider self-diffusiophoresis of axisymmetric particles using the continuum description of Golestanian et al. [“Designing phoretic micro-and nano-swimmers,” New J. Phys. 9, 126 (2007)], where the chemical reaction at the particle boundary is modelled by a prescribed distribution of solute absorption and the interaction of solute molecules with that boundary is represented by diffusio-osmotic slip. With a view towards modelling of needle-like particle shapes, commonly employed in experiments, the self-propulsion problem is analyzed using slender-body theory. For a particle of length 2L, whose boundary is specified by the axial distribution κ(z) of cross-sectional radius, we obtain the approximation −μ2DL∫−LLj(z)dκ(z)dz dz for the particle velocity, wherein j(z) is the solute-flux distribution, μ the diffusio-osmotic slip coefficient, and D the solute diffusivity. This approximation can accommodate discontinuous flux distributions, which are commonly used for describing bimetallic particles; it agrees strikingly well with the numerical calculations of Popescu et al. [“Phoretic motion of spheroidal particles due to self-generated solute gradients,” Eur. Phys. J. E: Soft Matter Biol. Phys. 31, 351–367 (2010)], performed for spheroidal particles.

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The motion of long slender bodies in a viscous fluid Part 1. General theory

Cited by 677 publications

References 12 publications

Permeability calculations in three-dimensional isotropic and oriented fiber networks

Permeability calculations in three-dimensional isotropic and oriented fiber networks

A 3D Motile Rod-Shaped Monotrichous Bacterial Model

Osmotic self-propulsion of slender particles

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