The motion of long slender bodies in a viscous fluid. Part 2. Shear flow

Cox, R. G.

doi:10.1017/s0022112071000259

Cited by 175 publications

(136 citation statements)

References 9 publications

(1 reference statement)

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“…Using a slender body rsif.royalsocietypublishing.org J. R. Soc. Interface 11: 20140314 approximation, Cox [27] determined an effective aspect ratiô a r ¼ 1:24a r / ffiffiffiffiffiffiffiffiffiffi ffi ln a r p to be used in Jeffery's formula for a rigid slender cylinder of aspect ratio a r . This effective aspect ratio (â r ¼ 10.95) would result in an approximate rotational period of t* ¼ 69.38.…”

Section: Diatoms In Shearmentioning

confidence: 99%

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Hydrodynamics of diatom chains and semiflexible fibres

Nguyen

Fauci

2014

J. R. Soc. Interface.

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Diatoms are non-motile, unicellular phytoplankton that have the ability to form colonies in the form of chains. Depending upon the species of diatoms and the linking structures that hold the cells together, these chains can be quite stiff or very flexible. Recently, the bending rigidities of some species of diatom chains have been quantified. In an effort to understand the role of flexibility in nutrient uptake and aggregate formation, we begin by developing a three-dimensional model of the coupled elastic -hydrodynamic system of a diatom chain moving in an incompressible fluid. We find that simple beam theory does a good job of describing diatom chain deformation in a parabolic flow when its ends are tethered, but does not tell the whole story of chain deformations when they are subjected to compressive stresses in shear. While motivated by the fluid dynamics of diatom chains, our computational model of semiflexible fibres illustrates features that apply widely to other systems. The use of an adaptive immersed boundary framework allows us to capture complicated buckling and recovery dynamics of long, semiflexible fibres in shear.

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Section: Diatoms In Shearmentioning

confidence: 99%

“…Firstly, the aspect ratio of this diatom chain does not fall well within the range valid for slender body approximation. Recently, Zhang et al [28] discussed the applicability of the slender body approximation [27] to fibres with smaller aspect ratios. Secondly, this fibre is not perfectly rigid.…”

Section: Diatoms In Shearmentioning

confidence: 99%

Hydrodynamics of diatom chains and semiflexible fibres

Nguyen

Fauci

2014

J. R. Soc. Interface.

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“…Comparison with existing theoretical results for a slender body in simple shear flow of a single unbounded fluid suggests strongly that this non-periodicity in the particle motion is a consequence of the slender-body approximation. In particular, Cox (1971) showed that the force and torque on an axisymmetric slender body that is at rest and oriented parallel to a simple shear flow(()= n1t) is 0((1/K) 2 e), which is very small compared with the O (e 2 ) terms retained in (28a-c), but is definitely non-zero. According to Cox's analysis, a slender body will rotate very slowly through the aligned, or nearly aligned, state, but will experience a periodic rotation for any large (but finite) K. Similar behaviour in the present problem of particle motion near an interface would imply that any real particle (with finite K) would both rotate and move in and out continuously.…”

Section: Simple Shear Flowmentioning

confidence: 99%

Particle motion in Stokes flow near a plane fluid–fluid interface. Part 2. Linear shear and axisymmetric straining flows

Yang

Leal

1984

J. Fluid Mech.

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275We consider the motion of a sphere or a slender body in the presence of a plane fluid-fluid interface with an arbitrary viscosity ratio, when the fluids undergo a linear undisturbed flow. First, the hydrodynamic relationships for the force and torque on the particle at rest in the undisturbed flow field are determined, using the method of reflections, from the spatial distribution of Stokeslets, rotlets and higher-order singularities in Stokes flow. These fundamental relationships are then applied, in combination with the corresponding solutions obtained in earlier publications for the translation and rotation through a quiescent fluid, to determine the motion of a neutrally buoyant particle freely suspended in the flow. The theory yields general trajectory equations for an arbitrary viscosity ratio which are in good agreement with both exact-solution results and experimental data for sphere motions near a rigid plane wall. Among the most interesting results for motion of slender bodies is the generalization of the Jeffrey orbit equations for linear simple shear flow.

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“…It has been further developed and applied in the recent studies of slender-body theory for low-Reynoldsnumber flows by Hancock (1953), Broersma (1960), Tuck (1964Tuck ( , 1970, Taylor (1969), Batchelor (1970a, b), Tillett (1970), Cox (1970Cox ( , 1971, Blake & Chwang (1974) and others. Through these investigations the relative simplicity and effectiveness of the method have gradually become more recognized.…”

Section: Introductionmentioning

confidence: 99%

Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows

1975

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The present study furthcr explores the fundamental singular solutions for Stokes flow that can be useful £or constructing solutions over a wide range of free-stream profiles and body shapes. The primary singularity is the Stokeslet, which is associatedwith a singular point force embedded in a Stokes flow. From its derivatives other fundamental singularities can be obtained, including rotlets, strcsslets, potential doublets and higher-order poles derived from them. For treating interior Stokes-flow problems new fundamental solutions are introduced; they include the Stokeson and its derivatives, called the roton and stresson.These fundamental singularities are employed here to construct exact solutions to a number of cxterior and interior Stokes-flow problems for several specific body shapes translating and rotating in a viscous fluid which may itself be providing a primary ilow. The different primary flows considered here include the uniform strcam, shear flows, parabolic profiles and extensional flows (hyperbolic profiles), while the body shapcs cover prolate spheroids, spheres and circular cylinders. The salient features of these exact solutions (all obtained in closed form) regarding the types of singularities required for tlhe construction of a solution in each specific case, their distribution densities and the rangc of validity of the solution, which may depend on the characteristic Reynolds numbers and governing geometrical parameters, arc discussed.

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The motion of long slender bodies in a viscous fluid. Part 2. Shear flow

Cited by 175 publications

References 9 publications

Hydrodynamics of diatom chains and semiflexible fibres

Hydrodynamics of diatom chains and semiflexible fibres

Particle motion in Stokes flow near a plane fluid–fluid interface. Part 2. Linear shear and axisymmetric straining flows

Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows

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