A general formulation of Bead Models applied to flexible fibers and active filaments at low Reynolds number

Delmotte, Blaise; Climent, Éric; Plouraboué, Franck

doi:10.1016/j.jcp.2015.01.026

Cited by 54 publications

(102 citation statements)

References 86 publications

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“…A recent review of these methods is found in [52]. In recent work [26] have elaborated upon basic bead models by introducing a new Lagrange multiplier method to impose constraints, and consider several flow problems -Jeffery orbits, buckling in shear, actuated swimming filaments -by using an approximate accounting of Stokesian hydrodynamics.…”

Section: G Bead-and-rod Modelsmentioning

confidence: 99%

“…They also addressed the role of rotational diffusion on the period of Jeffery orbits. Numerous investigations have observed the "snaking" dynamics numerically ( [26,97,131]) (see Fig. 4c).…”

Section: Fiber Morphology In Shear Flowsmentioning

confidence: 99%

“…The relevant control parameter is B = F g L 2 /E, with F g the gravitational force ( Fig. 6d) ( [22,26,84,119]). For small B the steady velocity is close to the horizontal settling velocity of a rigid fiber, while for large B, the fiber experiences large deformations and the velocity is close to the vertical settling velocity of a rigid fiber ( Fig.…”

Section: A Sedimenting Fibersmentioning

confidence: 99%

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Dynamics of Flexible Fibers in Viscous Flows and Fluids

Roure

Lindner

Nazockdast

et al. 2019

Annu. Rev. Fluid Mech.

165

156

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The dynamics and deformations of immersed flexible fibers are at the heart of important industrial and biological processes, induce peculiar mechanical and transport properties in the fluids that contain them, and are the basis for novel methods of flow control. Here we focus on the low Reynolds number regime where advances in studying these fiber-fluid systems have been especially rapid. On the experimental side this is due to new methods of fiber synthesis, microfluidic flow control, and of microscope based tracking measurement techniques. Likewise, there have been continuous improvements in the specialized mathematical modeling and numerical methods needed to capture the interactions of slender flexible fibers with flows, boundaries, and each other. arXiv:1905.09058v1 [physics.flu-dyn]

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Section: G Bead-and-rod Modelsmentioning

confidence: 99%

Section: Fiber Morphology In Shear Flowsmentioning

confidence: 99%

Section: A Sedimenting Fibersmentioning

confidence: 99%

See 1 more Smart Citation

Dynamics of Flexible Fibers in Viscous Flows and Fluids

Roure

Lindner

Nazockdast

et al. 2019

Annu. Rev. Fluid Mech.

165

156

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“…The second term on the right-hand side of the relation ( 20) describes the coupling of the twist with the writhe of the rod, which characterizes the formation of the loops. In the cases of the ferromagnetic and superparamagnetic rods when the magnetic energy terms are 3 …”

Section: Introductionmentioning

confidence: 99%

Flexible Magnetic Filaments and their Applications

Cēbers

Ērglis

2016

Adv Funct Materials

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This review of the properties of flexible magnetic filaments covers the problems of their buckling under the action of a magnetic field. The dependence of the buckling on the magnetic properties of the filaments is considered. It is shown that these filaments may be used as artificial analogues of structures with important roles in the living world: cilia, elastic tails of self‐propelling microorganisms etc. The main methods used to study the relevant phenomena are considered: models, numerical simulation algorithms, and the results of linear stability analysis. Special emphasis is placed on the possible uses of the flexible magnetic filaments as model systems to study the dynamics of magnetic fields using magnetometers based on optical detection of the magnetic resonance of NV− centers in diamonds.

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“…A central aspect of all of these examples is that the relevant dynamics is collective and not well-described by the dynamics of a single fiber.Given the importance of fluid-fiber systems, specialized computational methods have been developed to treat them, most especially in the zero Reynolds limit where flows are governed by the Stokes equation. These approaches include the use of nonlocal slender body theory [28,39], the immersed boundary method [19,29,33,37], bead-spring or -rod models [9,13,22,38], the regularized Stokeslet method [3,7,32,35], and overlapping grid methods [23]. See [20] for a recent review.…”

mentioning

confidence: 99%

Coarse graining the dynamics of immersed and driven fiber assemblies

Stein

Shelley

2019

Phys. Rev. Fluids

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An important class of fluid-structure problems involve the dynamics of ordered arrays of immersed, flexible fibers. While specialized numerical methods have been developed to study fluid-fiber systems, they become infeasible when there are many, rather than a few, fibers present, nor do these methods lend themselves to analytical calculation. Here, we introduce a coarse-grained continuum model, based on local-slender body theory, for elastic fibers immersed in a viscous Newtonian fluid. It takes the form of an anisotropic Brinkman equation whose skeletal drag is coupled to elastic forces. This model has two significant benefits: (1) the density effects of the fibers in a suspension become analytically manifest, and (2) it allows for the rapid simulation of dense suspensions of fibers in regimes inaccessible to standard methods. As a first validation, without fitting parameters, we achieve very reasonable agreement with 3D Immersed Boundary simulations of a bed of anchored fibers bent by a shear flow. Secondly, we characterize the effect of density on the relaxation time of fiber beds under oscillatory shear, and find close agreement to results from full numerical simulations. We then study buckling instabilities in beds of fibers, using our model both numerically and analytically to understand the role of fiber density and the structure of buckling transitions. We next apply our model to study the flow-induced bending of inclined fibers in a channel, as has been recently studied as a flow rectifier, examining the nature of the internal flows within the bed, and the emergence of inhomogeneous permeability. Finally, we extend the method to study a simple model of metachronal waves on beds of actuated fibers, as a model for ciliary beds. Our simulations reproduce qualitatively the pumping action of coordinated waves of compression through the bed. I. INTRODUCTIONMany fundamental hydrodynamic phenomena, particularly in biology, involve the interaction of structured arrays of immersed fibers, often anchored to a substrate [21]. For example, in eukaryotic cells, arrays of aligned microtubules in the spindle orchestrate the segregation of chromosomes, while those around centrosomes help position the spindle prior to cell division [14]. During midoogenesis of Drosophila, kinesin motors interacting with the microtubule cytoskeleton drive largescale coherent flows known as cytoplasmic streaming [10]. Another example is the beds of driven cilia that pump fluid, move mucus, or propel microorganisms [4]. In microfluidic engineering, fabricated arrays of flexible fibers are the elements of proposed soft flow rectifiers [1]. A central aspect of all of these examples is that the relevant dynamics is collective and not well-described by the dynamics of a single fiber.Given the importance of fluid-fiber systems, specialized computational methods have been developed to treat them, most especially in the zero Reynolds limit where flows are governed by the Stokes equation. These approaches include the use of nonlocal slender body the...

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A general formulation of Bead Models applied to flexible fibers and active filaments at low Reynolds number

Cited by 54 publications

References 86 publications

Dynamics of Flexible Fibers in Viscous Flows and Fluids

Dynamics of Flexible Fibers in Viscous Flows and Fluids

Flexible Magnetic Filaments and their Applications

Coarse graining the dynamics of immersed and driven fiber assemblies

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