Low-Reynolds-number fall of slender cylinders near boundaries

Mestre, N. J. De

doi:10.1017/s0022112073002387

Cited by 37 publications

(30 citation statements)

References 11 publications

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“…Indeed, the very recent theoretical and experimental work of de Mestre (1973) for a Newtonian suspending fluid had already suggested that the terminal velocity could be measurably affected for a ratio of particle length to tank width of the order of 0.05 or less. I n addition, de Mestre indicated that particle-wall interactions may cause the orientational behaviour of the particle to differ markedly from that expected in an unbounded body of the same Newtonian fluid.…”

Section: (69)mentioning

confidence: 99%

The slow motion of slender rod-like particles in a second-order fluid

1975

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The motion of a slender axisymmetric rod-like particle is investigated theoretically for translation through a quiescent second-order fluid and for rotation in a simple shear flow of the same material. The analysis consists of an asymptotic expansion about the limit of rheologically slow flow, coupled with an application of a generalized form of the reciprocal theorem of Lorentz to calculate the force and torque on the particle. It is shown that an arbitrarily oriented particle with fore-aft symmetry translates, to a first approximation, a t the same rate as in an equivalent Newtonian fluid, but that the motion of particles with no fore-aft symmetry may be modified a t the same level of approximation. I n addition, it is found that freely translating particles with fore-aft symmetry exhibit a single stable orientation with the axis of revolution vertical. In simple shear flow a t small and moderate shear rates, the non-Newtonian nature of the suspending fluid causes a drift through Jeffery orbits to the equilibrium orbit C = 0 in which the particle rotates about its axis of revolution. At larger shear rates, the particle aligns itself in the direction of flow and ceases to rot@e. Comparison with the available experimental data indicates that the measured rate of orbit drift may be used to determine the second normal stress difference parameter of the secondorder fluid model. Finally, in an appendix, some preliminary observations are reported of the motion of slender rod-like particles falling thmough a quiescent viscoelastic fluid.

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Section: (69)mentioning

confidence: 99%

The slow motion of slender rod-like particles in a second-order fluid

1975

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“…For slightly confined flows, wall correction terms increase the drag force. The configuration in which a small cylinder sediments half-way between parallel vertical plates separated by a large distance h 0 (d ≪ L ≪ h 0 < W ) has been studied experimentally by de Mestre [10]. In this case, one has λ = α 1 (ǫ + (α 2 L h0 + α 3 )ǫ 2 ), where the parameters α i are constants, depending only on the orientation of the cylinder which is either vertical or horizontal.…”

Section: Introductionmentioning

confidence: 99%

Influence of flow confinement on the drag force on a static cylinder

2009

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The influence of confinement on the drag force $F$ on a static cylinder in a viscous flow inside a rectangular slit of aperture $h_0$ has been investigated from experimental measurements and numerical simulations. At low enough Reynolds numbers, $F$ varies linearly with the mean velocity and the viscosity, allowing for the precise determination of drag coefficients $\lambda_{||}$ and $\lambda_{\bot}$ corresponding respectively to a mean flow parallel and perpendicular to the cylinder length $L$. In the parallel configuration, the variation of $\lambda_{||}$ with the normalized diameter $\beta = d/h_0$ of the cylinder is close to that for a 2D flow invariant in the direction of the cylinder axis and does not diverge when $\beta = 1$. The variation of $\lambda_{||}$ with the distance from the midplane of the model reflects the parabolic Poiseuille profile between the plates for $\beta \ll 1$ while it remains almost constant for $\beta \sim 1$. In the perpendicular configuration, the value of $\lambda_{\bot}$ is close to that corresponding to a 2D system only if $\beta \ll 1$ and/or if the clearance between the ends of the cylinder and the side walls is very small: in that latter case, $\lambda_{\bot}$ diverges as $\beta \to 1$ due to the blockage of the flow. In other cases, the side flow between the ends of the cylinder and the side walls plays an important part to reduce $\lambda_{\bot}$: a full 3D description of the flow is needed to account for these effects

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“…PDMS is lighter than Percoll but heavier than cell culture media. Hence, the swimmer floats at the interface between Percoll media and normal media B1 mm above the floor, where the wall effects from fluid interaction with the substrate are minimal 25,26 . Confining the motion of the swimmer to a horizontal plane is essential for imaging and subsequent analysis.…”

Section: Resultsmentioning

confidence: 99%

A self-propelled biohybrid swimmer at low Reynolds number

et al. 2014

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Many microorganisms, including spermatozoa and forms of bacteria, oscillate or twist a hairlike flagella to swim. At this small scale, where locomotion is challenged by large viscous drag, organisms must generate time-irreversible deformations of their flagella to produce thrust. To date, there is no demonstration of a self propelled, synthetic flagellar swimmer operating at low Reynolds number. Here we report a microscale, biohybrid swimmer enabled by a unique fabrication process and a supporting slender-body hydrodynamics model. The swimmer consists of a polydimethylsiloxane filament with a short, rigid head and a long, slender tail on which cardiomyocytes are selectively cultured. The cardiomyocytes contract and deform the filament to propel the swimmer at 5-10 mm s À 1 , consistent with model predictions. We then demonstrate a two-tailed swimmer swimming at 81 mm s À 1 . This small-scale, elementary biohybrid swimmer can serve as a platform for more complex biological machines.

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Low-Reynolds-number fall of slender cylinders near boundaries

Cited by 37 publications

References 11 publications

The slow motion of slender rod-like particles in a second-order fluid

The slow motion of slender rod-like particles in a second-order fluid

Influence of flow confinement on the drag force on a static cylinder

A self-propelled biohybrid swimmer at low Reynolds number

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