The motion of rigid particles in a shear flow at low Reynolds number

Bretherton, F. P.

doi:10.1017/s002211206200124x

Cited by 753 publications

(526 citation statements)

References 2 publications

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“…Numerical comparison of Stokes and inertial flow development along the channel near the pillar indicates that the presence of the pillars leads to deformation of streamlines and while this deformation possesses fore-aft symmetry in Stokes flow, in agreement with the mirror-symmetry time-reversal theorem 17 , the symmetry is broken in the presence of inertia (Fig. 2a).…”

Section: Resultssupporting

confidence: 65%

“…Notably, this net twisting of fluid around a pillar has been neglected in microfluidic systems because fluid inertia is often not important in a wide range of conventional microfluidic flow conditions 16 . Flow around a pillar in a straight channel without inertia (that is, Stokes flow) requires fore-aft symmetry because of the mirror-symmetry of the flow upon timereversal of the linear equations of motion 17 . Therefore, any secondary fluid motion directed within the channel crosssection 18 is completely reversed after passing the cylinder mid-plane.…”

Section: Resultsmentioning

confidence: 99%

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Engineering fluid flow using sequenced microstructures

et al. 2013

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Controlling the shape of fluid streams is important across scales: from industrial processing to control of biomolecular interactions. Previous approaches to control fluid streams have focused mainly on creating chaotic flows to enhance mixing. Here we develop an approach to apply order using sequences of fluid transformations rather than enhancing chaos. We investigate the inertial flow deformations around a library of single cylindrical pillars within a microfluidic channel and assemble these net fluid transformations to engineer fluid streams. As these transformations provide a deterministic mapping of fluid elements from upstream to downstream of a pillar, we can sequentially arrange pillars to apply the associated nested maps and, therefore, create complex fluid structures without additional numerical simulation. To show the range of capabilities, we present sequences that sculpt the cross-sectional shape of a stream into complex geometries, move and split a fluid stream, perform solution exchange and achieve particle separation. A general strategy to engineer fluid streams into a broad class of defined configurations in which the complexity of the nonlinear equations of fluid motion are abstracted from the user is a first step to programming streams of any desired shape, which would be useful for biological, chemical and materials automation.

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Section: Resultssupporting

confidence: 65%

Section: Resultsmentioning

confidence: 99%

Engineering fluid flow using sequenced microstructures

et al. 2013

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“…These theories predict a negative value for the coefficient K for pushers at low shear rates, meaning the suspension can exhibit a lower viscosity than the suspending fluid. The theoretical assessment of shear viscosity relies on an assumed statistical representation of the orientations of the bacteria, captured by a Fokker-Plank equation and a kinematic model for the swimming trajectories [25,26].Despite the large number of theoretical studies, few experiments have been conducted. With bacillus subtilis (pushers) trapped in a soap film Sokolov et al[12] have shown that a vorticity decay rate could be associated with a strong decrease of shear viscosity in the presence of bacteria.…”

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confidence: 99%

Non-Newtonian Viscosity ofEscherichia coliSuspensions

et al. 2013

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The viscosity of an active suspension of E-Coli bacteria is determined experimentally in the dilute and semi dilute regime using a Y shaped micro-fluidic channel. From the position of the interface between the pure suspending fluid and the suspension, we identify rheo-thickening and rheo-thinning regimes as well as situations at low shear rate where the viscosity of the bacteria suspension can be lower than the viscosity of the suspending fluid. In addition, bacteria concentration and velocity profiles in the bulk are directly measured in the micro-channel.PACS numbers: 47.57.Qk,The fluid mechanics of microscopic swimmers in suspension have been widely studied in recent years. Bacteria [1, 2], algae [3,4] or artificial swimmers [5] dispersed in a fluid display properties that differ strongly from those of passive suspensions [6]. The physical relationships governing momentum and energy transfer as well as constitutive equations vary drastically for these suspensions [7,8]. Unique physical phenomena caused by the activity of swimmers were recently identified such as enhanced Brownian diffusivity [1,[8][9][10]] uncommon viscosity [4,12,13], active transport and mixing [11] or the extraction of work from isothermal fluctuations [13,16]. The presence of living and cooperative species may also induce collective motion and organization at the mesoscopic or macroscopic level [17,18] impacting the constitutive relationships in the semi-diluted or dense regimes. The E.Coli bacterium possesses a quite sophisticated propulsion apparatus consisting of a collection of flagella (7-10 µm length) organized in a bundle and rotating counter-clockwise [20]. In a fluid at rest, the wild-type strain used here has the ability to change direction by unwinding some flagella and moving them in order to alter its swimming direction (a tumble) approximately once every second [21]. In spite of the inherent complexity of the propulsion features, low Reynolds number hydrodynamics impose a long range flow field which can be modeled as an effective force dipole. Due to the thrust coming from the rear, E.coli are described as "pushers", hence defining a sign for the force dipole which has a crucial importance on the rheology of active suspensions [7]. For a dilute suspension of force dipoles, Haines et al [22] and Saintillan [24] derived an explicit relation relating viscosity and shear rate. They obtained an effective viscosity similar in form to the classical Einstein relation for dilute suspensions : η = η 0 (1 + Kφ) (η 0 being the suspending fluid viscosity and φ the volume fraction). These theories predict a negative value for the coefficient K for pushers at low shear rates, meaning the suspension can exhibit a lower viscosity than the suspending fluid. The theoretical assessment of shear viscosity relies on an assumed statistical representation of the orientations of the bacteria, captured by a Fokker-Plank equation and a kinematic model for the swimming trajectories [25,26].Despite the large number of theoretical studies, few experimen...

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“…The discovery was verified by the subsequent experiment of Taylor. 34 Furthermore, Bretherton 35 extended Jeffery's conclusion to a revolution body, and demonstrated that the orientation of the axis of almost any body of revolution is a periodic function of time in any unidirectional flow. For a fiber, Jeffery's result induces the following equation:…”

Section: A Deterministic Rotational Dynamics Of Fibersmentioning

confidence: 95%

Solution of three-dimensional fiber orientation in two-dimensional fiber suspension flows

2007

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Effects of bending and torsion rigidity on deformation and breakage of flexible fibers: A direct simulation study J. Chem. Phys. 136, 074903 (2012) Clouds of particles in a periodic shear flow Phys. Fluids 24, 021703 (2012) Steady-state hydrodynamics of a viscous incompressible fluid with spinning particles J. Chem. Phys. 135, 234901 (2011) Orientational order in concentrated suspensions of spherical microswimmers Phys. The orientation of fibers in simple two-dimensional flows is investigated. According to different ranges of the Péclet number, Pe, defined as the ratio of a characteristic rotational speed of fibers and the orientational diffusivity, three methods are developed: characteristic method for Pe= ϱ, regular perturbation method for Peӷ 1, and spectral method for everything else. All the methods subtly utilize the evolving solution of the rotational dynamics of fibers, which is also given in this paper. Especially, the adoption of spherical harmonics in the spectral method eliminates the singularity of the Fokker-Planck equation in spherical coordinates, and provides high precision and efficiency. The evolving solution of orientation distribution with Pe= ϱ is obtained through the solution of rotational dynamics. Using a regular perturbation method, the solution of orientation distribution with Pe= ϱ is extended for the condition of Peӷ 1. This paper provides systematical and high efficient techniques to deal with the fiber orientation.

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The motion of rigid particles in a shear flow at low Reynolds number

Cited by 753 publications

References 2 publications

Engineering fluid flow using sequenced microstructures

Engineering fluid flow using sequenced microstructures

Non-Newtonian Viscosity ofEscherichia coliSuspensions

Solution of three-dimensional fiber orientation in two-dimensional fiber suspension flows

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