Fundamental singularities of viscous flow

Blake, J. R.; Chwang, Allen T.

doi:10.1007/bf02353701

Cited by 324 publications

(287 citation statements)

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“…Furthermore, we include all terms due to the images as originally introduced by Blake to account for the no-slip boundary condition at the surface (for a complete description of the image system see ref. 24). In fact, it is these images that are responsible for the movement of the chains because they emulate the effect of the wall.…”

Section: Resultsmentioning

confidence: 99%

Controlled surface-induced flows from the motion of self-assembled colloidal walkers

Sing

Schmid

Schneider

et al. 2009

Proc. Natl. Acad. Sci. U.S.A.

221

206

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Biological flows at the microscopic scale are important for the transport of nutrients, locomotion, and differentiation. Here, we present a unique approach for creating controlled, surface-induced flows inspired by a ubiquitous biological system, cilia. Our design is based on a collection of self-assembled colloidal rotors that "walk" along surfaces in the presence of a rotating magnetic field. These rotors are held together solely by magnetic forces that allow for reversible assembly and disassembly of the chains. Furthermore, rotation of the magnetic field allows for straightforward manipulation of the shape and motion of these chains. This system offers a simple and versatile approach for designing microfluidic devices as well as for studying fundamental questions in cooperative-driven motion and transport at the microscopic level.Biological flows | Cilia | Magnetic | Microfluidics | Transport

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Section: Resultsmentioning

confidence: 99%

Controlled surface-induced flows from the motion of self-assembled colloidal walkers

Sing

Schmid

Schneider

et al. 2009

Proc. Natl. Acad. Sci. U.S.A.

221

206

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“…͑13͒ represents a line integral of Blake's image system for no-slip walls. 52 The streamlines for the complete image system are displayed in Fig. 2.…”

Section: ͑15͒mentioning

confidence: 99%

“…Subtleties do exist, however, so care should be taken. 52 Derivatives along the plane of the wall can be computed in a straightforward fashion, but derivatives perpendicular to the wall are more subtle, because the amplitude of the image singularities depends on the distance from the wall. In general, the correct image system will always be obtained if the derivative is calculated by taking the limit of two such opposing singularities ͑since each solution obeys the correct boundary condition on the wall in the first place͒.…”

Section: E Higher-order Singularitiesmentioning

confidence: 99%

Brownian motion near a partial-slip boundary: A local probe of the no-slip condition

2005

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Motivated by experimental evidence of violations of the no-slip boundary condition for liquid flow in micrometer-scale geometries, we propose a simple, complementary experimental technique that has certain advantages over previous studies. Instead of relying on externally induced flow or probe motion, we suggest that colloidal diffusivity near solid surfaces contains signatures of the degree of fluid slip exhibited on those surfaces. To investigate, we calculate the image system for point forces ͑Stokeslets͒ oriented perpendicular and parallel to a surface with a finite slip length, analogous to Blake's solution for a Stokeslet near a no-slip wall. Notably, the image system for the point source and perpendicular Stokeslet contain the same singularities as Blake's solution; however, each is distributed along a line with a magnitude that decays exponentially over the slip length. The image system for the parallel Stokeslet involves a larger set of fundamental singularities, whose magnitude does not decay exponentially from the surface. Using these image systems, we determine the wall-induced correction to the diffusivity of a small spherical particle located "far" from the wall. We also calculate the coupled diffusivities between multiple particles near a partially slipping wall. Because, in general, the diffusivity depends on "local" wall conditions, patterned surfaces would allow differential measurements to be obtained within a single experimental cell, eliminating potential cell-to-cell variability encountered in previous experiments. In addition to motivating the proposed experiments, our solutions for point forces and sources near a partial-slip wall will be useful for boundary integral calculations in slip systems.

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“…For a liquid-air interface, the image reduces to a particle rotating in the opposite sense than the actuated colloid, while for a solid surface an additional stresslet and source doublet must be added [49].…”

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confidence: 99%

Colloidal Microworms Propelling via a Cooperative Hydrodynamic Conveyor Belt

et al. 2015

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We study propulsion arising from microscopic colloidal rotors dynamically assembled and driven in a viscous fluid upon application of an elliptically polarized rotating magnetic field. Close to a confining plate, the motion of this self-assembled microscopic worm results from the cooperative flow generated by the spinning particles which act as a hydrodynamic "conveyor belt." Chains of rotors propel faster than individual ones, until reaching a saturation speed at distances where induced-flow additivity vanishes. By combining experiments and theoretical arguments, we elucidate the mechanism of motion and fully characterize the propulsion speed in terms of the field parameters. DOI: 10.1103/PhysRevLett.115.138301 PACS numbers: 82.70.Dd, 87.85.gj Propulsion in viscous fluids plays a key role in many different contexts of biology, physics, and chemistry. From a fundamental perspective, the transport of microscopic objects in a liquid medium poses the appealing challenge to find an adequate swimming strategy due to the negligible role of inertial force compared to viscous one. At low Reynolds number the Navier-Stokes equations become time reversible [1], and any strategy based on reciprocal motion, i.e., a motion composed by symmetric backward and forward displacements, will fail to produce net propulsion [2].Facing this challenge, the last few years have witnessed the theoretical propositions of several suitable geometries and procedures to propel micromachines in viscous fluids [3][4][5][6][7][8][9]. Parallel advances in miniaturization have led to the generation of new classes of chemically powered [10,11] or externally actuated [12][13][14][15] prototypes with exciting applications in emerging fields such as microsurgery [16,17] or lab-on-a-chip technology [18,19].In contrast to reaction driven microswimmers, actuated magnetic micropropellers do not present the autonomous behavior that distinguishes force-and torque-free motion of biological organisms [20], but instead avoid efficiency reduction due to fuel shortage or directional randomization. To date, three main approaches have been developed to transport microscopic particles in a viscous fluid using uniform magnetic fields [21], namely, by actuating flexible magnetic tails [12,22], by rotating helical shaped structures [23,24], or by using the close proximity to a bounding wall [25,26]. In the latter case, it is well established that in the Stokes regime the rotational motion of a body close to a surface can be rectified into net translation due to the hydrodynamic interaction with the boundary [27]. Surface rotors are optimal to work in confined geometries such as microfluidic channels or biological networks characterized by narrow pores.In this Letter we show that an ensemble of rotors dynamically self-assembled via attractive dipolar interactions can be propelled by a hydrodynamic "conveyor-belt" effect generated by the cooperative flow of the spinning particles close to a surface. Recent theoretical works [28][29][30] have addressed the rich dynamic...

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Fundamental singularities of viscous flow

Cited by 324 publications

References 4 publications

Controlled surface-induced flows from the motion of self-assembled colloidal walkers

Controlled surface-induced flows from the motion of self-assembled colloidal walkers

Brownian motion near a partial-slip boundary: A local probe of the no-slip condition

Colloidal Microworms Propelling via a Cooperative Hydrodynamic Conveyor Belt

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