Torsional oscillations of a sphere in a Stokes flow

Box, Finn; Thompson, A. R.; Mullin, T.

doi:10.1007/s00348-015-2075-7

Cited by 8 publications

(10 citation statements)

References 35 publications

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“…where (i = √ −1). The Mason Number, M a = B 0 m/(8πµa 3 ω) ≈ 8 1 so we may assume small angle oscillations (Box et al 2015). This allows us to isolate magnetic forcing from the fluid dynamics by assuming that the sphere undergoes angular oscillations of amplitude θ 0 , so…”

Section: Oscillating Sphere In a Stokes Flowmentioning

confidence: 99%

“…Here, we progress the understanding of the fundamental fluid dynamics of rotationally oscillating spheres in the presence of solid boundaries. In doing so, we use the novel experimental technique of Box et al (2015) to magnetically induce torsional oscillations in a sphere in a viscous fluid. The controlled oscillations are operated at constant driving torque and we refer to the sphere which moves in response to the magnetic field as 'active'.…”

Section: Introductionmentioning

confidence: 99%

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The interaction between rotationally oscillating spheres and solid boundaries in a Stokes flow

2018

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We present the results of an experimental and theoretical investigation into the influence of proximate boundaries on the motion of an rotationally oscillating sphere in a viscous fluid. The angular oscillations of the sphere are controlled using the magnetic torque generated by a spatially uniform, oscillatory magnetic field which interacts with a small magnet embedded within the sphere. We study the motion of the sphere in the vicinity of stationary walls that are parallel and perpendicular to the rotational axis of the sphere, and near a second passive sphere that is non-magnetic and free to move. We find that rigid boundaries introduce viscous resistance to motion that acts to suppress the oscillations of the driven sphere. The amount of viscous resistance depends on the orientation of the wall with respect to the axis of rotation of the oscillating sphere. A passive sphere also introduces viscous resistance to motion, but for this case the rotational oscillations of the active sphere establish a standing wave that imparts vorticity to the fluid and induces oscillations of the passive sphere. The standing wave is analogous to the case of an oscillating plate in a viscous fluid; the amplitude of the wave decays exponentially with radial distance from the surface of the oscillating sphere. The standing wave introduces a phase lag between the motion of the active sphere and the response of the passive sphere which increases linearly with separation distance.

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Section: Oscillating Sphere In a Stokes Flowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The interaction between rotationally oscillating spheres and solid boundaries in a Stokes flow

2018

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“…A macroscopic equivalent of the discussed torsional oscillation of a sphere has been presented earlier 37 using cm-sized ferromagnetic spheres in a highly viscous fluid exposed to an oscillating magnetic field. There, the constant aligning torque has been realized by gravitational forces that act on a sphere with non-symmetric mass distribution.…”

Section: Discussionmentioning

confidence: 98%

“…We drive dipolar particles with an oscillating field, which gives a time-dependent torsional oscillation angle θ ( t ) of the particles. The angular amplitude θ A serves as the measurable quantity 37 38 . Experimentally, θ A can be obtained, for example, with transmission light microscopy for particles with optical inhomogeneity 39 40 41 .…”

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confidence: 99%

Rotational friction of dipolar colloids measured by driven torsional oscillations

Steinbach

Gemming

Erbe

2016

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Despite its prominent role in the dynamics of soft materials, rotational friction remains a quantity that is difficult to determine for many micron-sized objects. Here, we demonstrate how the Stokes coefficient of rotational friction can be obtained from the driven torsional oscillations of single particles in a highly viscous environment. The idea is that the oscillation amplitude of a dipolar particle under combined static and oscillating fields provides a measure for the Stokes friction. From numerical studies we derive a semi-empirical analytic expression for the amplitude of the oscillation, which cannot be calculated analytically from the equation of motion. We additionally demonstrate that this expression can be used to experimentally determine the rotational friction coefficient of single particles. Here, we record the amplitudes of a field-driven dipolar Janus microsphere with optical microscopy. The presented method distinguishes itself in its experimental and conceptual simplicity. The magnetic torque leaves the local environment unchanged, which contrasts with other approaches where, for example, additional mechanical (frictional) or thermal contributions have to be regarded.Frictional forces play a fundamental role in the dynamics of mesoscopic objects, which are omnipresent in microfluidic and biological systems. The frictional interaction of moving objects with the viscous environment affects e.g. transport, demixing, diffusion, and propulsion [1][2][3][4][5] . The study of friction during these processes also gives access to the rheological and the aggregation behavior of colloids such as ferrofluids and gels [6][7][8][9] . In incompressible fluids, the key quantity is the Stokes friction coefficient f, which is the proportionality factor between the particle velocity and the drag force. Often, many-body effects in dense systems can be expressed as an expansion of the single-particle friction. An explicit, simple equation of f exists for single spheres in an ideally homogeneous medium by the Stokes law. Real systems, however, face deviations from that, caused either by a non-spherical object shape [10][11][12][13][14][15] or by anisotropic environments such as in non-ideal fluids or at surfaces/interfaces [16][17][18][19][20] , e.g. in a cell or a microchannel [21][22][23] . As most of these problems cannot be solved analytically one relies on approximate solutions 24 or on experimental measurements. Friction from translational motion behaves differently from the friction during rotational motion 16,25,26 ; for analysis sometimes both need to be decoupled 27,28 . Experimentally, the translational friction, f t , can be simply derived from the spatial displacement of a diffusing particle via optical methods. Rotational friction, f r , however, remains difficult to determine since additionally the orientation of the object has to be determined, which requires optical or shape anisotropy.For nanoscopic objects, measurement methods rely on, e.g., scattering techniques 13,29,30 , time-resolved phospho...

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“…1, and details of the experimental apparatus used for magnetic actuation and flow visualization are given in Box et al (2015). The connected spheres were in a viscous liquid inside a rectangular tank with internal dimensions of width 125 mm, length 115 mm, and height 200 mm.…”

Section: Methodsmentioning

confidence: 99%