Creeping Flow around a Sphere in a Shear Flow Close to a Wall

Chaoui, Mohamed; Feuillebois, François

doi:10.1093/qjmam/56.3.381

Cited by 82 publications

(78 citation statements)

References 17 publications

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“…Accurate estimates of f v w for the indicated values of h / a in Table II were previously determined by Brenner 22 and for f h w and t h w by Chaoui and Feuillebois. 28 Results presented here are in perfect agreement with their investigations.…”

Section: ͑36͒supporting

confidence: 92%

“…The results for the parabolic flow coefficients, i.e., for f G and t G , were obtained previously by Pasol et al 29 As can be seen in Table I, our technique yields accurate estimates of all these four coefficients. It may be noted that prior to Chaoui and Feuillebois, 28 O'Neill 25 also obtained estimates for f ␥ and t ␥ . His estimates ͑1.7009 and 0.943 993͒ are also in agreement with the results presented here-a slight discrepancy is observed only in the fifth digit for the value of f ␥ .…”

Section: ͑36͒mentioning

confidence: 89%

“…[22][23][24][25][26][27][28][29][30][31][32][33] We first consider the case of a single spherical particle of radius a held fixed in a parabolic flow given by…”

Section: Particles Near a Wallmentioning

confidence: 99%

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A method for determining Stokes flow around particles near a wall or in a thin film bounded by a wall and a gas-liquid interface

Ozarkar

Sangani

2008

Physics of Fluids

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A method for determining Stokes flow around particles near a wall or in a thin film bounded by a wall on one side and a nondeformable gas-liquid interface on the other side is developed. The no-slip boundary conditions at the wall are satisfied by constructing an image system based on Lamb's multipoles. Earlier results for the image systems for the flow due to a point force or a force dipole are extended to image systems for force or source multipoles of arbitrary orders. For the case of a film, the image system consists of an infinite series of multipoles on both sides of the film. Accurate evaluation of the flow due to these images is discussed, including the use of Shanks transforms. The method is applied to several problems including chains of particles, radially expanding particles, drops, and porous particles.

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Section: ͑36͒supporting

confidence: 92%

Section: ͑36͒mentioning

confidence: 89%

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A method for determining Stokes flow around particles near a wall or in a thin film bounded by a wall and a gas-liquid interface

Ozarkar

Sangani

2008

Physics of Fluids

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“…Note that, as expected, for K * = 10 −2 the coefficient f 33 decreases as the slip length λ increases, since the shear rate of the flow taking place in the slab-sphere gap is smaller when λ is bigger and thus the lubrication force is then smaller. Using the bipolar coordinates method, Michalopoulou et al (1992) considered the axisymmetric translation of a solid sphere towards another motionless and porous Davis, Kezirian & Brenner (1994) using the bipolar coordinates method ( for λ = 0.1, and ♦ for λ = 0.01) and by Luo & Pozrikidis (2008) using the boundary integral equations technique ( for λ = 0.1), and the results obtained for a solid wall and a no-slip particle by Luo & Pozrikidis (2008) (⋆ for λ = 0) and by Chaoui & Feuillebois (2003) …”

Section: Friction Coefficientsmentioning

confidence: 99%

“…This means that it is easier to move (translate or rotate) the sphere parallel with the slab than normal to it. For the weak permeability K * = 10 −4 , the porous slab behaves as an impermeable boundary of solid nature if λ 0.01 (see the comparisons with Chaoui & Feuillebois (2003) and Luo & Pozrikidis (2008) for λ = 0) or of slipping nature for λ large enough (see the comparisons with Davis et al (1994) and Luo & Pozrikidis (2008) for λ = 0.1). The coefficients f 12 and c 21 , displayed in figure 5, exhibit the same behaviours versus (d * , K * , λ) as the coefficients f 11 and c 22 but are of weaker magnitudes.…”

Section: (•)mentioning

confidence: 99%

Motion of a solid particle in a shear flow along a porous slab

et al. 2012

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The flow field around a solid particle moving in a shear flow along a porous slab is obtained by solving the coupled Stokes-Darcy problem with the Beavers and Joseph slip boundary condition on the slab interfaces. The solution involves the Green's function of this coupled problem, which is given here. It is shown that the classical boundary integral method using this Green's function is inappropriate because of supplementary contributions due to the slip on the slab interfaces. An 'indirect boundary integral method' is therefore proposed, in which the unknown density on the particle surface is not the actual stress, but yet allows calculation of the force and torque on the particle. Various results are provided for the normalized force and torque, namely friction factors, on the particle. The cases of a sphere and an ellipsoid are considered. It is shown that the relationships between friction coefficients (torque due to rotation and force due to translation) that are classical for a no-slip plane do not apply here. This difference is exhibited. Finally, results for the velocity of a freely moving particle in a linear and a quadratic shear flow are presented, for both a sphere and an ellipsoid.

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Measuring local properties inside a cell‐mimicking structure using rotating optical tweezers

Zhang

Gibson

Stilgoe

et al. 2019

Journal of Biophotonics

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Exploring the rheological properties of intracellular materials is essential for understanding cellular and subcellular processes. Optical traps have been widely used for physical manipulation of micro and nano objects within fluids enabling studies of biological systems. However, experiments remain challenging as it is unclear how the probe particle's mobility is influenced by the nearby membranes and organelles. We use liposomes (unilamellar lipid vesicles) as a simple biomimetic model of living cells, together with a trapped particle rotated by optical tweezers to study mechanical and rheological properties inside a liposome both theoretically and experimentally. Here, we demonstrate that this system has the capacity to predict the hydrodynamic interaction between three‐dimensional spatial membranes and internal probe particles within submicron distances, and it has the potential to aid in the design of high resolution optical micro/nanorheology techniques to be used inside living cells.

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Creeping Flow around a Sphere in a Shear Flow Close to a Wall

Cited by 82 publications

References 17 publications

A method for determining Stokes flow around particles near a wall or in a thin film bounded by a wall and a gas-liquid interface

A method for determining Stokes flow around particles near a wall or in a thin film bounded by a wall and a gas-liquid interface

Motion of a solid particle in a shear flow along a porous slab

Measuring local properties inside a cell‐mimicking structure using rotating optical tweezers

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