Slow viscous motion of a sphere parallel to a plane wall—I Motion through a quiescent fluid

Goldman, A.J.; Cox, R. G.; Brenner, Howard

doi:10.1016/0009-2509(67)80047-2

Cited by 1,204 publications

(907 citation statements)

References 7 publications

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“…It should be mentioned here that the calculation of Dean & O'Neill (1963) was numerically erroneous (cf. Goldman, Cox & Brenner 1967) and, thus, does not agree with our results fori\ = ro. The fact that exact results are available for the force andjor torque provides an opportunity to see whether the asymptotic results of part 1 can be improved at all.…”

Section: S H Lee and L G Lealcontrasting

confidence: 97%

“…When the sphere is very close to the interface, on the other hand, so that l-1 ~ 1, lubrication theory can be applied, in principle, to obtain asymptotic solutions. Indeed, Goldman, Cox & Brenner (1967) used this technique to study the translation and rotation of a sphere near a plane solid wall. However, they found that the lubrication-theory results for force and/or torque were quite poor when compared with the numerically exact results of Dean & O'Neill (1963) and O'Neill (1964).…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

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Motion of a sphere in the presence of a plane interface. Part 2. An exact solution in bipolar co-ordinates

1980

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A general solution for Stokes' equation in bipolar co-ordinates is derived, and then applied to the arbitrary motion of a sphere in the presence of a plane fluid/fluid interface. The drag force and hydrodynamic torque on the sphere are then calculated for four specific motions of the sphere; namely, translation perpendicular and parallel to the interface and rotation about an axis which is perpendicular and parallel, respectively, to the interface. The most significant result of the present work is the comparison between these numerically exact solutions and the approximate solutions from part 1. The latter can be generalized to a variety of particle shapes, and it is thus important to assess their accuracy for this case of spherical particles where an exact solution can be obtained. In addition to comparisons with the approximate solutions, we also examine the predicted changes in the velocity, pressure and vorticity fields due to the presence of the plane interface. One particularly interesting feature of the solutions is the fact that the direction of rotation of a freely suspended sphere moving parallel to the interface can either be the same as for a sphere rolling along the interface (as might be intuitively expected), or opposite depending upon the location of the sphere centre and the ratio of viscosities for the two fluids.

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Section: S H Lee and L G Lealcontrasting

confidence: 97%

Section: Numerical Results and Discussionmentioning

confidence: 99%

Motion of a sphere in the presence of a plane interface. Part 2. An exact solution in bipolar co-ordinates

1980

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“…Independently of the ratio of radius to distance, Brenner [15] [17,18] developed asymptotic solutions for the near-wall hydrodynamic forces when a particle flows past an obstacle.…”

Section: Figurementioning

confidence: 99%

Using the DEM-CFD method to predict Brownian particle deposition in a constricted tube

Chaumeil

Crapper

2014

Particuology

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The modelling of the agglomeration and deposition on a constricted tube collector of colloidal size particles immersed in a liquid is investigated using the Discrete Element Method (DEM). The ability of this method to model surface interactions allows the modelling of particle agglomeration and deposition at the particle scale.The numerical model adopts a mechanistic approach to represent the forces involved in colloidal suspension by including near wall drag retardation, surface interaction and Brownian forces. The model is implemented using the commercially available DEM package EDEM 2.3®, so that results can be replicated in a standard and user-friendly framework. The effect of various particle-tocollector size ratios, inlet fluid flow-rates and particle concentrations are examined and it is found that deposition efficiency is strongly dependent on inter-relation of these parameters.

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“…These two quantities allow two independent determinations of the slip length b with an accuracy of 10 nm in both cases. The speed profile straightforwardly provides a direct measurement of b and the variations in the diffusion coefficient are a function of the slip length value due to hydrodynamic coupling of the particle with the surface (Goldman et al 1967;Lauga & Squires 2005). It appears that on the hydrophilic surfaces no slippage was observed: bZ3G7 nm with the speed profile and bZK1G12 nm with the diffusion coefficient profile ( figure 8a,c).…”

Section: Micro-and Nanovelocimetrymentioning

confidence: 99%

Using surface force apparatus, diffusion and velocimetry to measure slip lengths

Bouzigues

Bocquet

Charlaix

et al. 2007

Phil. Trans. R. Soc. A.

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Determining the slip lengths for liquids flowing close to smooth walls is challenging. The reason lies in the fact that the scales that must be addressed range between a few and hundreds of nanometres. Several techniques have been used over the last few years. Here, we consider three of them based on surface force apparatus, diffusion and velocimetry, respectively. The descriptions offered here incorporate recent instrumental progress made in the field.

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Slow viscous motion of a sphere parallel to a plane wall—I Motion through a quiescent fluid

Cited by 1,204 publications

References 7 publications

Motion of a sphere in the presence of a plane interface. Part 2. An exact solution in bipolar co-ordinates

Motion of a sphere in the presence of a plane interface. Part 2. An exact solution in bipolar co-ordinates

Using the DEM-CFD method to predict Brownian particle deposition in a constricted tube

Using surface force apparatus, diffusion and velocimetry to measure slip lengths

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