1967
DOI: 10.1016/0009-2509(67)80047-2
|View full text |Cite
|
Sign up to set email alerts
|

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

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1
1

Citation Types

38
864
3
2

Year Published

1980
1980
2018
2018

Publication Types

Select...
7
2

Relationship

0
9

Authors

Journals

citations
Cited by 1,228 publications
(907 citation statements)
references
References 7 publications
38
864
3
2
Order By: Relevance
“…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%
See 1 more Smart Citation
“…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%
“…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%
“…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%