The lift on a small sphere in a slow shear flow
- Creators
- Saffman, P. G.
Abstract
It is shown that a sphere moving through a very viscous liquid with velocity V relative to a uniform simple shear, the translation velocity being parallel to the streamlines and measured relative to the streamline through the centre, experiences a lift force 81·2μVa^2k^(½)/v^(½ )+ smaller terms perpendicular to the flow direction, which acts to deflect the particle towards the streamlines moving in the direction opposite to V. Here, a denotes the radius of the sphere, κ the magnitude of the velocity gradient, and μ and v the viscosity and kinematic viscosity, respectively. The relevance of the result to the observations by Segrée & Silberberg (1962) of small spheres in Poiseuille flow is discussed briefly. Comments are also made about the problem of a sphere in a parabolic velocity profile and the functional dependence of the lift upon the parameters is obtained.
Additional Information
© 1965 Cambridge University Press. (Received 29 October 1964) This work was started while acting as a vacation consultant at the National Physical Laboratory, Teddington. I am grateful to Dr J.T.Stuart for reawakening my interest in the subject.Attached Files
Published - lift_on_a_small_sphere_in_a_slow_shear_flow.pdf
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Additional details
- Eprint ID
- 91056
- Resolver ID
- CaltechAUTHORS:20181119-161053473
- Created
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2018-11-20Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field