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The lift on a small sphere in a slow shear flow

Saffman, P. G. (1965) The lift on a small sphere in a slow shear flow. Journal of Fluid Mechanics, 22 (2). pp. 385-400. ISSN 0022-1120. doi:10.1017/s0022112065000824.

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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.

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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.
Issue or Number:2
Record Number:CaltechAUTHORS:20181119-161053473
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Official Citation:Saffman, P. (1965). The lift on a small sphere in a slow shear flow. Journal of Fluid Mechanics, 22(2), 385-400. doi:10.1017/S0022112065000824
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91056
Deposited By: George Porter
Deposited On:20 Nov 2018 16:04
Last Modified:16 Nov 2021 03:38

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