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The lift on a small sphere in a slow shear flow

  • P. G. Saffman (a1)
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 81·2μVa2k½/v½ + 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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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

Bretherton, F. P. 1962a J. Fluid Mech. 12, 591.

Bretherton, F. P. 1962b J. Fluid Mech. 14, 284.

Goldsmith, H. L. & Mason, S. G.1962J. Coll. Sci.17, 448.

Proudman, I. & Pearson, J. R. A.1957J. Fluid Mech.2, 237.

Saffman, P. G.1956bJ. Fluid Mech.1, 540.

Segré, G. & Silberberg, A. 1962 J. Fluid Mech. 14, 115, 136.

Simha, R.1936Kolloid Z.76, 16.

Rubinow, S. I. & Keller, J. B. 1961 J. Fluid Mech. 11, 447.

Townsend, A. A.1951Proc. Roy. Soc. A, 209, 418.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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