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The lift on a small sphere in a slow shear flow

  • P. G. Saffman (a1)

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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Childress, W. S. 1964 J. Fluid Mech. 20, 305.

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.

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

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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