The lift on a small sphere in a slow shear flow

Journal of Fluid Mechanics - Tập 22 Số 2 - Trang 385-400 - 1965
P. G. Saffman1
1California institute of Technology, Pasadena, California#TAB#

Tóm tắt

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.

Từ khóa


Tài liệu tham khảo

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

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

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

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

Poiseuille, J. L. M. 1836 Ann. Sci. Nat. 5,111.

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

Saffman, P. G. 1956b J. Fluid Mech. 1,540.

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

Lamb, H. 1932 Nature,194,1269.

Saffman, P. G. 1956a Ph.D. Thesis. Cambridge University.

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

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

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

Kaplun, S. & Lagerstrom, P. A. 1957 J. Math. Mech. 6,585.

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Thông tin xuất bản

Journal of Fluid Mechanics

Tập 22 Số 2

385-400

Thông tin tác giả