The lift on a small sphere in a slow shear flow
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In this article, it was 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 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 streamline moving in the direction opposite to V.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 Segree & 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.read more
Citations
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References
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The transverse force on a spinning sphere moving in a viscous fluid
S. I. Rubinow,Joseph B. Keller +1 more
TL;DR: In this article, the Stokes and Oseen expansions of the Oseen equation are used to calculate the transverse force of a spinning sphere in a viscous fluid, which is in such a direction as to account for the curving of a pitched baseball, the long range of a flying golf ball, etc.
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The motion of rigid particles in a shear flow at low Reynolds number
TL;DR: In this paper, the authors investigated how far the orbit of a particle of more general shape in a non-uniform shear in the presence of rigid boundaries may be expected to be qualitatively similar.
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Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder
Ian Proudman,J. R. A. Pearson +1 more
TL;DR: In this paper, the Navier-Stokes equation is replaced by a set of differential equations for the coefficients ψn and Ψn, but only one set of physical boundary conditions is applicable to each expansion (the no-slip conditions for the Stokes expansion, and the uniform-stream condition for the Oseen expansion).
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Behaviour of macroscopic rigid spheres in Poiseuille flow Part 1. Determination of local concentration by statistical analysis of particle passages through crossed light beams
G. Segré,A. Silberberg +1 more
TL;DR: In this paper, an apparatus is described for determining particle passages through any selected point on a tube cross-section, based on the simultaneous blocking out of two mutually perpendicular light beams by a particle passing through their common region.
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The flow of suspensions through tubes. I. Single spheres, rods, and discs
H.L Goldsmith,S. G. Mason +1 more
TL;DR: In this article, the motions of single rigid spheres, rods, and discs, and of fluid drops suspended in liquids undergoing Poiseuille flow have been studied, with the exception of effects due to interaction with the wall and neglect of particle size, provided that the equivalent axis ratio re was used instead of the particle axis ratio rp.
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