The lift on a small sphere in a slow shear flow

作者：P. G. Saffman · 发表于：Journal of Fluid Mechanics · 年份：1965 · DOI：10.1017/s0022112065000824 · 被引用次数：3401 · 研究领域：Granular flow and fluidized beds、Lattice Boltzmann Simulation Studies、Particle Dynamics in Fluid Flows

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 81·2μ Va 2 k 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.