Saffinan force

For a fixed spherical particle in a fully developed laminar pipe flow, determine the Saffinan force on the particle at various radial positions. Identify the location of the maximum Saffman force. Discuss the case if the flow is turbulent (using the 1/7 power law for the velocity profile). 

Saffman had interests in turbulence, viscous flows, vortex motion and water waves. He made valuable theoretical contributions to different areas of low-Reynolds-number hydrodynamics. These included the lifting force on a sphere in a shear flow at small but finite Reynolds numbers, the Brownian motion in thin liquid films, and particle motion in rapidly rotating flows. Saffinan s other contributions include dispersion in porous media, average velocity of sedimenting suspensions, and compressible low-Reynolds-number flows. 

Saffinan showed that viscosity produces, for the configuration of Figure 16.3(b), a lift force ... 

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