Singularities of viscous flow

SummaryThe force and torque on a slender body in Stokes flow is obtained by using a distribution of singularities along the centreline and the required image system to satisfy the no-slip condition and the plane boundary. It is found that the force on a slender body increases rapidly as it approaches within a body length of the boundary, but not the torque. To rule out “wall effects”, experiments on slender bodies, such as flagellated or ciliated micro-organisms, should be carried out a distance of many body lengths (not radii!) from all boundaries. The ratio of normal to tangential resistance coefficients is found to be greater than 2 (the maximum in an infinite fluid) in the presence of walls.

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