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The stokeslet approximation

The flow field generated by a moving sphere (Eq. (18)) is essentially independent of the sphere's radius when viewed at sufficiently large distances. Consequently, we may approximate the flow field around a sphere driven through an unbounded fluid by the flow due to a unit force on a point within the fluid. The corresponding Oseen tensor is the Green's function for the system:

$\displaystyle \ensuremath{\mathsf{G}}\xspace ^S_\ensuremath{{\alpha\beta}}(\vec...
...ac{\delta_\ensuremath{{\alpha\beta}}}{r} + \frac{r_\alpha r_\beta}{r^3}\right).$ (27)

This Green's function plays an important role in many hydrodynamic problems and is known as a stokeslet. Comparison with Eq. (18) shows that $ \ensuremath{\mathsf{G}}\xspace ^S$ is indeed a good approximation for $ \mathsf{H}$ when $ r \gg a$.



David G. Grier 2001-01-16