# Solution of Navier-Stokes eq for a single particle?

## Main Question or Discussion Point

Solution of Navier-Stokes eq for a single particle???

Hi!

I'm reading this paper on fluid dynamics:
http://jcp.aip.org/resource/1/jcpsa6/v50/i11/p4831_s1 [Broken]
Its equation (13) is the velocity distribution around a single bead of radius a subjecting to force fi in solution. (the subscript i is irrelevant here). The bead is located at the origin and $\mathbf\rho^{'}$ is the coordinate for an arbitrary point in space.

Equation (13):
$\mathbf u_{i}(\mathbf\rho^{'}) = (8\pi\eta a)^{-1}\left [ \left ( \frac{a}{\rho ^{'}}+ \frac{1}{3}\frac{a^3}{\rho ^{'3}} \right ) \mathbf f_i + \left ( \frac{a}{\rho ^{'3}}- \frac{a^3}{\rho ^{'5}} \right ) \mathbf f_i \cdot \mathbf\rho^{'}\mathbf\rho^{'} \right ]$

There is not even citation for this equation, it looks like some textbook solution of the Navier-Stokes equation for this simple system. I just want to know how this can be derived? Could anyone provide me some resource to look at???

Thanks sooo much!

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