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If we also assume that all particles are nearly spherical and move slowly enough that stokes flow (Re=O(0.1)) can describe the motion of the particles, the critical settling velocity can be further simplified to the following:
 

{latex}
\large
$$
V_s  = {{g(\rho _p  - \rho _w )d^2 } \over {18\mu }}
$$
{latex}