Stokesian dynamics, SD, simulations of model colloidal dispersions und
er shear flow are presented. The behaviour of the Ermak Rouse-level mo
del, which has no many-body hydrodynamics, MBH, is compared with the E
rmak-McCammon algorithm which introduces MBH at the Rotne-Prager far-f
ield level. Despite the inclusion of far field many-body hydrodynamics
, the model colloidal systems still form ordered phases under shear ve
ry similar to those formed by the Rouse model, over what is now consid
ered to be an unrealistically large part of the non-equilibrium shear
rate vs. volume fraction phase diagram. There is even evidence that th
ese many-body hydrodynamics promote the formation of ordered phases. W
e conclude that it is essential to have a better representation of sho
rt-range hydrodynamics (e.g. lubrication) forces in any realistic impl
ementation of MBH in a SD simulation.