  We study numerically the crystallization process in a supersaturated
suspension of repulsive colloidal particles driven by simple shear flow. The
effect of the shear flow on crystallization is two-fold: while it suppresses
the initial nucleation, once a large enough critical nucleus has formed its
growth is enhanced by the shear flow. Combining both effects implies an optimal
strain rate at which the overall crystallization rate has a maximum. To gain
insight into the underlying mechanisms, we employ a discrete state model
describing the transitions between the local structural configurations around
single particles. We observe a time-scale separation between these transitions
and the overall progress of the crystallization allowing for an effective
Markovian description. By using this model, we demonstrate that the suppression
of nucleation is due to the inhibition of a pre-structured liquid.
