  We develop a fully continuous model for colloidal suspensions with
hydrodynamic interactions. The Navier Stokes Phase Field Crystal (NS-PFC) model
combines ideas of dynamic density functional theory with particulate flow
approaches and is derived in detail and related to other dynamic density
functional theory approaches with hydrodynamic interactions. The derived system
is numerically solved using adaptive finite elements and used to analyse
colloidal crystallization in flowing environments demonstrating a strong
coupling in both directions between the crystal shape and the flow field. We
further validate the model against other computational approaches for
particulate flow systems for various colloidal sedimentation problems.
