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

A Navier Stokes Phase Field Crystal Model for Colloidal Suspensions