A Navier-Stokes phase-field crystal model for colloidal suspensions

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.