A pairwise hydrodynamic theory for flow-induced structuring in dilute suspensions.

A modified diffusive flux model is presented for flow-induced particle structuring resulting from pair interactions in suspensions undergoing shear and pressure-driven flows. The analysis reveals the formation of an O(r_c) boundary layer in regions of vanishing shear rates (e.g., centerline of planar Poiseuille flow) where r_c is the radius of the upstream collision cross-section for pairwise particle interactions.  By contrast to the current theories for suspension microstructure, a non-singular spatial distribution of particles is predicted.  Particle segregation is predicted in bidisperse suspensions in regions of vanishing shear rate with enrichment and depletion depending principally on size ratio. Large particles are enriched in suspensions of rough particles; the opposite is true in emulsions.