We review the analysis of single and N–component lattice Boltzmann methods for fluid flow simulation. Results are presented for the emergent pressure field of a single phase incompressible liquid flowing over a backward–facing step, at moderate Reynolds Number, which is compared with the experimental data of Denham & Patrick (1974 Trans. IChE 52, 361–367). We then access the potential of the N–component method for transport of high volume fraction suspensions of deformable particles in pressure–driven flow. The latter are modelled as incompressible, closely packed liquid drops. We demonstrate the technique by investigating the particle's transverse migration in a uniform shear (‘lift’), and profile blunting and chaining.