  The superadiabatic dynamical density functional theory (superadiabatic-DDFT)
is a promising new method for the study of colloidal systems
out-of-equilibrium. Within this approach the viscous forces arising from
interparticle interactions are accounted for in a natural way by treating
explicitly the dynamics of the two-body correlations. For bulk systems subject
to spatially homogeneous shear we use the superadiabatic-DDFT framework to
calculate the steady-state pair distribution function and the corresponding
viscosity for low values of the shear-rate. We then consider a variant of the
central approximation underlying this superadiabatic theory and obtain an
inhomogeneous generalization of a rheological bulk theory due to Russel and
Gast. This paper thus establishes for the first time a connection between DDFT
approaches, formulated to treat inhomogeneous systems, and existing work
addressing nonequilibrium microstructure and rheology in bulk colloidal
suspensions.
