A fundamental assumption of the dynamical density functional theory (DDFT) of colloidal systems is that a grand-canonical free-energy functional may be employed to generate the thermodynamic driving forces. Using one-dimensional hard rods as a model system, we analyze the validity of this key assumption and show that unphysical self-interactions of the tagged particle density fields, arising from coupling to a particle reservoir, are responsible for the excessively fast relaxation predicted by the theory. Moreover, our findings suggest that even employing a canonical functional would not lead to an improvement for many-particle systems, if only the total density is considered. We present several possible schemes to suppress these effects by incorporating tagged densities. When applied to confined systems, we demonstrate, using a simple example, that DDFT necessarily leads to delocalized tagged particle density distributions, which do not respect the fundamental geometrical constraints apparent in Brownian dynamics simulation data. The implication of these results for possible applications of DDFT to treat the glass transition are discussed.

-We present a density functional based closure of the pair Smoluchowski equation for Brownian particles under shear flow. Given an equilibrium free energy functional as input the theory provides first-principles predictions for the flow-distorted pair correlation function and associated rheological quantities over a wide range of volume fractions and flow rates. Taking twodimensional hard-disks under shear flow as an illustrative model we calculate the pair correlation function, viscosity and normal stress difference under both steady and start-up shear.Introduction. -The addition of colloidal particles to a Newtonian liquid gives rise to a nonlinear rheological response, characterized by a rate dependent viscosity, finite normal stress differences and nontrivial transient dynamics [1]. Understanding the interplay between particle interactions and external stress or strain fields remains a major theoretical challenge and much effort has been invested in the search for tractable closure relations which capture the essential physics of systems driven out-of-equilibrium [2]. Realistic models for which the competing effects of Brownian motion, potential and hydrodynamic interactions are simultaneously active pose particular difficulties [3].

We investigate the microstructural and microrheological response to a tracer particle of a two-dimensional colloidal suspension under thermodynamic conditions close to a liquid-gas phase boundary. On the liquid side of the binodal, increasing the velocity of the (repulsive) tracer leads to the development of a pronounced cavitation bubble, within which the concentration of colloidal particles is strongly depleted. The tendency of the liquid to cavitate is characterized by a dimensionless "colloidal cavitation" number. On the gas side of the binodal, a pulled (attractive) tracer leaves behind it an extended trail of colloidal liquid, arising from downstream advection of a wetting layer on its surface. For both situations the velocity dependent friction is calculated.

We calculate tractable microscopic expressions for the low-shear normal-stress coefficients of colloidal dispersions. Although restricted to the low rate regime, the presented formulas are valid for all volume fractions below the glass transition and for any interaction potential. Numerical results are presented for a system of colloids interacting via a hard-core attractive Yukawa potential, for which we explore the interplay between attraction strength and volume fraction. We show that the normal-stress coefficients exhibit nontrivial features close to the critical point and at high volume fractions in the vicinity of the reentrant glass transition. Finally, we exploit our formulas to make predictions about rod-climbing effects in attractive colloidal dispersions.