Dynamical density functional theory for dense suspensions of colloidal hard spheres

Abstract: We study structural relaxation of colloidal hard spheres undergoing Brownian motion using dynamical density functional theory. Contrary to the partial linearization route [Stopper {\em et al.}, Phys. Rev. E {\bf 92}, 022151 (2015)] which amounts to using different free energy functionals for the self and distinct part of the van Hove function $G(r,t)$, we put forward a unified description employing a single functional for both components. To this end, interactions within the self part are removed via the zero-dimensional limit of the functional with a quenched self component. In addition, we make use of a theoretical result for the long-time mobility in hard-sphere suspensions, which we adapt to the inhomogeneous fluid. Our results for $G(r,t)$ are in excellent agreement with numerical simulations even in the dense liquid phase. In particular, our theory accurately yields the crossover from free diffusion at short times to the slower long-time diffusion in a crowded environment.