Engineering Design Handbooks

Beyond dynamic density functional theory: the role of inertia

“…In practice, only the information contained in the first two reduced distribution functions, f (1) and f (2) , obtained from f (N ) by integrating over the phase-space coordinates of (N −1) and (N −2) particles, respectively, is relevant to our study. The equation for f (1) is ∂ ∂t f (1) …”

“…We identify the moment 0 (X, τ ) = dV P(X, V, τ ) with the number density, ρ(X, τ ), 1 (X, τ ) = dV V P(X, V, τ ) with the momentum density J (X, τ ) or particle current, and 2 (X, τ ) + 0 (X, τ )/2 = 1/2 dV V 2 P(X, V, τ ) with the kinetic energy density.…”

“…Among these, density functional theory (DFT) [1] is perhaps the most versatile. In contrast, we do not have a similar control over the behavior of systems in generic non-equilibrium situations.…”

Density functional theory for a model colloid polymer mixture: bulk fluid phases

“…The main benefit of DFT is that powerful approximate theories can be obtained, provided the (generally unknown) excess part F exc is prescribed. The effects caused by different classes of (time-independent) external potentials can all be treated within the same theory, as F exc is independent of V i,ext ; it is a unique functional of {ρ i (r)} for a given choice of interparticle potential functions [16,17]. Of course, the difficult part of any approximate DFT is finding a suitable prescription or recipe for F exc that will incorporate the essential physics of short-range correlations (arising from the packing of the particles) and of attractive forces (if these are present) between the particles.…”

“…Rather we treat colloid and polymer on equal footing and develop a DFT specifically tailored for the AO mixture. DFT is recognized as powerful tool for describing the equilibrium properties of inhomogeneous fluids [16,17]. Most effort has been expended on HS fluids, and the fundamental measure theory (FMT) introduced by Rosenfeld [18] and subsequently refined [19][20][21][22] has proved particularly versatile and reliable in a wide variety of applications to both pure HS and to mixtures.…”