Pseudospectral methods for density functional theory in bounded and unbounded domains

Abstract

Classical Density Functional Theory (DFT) is a statistical-mechanical framework to analyze fluids, which accounts for nanoscale fluid inhomogeneities and non-local intermolecular interactions. DFT can be applied to a wide range of interfacial phenomena, as well as problems in adsorption, colloidal science and phase transitions in fluids. Typical DFT equations are highly non-linear, stiff and contain several convolution terms. We propose a novel, efficient pseudo-spectral collocation scheme for computing the non-local terms in real space with the help of a specialized Gauss quadrature. Due to the exponential accuracy of the quadrature and a convenient choice of collocation points near interfaces, we can use grids with a significantly lower number of nodes than most other reported methods. We demonstrate the capabilities of our numerical methodology by studying equilibrium and dynamic two-dimensional test cases with single- and multispecies hard-sphere and hard-disc particles modelled with fundamental measure theory, with and without van der Waals attractive forces, in bounded and unbounded physical domains. We show that our results satisfy statistical mechanical sum rules.

References in corpus (17)

• Dynamic Density Functional Theory of Fluids
• Dynamical density functional theory and its application to spinodal decomposition
• Dynamical density functional theory for molecular and colloidal fluids: a microscopic approach to fluid mechanics
• Generalized dynamical density functional theory for classical fluids and the significance of inertia and hydrodynamic interactions
• An Efficient Algorithm for Classical Density Functional Theory in Three Dimensions: Ionic Solutions
• Fundamental measure theory for the electric double layer: implications for blue-energy harvesting and water desalination
• Critical Point Wedge Filling
• Geometry-induced phase transition in fluids: capillary prewetting
• Fluid structure in the immediate vicinity of an equilibrium three-phase contact line and assessment of disjoining pressure models using density functional theory
• The overdamped limit of dynamic density functional theory: Rigorous results
• Equilibrium gas-liquid-solid contact angle from density-functional theory
• Do the repulsive and attractive pair forces play separate roles for the physics of liquids?
• Relationship between Local Molecular Field Theory and Density Functional Theory for non-uniform liquids
• Beyond the Dynamic Density Functional theory for steady currents. Application to driven colloidal particles in a channel
• Capillary Contact Angle in a Completely Wet Groove
• Nanoscale fluid structure of liquid-solid-vapour contact lines for a wide range of contact angles
• Non equilibrium inertial dynamics of colloidal systems

Cited by in corpus (8)

• Classical dynamical density functional theory: from fundamentals to applications
• Noisy bounded confidence models for opinion dynamics: the effect of boundary conditions on phase transitions
• Local and Global Perspectives on Diffusion Maps in the Analysis of Molecular Systems
• A density functional approach to ferrogels
• Modelling inelastic granular media using Dynamical Density Functional Theory
• Well-Posedness and Equilibrium Behaviour of Overdamped Dynamic Density Functional Theory
• Hydrodynamic density-functional theory for the moving contact-line problem reveals fluid structure and emergence of a spatially distinct pattern
• PDE-Constrained Optimization Models and Pseudospectral Methods for Multiscale Particle Dynamics