Liquid drops on a surface: using density functional theory to calculate the binding potential and drop profiles and comparing with results from mesoscopic modelling

Abstract

The contribution to the free energy for a film of liquid of thickness $h$ on a solid surface, due to the interactions between the solid-liquid and liquid-gas interfaces is given by the binding potential, $g(h)$. The precise form of $g(h)$ determines whether or not the liquid wets the surface. Note that differentiating $g(h)$ gives the Derjaguin or disjoining pressure. We develop a microscopic density functional theory (DFT) based method for calculating $g(h)$, allowing us to relate the form of $g(h)$ to the nature of the molecular interactions in the system. We present results based on using a simple lattice gas model, to demonstrate the procedure. In order to describe the static and dynamic behaviour of non-uniform liquid films and drops on surfaces, a mesoscopic free energy based on $g(h)$ is often used. We calculate such equilibrium film height profiles and also directly calculate using DFT the corresponding density profiles for liquid drops on surfaces. Comparing quantities such as the contact angle and also the shape of the drops, we find good agreement between the two methods. We also study in detail the effect on $g(h)$ of truncating the range of the dispersion forces, both those between the fluid molecules and those between the fluid and wall. We find that truncating can have a significant effect on $g(h)$ and the associated wetting behaviour of the fluid.

16 pages, 13 figs

References in corpus (21)

• Dynamic Density Functional Theory of Fluids
• Dynamical density functional theory and its application to spinodal decomposition
• Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic?
• Why is surface tension a force parallel to the interface?
• Dynamical density functional theory for molecular and colloidal fluids: a microscopic approach to fluid mechanics
• Local mean-field study of capillary condensation in silica aerogels
• Dynamical density functional theory for dense atomic liquids
• Modelling the formation of structured deposits at receding contact lines of evaporating solutions and suspensions
• Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growth
• Parameter passing between Molecular Dynamics and continuum models for droplets on solid substrates - The static case
• An Introduction to Microscopic Theories for Inhomogeneous Liquids: Getting Started with Density Functional Theory
• Fluid structure in the immediate vicinity of an equilibrium three-phase contact line and assessment of disjoining pressure models using density functional theory
• Equilibrium gas-liquid-solid contact angle from density-functional theory
• Derivation of a Non-Local Interfacial Hamiltonian for Short-Ranged Wetting II: General Diagrammatic Structure
• Modelling the evaporation of thin films of colloidal suspensions using Dynamical Density Functional Theory
• Capillary Fluctuations and Film-Height-Dependent Surface Tension of an Adsorbed Liquid Film
• Relationship between Local Molecular Field Theory and Density Functional Theory for non-uniform liquids
• Nucleation of liquid droplets in a fluid with competing interactions
• Sedimentation of a two-dimensional colloidal mixture exhibiting liquid-liquid and gas-liquid phase separation: a dynamical density functional theory study
• Wetting in electrolyte solutions
• Order of wetting transitions in electrolyte solutions

Cited by in corpus (29)

• Classical dynamical density functional theory: from fundamentals to applications
• A unified description of hydrophilic and superhydrophobic surfaces in terms of the wetting and drying transitions of liquids
• Gradient dynamics models for liquid films with soluble surfactant
• Recent advances in and future challenges for mesoscopic hydrodynamic modelling of complex wetting
• Equilibrium contact angle and adsorption layer properties with surfactants
• Influence of the fluid structure on the binding potential: comparing liquid drop profiles from density functional theory with results from mesoscopic theory
• Films, layers and droplets: The effect of near-wall fluid structure on spreading dynamics
• A macroscopic model for sessile droplet evaporation on a flat surface
• Capillary Wave Theory of Adsorbed Liquid Films and the Structure of the Liquid-Vapor Interface
• Instabilities of layers of deposited molecules on chemically stripe patterned substrates: Ridges vs. drops
• Discrete self-similarity in interfacial hydrodynamics and the formation of iterated structures
• Soft wetting with (a)symmetric Shuttleworth effect
• Lifshitz theory of wetting films at three phase coexistence: The case of ice nucleation on Silver Iodide (AgI)
• Dynamical density functional theory for the evaporation of droplets of nanoparticle suspension
• Comparing kinetic Monte Carlo and Thin-Film Modeling of Transversal Instabilities of Ridges on Patterned Substrates
• Binding potential and wetting behaviour of binary liquid mixtures on surfaces
• Experimental and Theoretical Bulk Phase Diagram and Interfacial Tension of Ouzo
• Modelling the evaporation of nanoparticle suspensions from heterogeneous surfaces
• Thermal fluctuations of an interface near a contact line
• Kinetic Monte Carlo and hydrodynamic modelling of droplet dynamics on surfaces, including evaporation and condensation
• Nudged Elastic Band calculation of the binding potential for liquids at interfaces
• Deformation and dewetting of liquid films under gas jets
• Phase Field Simulation of Liquid Filling on Grooved Surfaces for Complete, Partial and Pseudo-partial Wetting Cases
• Coexisting multiphase and interfacial behaviour of ouzo
• Dynamics of particle aggregation in dewetting films of complex liquids
• Stability of nanoparticle laden aerosol liquid droplets
• Binding potentials for vapour nanobubbles on surfaces using density functional theory
• Classical density functional theory for nanoparticle-laden droplets
• Interactions between droplets in immiscible liquid suspensions and the influence of surfactants