Modelling Interfacial Dynamics Using Hydrodynamic Density Functional Theory: Dynamic Contact Angles and the Role of Local Viscosity

Abstract

Hydrodynamic density functional theory (DFT) is applied to analyse dynamic contact angles of droplets in order to assess its predictive capability regarding wetting phenomena at the microscopic scale and to evaluate its feasibility for multiscale modelling. Hydrodynamic DFT incorporates the influence of fluid-fluid and solid-fluid interfaces into a hydrodynamic theory by including a thermodynamic model based on classical DFT for the chemical potential of inhomogeneous fluids. It simplifies to the isothermal Navier-Stokes equations far away from interfaces, thus connecting microscopic molecular modelling and continuum fluid dynamics. In this work we use a Helmholtz energy functional based on the perturbed-chain statistical associating fluid theory (PC-SAFT) and the viscosity is obtained from generalised entropy scaling, a one-parameter model which takes microscopic information of the fluid and solid phase into account. Deterministic (noise-free) density and velocity profiles reveal wetting phenomena including different advancing and receding contact angles, the transition from equilibrium to steady state and the rolling motion of droplets. Compared to a viscosity model based on bulk values, generalised entropy scaling provides more accurate results, which stresses the importance of including microscopic information in the local viscosity model. Hydrodynamic DFT is transferable as it captures the influence of different external forces, wetting strengths and (molecular) solid roughness. For all results good quantitative agreement with non-equilibrium molecular dynamics simulations is found, which emphasises that hydrodynamic DFT is able to predict wetting phenomena at the microscopic scale.

31 pages, 27 figures

References in corpus (23)

• Instantaneous Liquid Interfaces
• Dynamical density functional theory and its application to spinodal decomposition
• A variational approach to the moving contact line hydrodynamics
• Classical dynamical density functional theory: from fundamentals to applications
• Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic?
• DuMu${}^{\text{x}}$ 3 -- an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling
• Hydrodynamic theory of de-wetting
• Dynamical density functional theory for molecular and colloidal fluids: a microscopic approach to fluid mechanics
• The van Hove distribution function for Brownian hard spheres: dynamical test particle theory and computer simulations for bulk dynamics
• Power functional theory for Brownian dynamics
• Generalized dynamical density functional theory for classical fluids and the significance of inertia and hydrodynamic interactions
• Dynamical density functional theory for dense atomic liquids
• Dynamical density functional theory: binary phase-separating colloidal fluid in a cavity
• Dynamic Density Functional Theory with hydrodynamic interactions and fluctuations
• Mori-Zwanzig projection operator formalism for systems with time-dependent Hamiltonians
• Velocity gradient power functional for Brownian dynamics
• Equilibrium gas-liquid-solid contact angle from density-functional theory
• Coupling Staggered-Grid and MPFA Finite Volume Methods for Free Flow/Porous-Medium Flow Problems
• Modeling diffusion in colloidal suspensions by dynamical density functional theory using fundamental measure theory of hard spheres
• Dynamical density functional theory for dense suspensions of colloidal hard spheres
• Nonequilibrium phase transitions of sheared colloidal microphases: Results from dynamical density functional theory
• Dynamical density functional theory for orientable colloids including inertia and hydrodynamic interactions
• Hydrodynamic density-functional theory for the moving contact-line problem reveals fluid structure and emergence of a spatially distinct pattern