Lattice Boltzmann - Langevin simulations of binary mixtures

Abstract

We report a hybrid numerical method for the solution of the model H fluctuating hydrodynamic equations for binary mixtures. The momentum conservation equations with Landau-Lifshitz stresses are solved using the fluctuating lattice Boltzmann equation while the order parameter conservation equation with Langevin fluxes are solved using the stochastic method of lines. Two methods, based on finite difference and finite volume, are proposed for spatial discretisation of the order parameter equation. Special care is taken to ensure that the fluctuation-dissipation theorem is maintained at the lattice level in both cases. The methods are benchmarked by comparing static and dynamic correlations and excellent agreement is found between analytical and numerical results. The Galilean invariance of the model is tested and found to be satisfactory. Thermally induced capillary fluctuations of the interface are captured accurately, indicating that the model can be used to study nonlinear fluctuations.

References in corpus (6)

• A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales
• Statistical Mechanics of the Fluctuating Lattice Boltzmann Equation
• On the spectrum of fluctuations of a liquid surface: From the molecular scale to the macroscopic scale
• Singular forces and point-like colloids in lattice Boltzmann hydrodynamics
• Spatially Adaptive Stochastic Multigrid Methods for Fluid-Structure Systems with Thermal Fluctuations
• Thermal fluctuations in the lattice Boltzmann method for non-ideal fluids

Cited by in corpus (17)

• A novel coarsening mechanism of droplets in immiscible fluid mixtures
• Do liquid drops roll or slide on inclined surfaces?
• Mesoscale Structures at Complex Fluid-Fluid Interfaces: a Novel Lattice Boltzmann / Molecular Dynamics Coupling
• Modeling Multi-phase Flow using Fluctuating Hydrodynamics
• Stochastic Simulation of Reaction-Diffusion Systems: A Fluctuating-Hydrodynamics Approach
• Low Mach Number Fluctuating Hydrodynamics of Diffusively Mixing Fluids
• Low Mach Number Fluctuating Hydrodynamics of Binary Liquid Mixtures
• Fluctuating Multicomponent Lattice Boltzmann Model
• Lattice Boltzmann Electrokinetics simulation of nanocapacitors
• Effects of thermal fluctuations in the fragmentation of a nano-ligament
• A Fluctuating Lattice Boltzmann Method for the Diffusion Equation
• Integer Lattice Gas with Monte Carlo collision operator recovers the entropic lattice Boltzmann method with Poisson distributed fluctuations
• Discrete unified gas kinetic scheme for nonlinear convection-diffusion equations
• Large fluctuations in non-ideal coarse-grained systems
• Fluctuation-induced dynamics of nematic topological defects
• Simulation of static critical phenomena in non-ideal fluids with the Lattice Boltzmann method
• Isotropic finite-difference discretization of stochastic conservation laws preserving detailed balance