Fluctuating Multicomponent Lattice Boltzmann Model

Abstract

Current implementations of fluctuating lattice Boltzmann equations (FLBE) describe single component fluids. In this paper, a model based on the continuum kinetic Boltzmann equation for describing multicomponent fluids is extended to incorporate the effects of thermal fluctuations. The thus obtained fluctuating Boltzmann equation is first linearized to apply the theory of linear fluctuations, and expressions for the noise covariances are determined by invoking the fluctuation-dissipation theorem (FDT) directly at the kinetic level. Crucial for our analysis is the projection of the Boltzmann equation onto the ortho-normal Hermite basis. By integrating in space and time the fluctuating Boltzmann equation with a discrete number of velocities, the FLBE is obtained for both ideal and non-ideal multicomponent fluids. Numerical simulations are specialized to the case where mean-field interactions are introduced on the lattice, indicating a proper thermalization of the system.

30 pages, 6 figures

References in corpus (5)

• State-dependent diffusion: thermodynamic consistency and its path integral formulation
• Statistical Mechanics of the Fluctuating Lattice Boltzmann Equation
• Singular forces and point-like colloids in lattice Boltzmann hydrodynamics
• Thermal fluctuations in the lattice Boltzmann method for non-ideal fluids
• Langevin theory of fluctuations in the discrete Boltzmann equation

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