When simulating multicomponent mixtures via the Lattice Boltzmann Method, it is desirable to control the mutual diffusivity between species while maintaining the viscosity of the solution fixed. This goal is herein achieved by a modification of the multicomponent Bhatnagar-Gross-Krook (BGK) evolution equations by introducing two different timescales for mass and momentum diffusion. Diffusivity is thus controlled by an effective drag force acting between species. Numerical simulations confirm the accuracy of the method for neutral binary and charged ternary mixtures in bulk conditions. The simulation of a charged mixture in a charged slit channel show that the conductivity and electro-osmotic mobility exhibit a departure from the Helmholtz-Smoluchowski prediction at high diffusivity.
A new lattice Boltzmann model for reactive ideal gas mixtures is presented. The model is an extension to reactive flows of the recently proposed multi-component lattice Boltzmann model for compressible ideal gas mixtures with Stefan-Maxwell diffusion for species interaction. First, the kinetic model for the Stefan--Maxwell diffusion is enhanced to accommodate a source term accounting the change of the mixture composition due to chemical reaction. Second, by including the heat of formation in the energy equation, the thermodynamic consistency of the underlying compressible lattice Boltzmann mod…
In the present paper, a new model of the collision term, of the Boltzmann Kinetic equation dealing with binary gas mixture affected by a centrifugal field, is introduced. The new model is representing a modification of the BGK (Bhatnagar-Gross-Krook) model of the Boltzmann kinetic equation to be suitable for studying the influence of centrifugal field affected on gases mixture. The scientific achievement of the new model is that it is a very simple model without any mathematical complexity; but without any loss of generality. We shed light upon that the new model is satisfied the conservation …
Exact bulk correlation functions in one-dimensional nonadditive hard-core mixtures
在最近的一篇论文[Phys. Rev. E \textbf{76}，031202（2007）]中，Schmidt提出了一维非加性硬棒流体混合物的基本测度密度泛函理论，并将其对体结构性质的预测与蒙特卡罗模拟进行了比较。这份简要报告的目的是回顾这个问题承认一个确切的解决方案，这是简要地总结在一个独立的方式。
A new lattice Boltzmann model (LBM) for chemically reactive mixtures is presented. The approach capitalizes on the recently introduced thermodynamically consistent LBM for multicomponent mixtures of ideal gases. Similar to the non-reactive case, the present LBM features Stefan--Maxwell diffusion of chemical species and a fully on-lattice mean-field realization of the momentum and energy of the flow. Besides introducing the reaction mechanism into the kinetic equations for the species, the proposed LBM also features a new realization of the compressible flow by using a concept of extended equil…
We consider the effects of thermal noise on the Batchelor-Kraichnan theory of high Schmidt-number mixing in the viscous-dissipation range of turbulent flows. Using fluctuating hydrodynamics for a binary fluid mixture at low Mach numbers, we justify linearization around the deterministic Navier-Stokes solution in the dissipation range. For the latter solution we adopt the standard Kraichnan model and derive asymptotic high-Schmidt limiting equations for the concentration field, in which the thermal velocity fluctuations are exactly represented by a Gaussian random velocity which is white in tim…
In dilute gas kinetic theory, model collision dynamics such as Bhatnagar-Gross-Krook (BGK) model is often used to get a better insight and numerical modelling. BGK model and its variants assume that highly nonlinear collision term can be replaced by a simple relaxation dynamics towards Maxwell-Boltzmann distribution. Lebowitz et al., proposed an alternative framework for the collision model, known as Fokker-Planck model, where the relaxation of an arbitrary distribution towards Maxwell-Boltzmann distribution is modelled as a drift-diffusion process in velocity space. In the present manuscript,…
Applications of the kinetic theory for a model of a confined quasi-two dimensional granular mixture: Stability analysis and thermal diffusion segregation
In this work we study a r-species mixture of gases within the relativistic kinetic theory point of view. We use the relativistic covariant full Boltzmann equation and we incorporate the Schwarzschild metric. The method of solution of the Boltzmann equation is a combination of the Chapman-Enskog and Grad representations. The thermodynamic fluxes are expressed as functions of the thermodynamic forces so that the generalized expressions for the Navier-Stokes, Fick and Fourier laws are obtained. The constitutive equations for the diffusion and heat fluxes of the mixture are functions of thermal an…
The dynamical properties of a tracer or impurity particle immersed in a host gas of inelastic and rough hard spheres in the homogeneous cooling state is studied. Specifically, the breakdown of energy equipartition as characterized by the tracer/host ratios of translational and rotational temperatures is analyzed by exploring a wide spectrum of values of the control parameters of the system (masses, moments of inertia, sizes, and coefficients of restitution). Three complementary approaches are considered. On the theoretical side, the Boltzmann and Boltzmann--Lorentz equations (both assuming the…
We solve the Cauchy problem for the full non-linear homogeneous Boltzmann system of equations describing multi-component monatomic gas mixtures for binary interactions in three dimensions. More precisely, we show existence and uniqueness of the vector value solution by means of an existence theorem for ODE systems in Banach spaces under the transition probability rates assumption corresponding to hard potentials rates in the interval $(0,1]$, with an angular section modeled by an integrable function of the angular transition rates modeling binary scattering effects. The initial data for the ve…
