Lattice ellipsoidal statistical BGK model for thermal non-equilibrium flows

A thermal lattice Boltzmann model is constructed on the basis of the ellipsoidal statistical Bhatnagar-Gross-Krook (ES-BGK) collision operator via the Hermite moment representation. The resulting lattice ES-BGK model uses a single distribution function and features an adjustable Prandtl number. Numerical simulations show that using a moderate discrete velocity set, this model can accurately recover steady and transient solutions of the ES-BGK equation in the slip-flow and early transition regimes in the small Mach number limit that is typical of microscale problems of practical interest. In the transition regime in particular, comparisons with numerical solutions of the ES-BGK model, direct Monte Carlo and low-variance deviational Monte Carlo simulations show good accuracy for values of the Knudsen number up to approximately 0:5. On the other hand, highly non-equilibrium phenomena characterized by high Mach numbers, such as viscous heating and force-driven Poiseuille flow for large values of the driving force, are more difficult to capture quantitatively in the transition regime using discretizations that have been chosen with computational efficiency in mind such as the one used here, although improved accuracy is observed as the number of discrete velocities is increased

A mesoscopic model for microscale hydrodynamics and interfacial phenomena: Slip, films, and contact angle hysteresis

We present a model based on the lattice Boltzmann equation that is suitable for the simulation of dynamic wetting. The model is capable of exhibiting fundamental interfacial phenomena such as weak adsorption of fluid on the solid substrate and the presence of a thin surface film within which a disjoining pressure acts. Dynamics in this surface film, tightly coupled with hydrodynamics in the fluid bulk, determine macroscopic properties of primary interest: the hydrodynamic slip; the equilibrium contact angle; and the static and dynamic hysteresis of the contact angles. The pseudo- potentials employed for fluid-solid interactions are composed of a repulsive core and an attractive tail that can be independently adjusted. This enables effective modification of the functional form of the disjoining pressure so that one can vary the static and dynamic hysteresis on surfaces that exhibit the same equilibrium contact angle. The modeled solid-fluid interface is diffuse, represented by a wall probability function which ultimately controls the momentum exchange between solid and fluid phases. This approach allows us to effectively vary the slip length for a given wettability (i.e. the static contact angle) of the solid substrate

Mesoscopic simulation of diffusive contaminant spreading in gas flows at low pressure

Many modern production and measurement facilities incorporate multiphase systems at low pressures. In this region of flows at small, non-zero Knudsen- and low Mach numbers the classical mesoscopic Monte Carlo methods become increasingly numerically costly. To increase the numerical efficiency of simulations hybrid models are promising. In this contribution, we propose a novel efficient simulation approach for the simulation of two phase flows with a large concentration imbalance in a low pressure environment in the low intermediate Knudsen regime. Our hybrid model comprises a lattice-Boltzmann method corrected for the lower intermediate Kn regime proposed by Zhang et al. for the simulation of an ambient flow field. A coupled event-driven Monte-Carlo-style Boltzmann solver is employed to describe particles of a second species of low concentration. In order to evaluate the model, standard diffusivity and diffusion advection systems are considered.Comment: 9 pages, 8 figure

Multiple-relaxation-time discrete Boltzmann modeling of multicomponent mixture with nonequilibrium effects

A multiple-relaxation-time discrete Boltzmann model (DBM) is proposed for multicomponent mixtures, where compressible, hydrodynamic, and thermodynamic nonequilibrium effects are taken into account. It allows the specific heat ratio and the Prandtl number to be adjustable, and is suitable for both low and high speed fluid flows. From the physical side, besides being consistent with the multicomponent Navier-Stokes equations, Fick's law, and Stefan-Maxwell diffusion equation in the hydrodynamic limit, the DBM provides more kinetic information about the nonequilibrium effects. The physical capability of DBM to describe the nonequilibrium flows, beyond the Navier-Stokes representation, enables the study of the entropy production mechanism in complex flows, especially in multicomponent mixtures. Moreover, the current kinetic model is employed to investigate nonequilibrium behaviors of the compressible Kelvin-Helmholtz instability (KHI). The entropy of mixing, the mixing area, the mixing width, the kinetic and internal energies, and the maximum and minimum temperatures are investigated during the dynamic KHI process. It is found that the mixing degree and fluid flow are similar in the KHI process for cases with various thermal conductivity and initial temperature configurations, while the maximum and minimum temperatures show different trends in cases with or without initial temperature gradients. Physically, both heat conduction and temperature exert slight influences on the formation and evolution of the KHI morphological structure

Multi-Particle Collision Dynamics -- a Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids

In this review, we describe and analyze a mesoscale simulation method for fluid flow, which was introduced by Malevanets and Kapral in 1999, and is now called multi-particle collision dynamics (MPC) or stochastic rotation dynamics (SRD). The method consists of alternating streaming and collision steps in an ensemble of point particles. The multi-particle collisions are performed by grouping particles in collision cells, and mass, momentum, and energy are locally conserved. This simulation technique captures both full hydrodynamic interactions and thermal fluctuations. The first part of the review begins with a description of several widely used MPC algorithms and then discusses important features of the original SRD algorithm and frequently used variations. Two complementary approaches for deriving the hydrodynamic equations and evaluating the transport coefficients are reviewed. It is then shown how MPC algorithms can be generalized to model non-ideal fluids, and binary mixtures with a consolute point. The importance of angular-momentum conservation for systems like phase-separated liquids with different viscosities is discussed. The second part of the review describes a number of recent applications of MPC algorithms to study colloid and polymer dynamics, the behavior of vesicles and cells in hydrodynamic flows, and the dynamics of viscoelastic fluids

Discrete Boltzmann modeling of unsteady reactive flows with nonequilibrium effects

A multiple-relaxation-time discrete Boltzmann model (DBM) is developed for compressible thermal reactive flows. A unified Boltzmann equation set is solved for hydrodynamic and thermodynamic quantities as well as higher order kinetic moments. The collision, reaction, and force terms are uniformly calculated with a matrix inversion method, which is physically accurate, numerically efficient, and convenient for coding. Via the Chapman-Enskog analysis, the DBM is demonstrated to recover reactive Navier-Stokes (NS) equations in the hydrodynamic limit. Both specific heat ratio and Prandtl number are adjustable. Moreover, it provides quantification of hydrodynamic and thermodynamic nonequilibrium effects beyond the NS equations. The capability of the DBM is demonstrated through simulations of chemical reactions in the free falling process, sound wave, thermal Couette flow, and steady and unsteady detonation cases. Moreover, nonequilibrium effects on the predicted physical quantities in unsteady combustion are quantified via the DBM. It is demonstrated that nonequilibrium effects suppress detonation instability and dissipate small oscillations of fluid flows

The shear viscosity of interacting graphene

One of the hallmark properties of fluids is their shear viscosity which is, among other things, responsible for parabolic flow profiles through narrow channels. In recent years, there has been a growing number of observations of said flow profiles in electronic transport measurements in a variety of material systems, most notably in graphene. In this paper, we investigate the shear viscosity of interacting graphene from a theoretical point of view. We study both a phenomenological as well as a microscopic model and find excellent agreement between the two. Our main finding is collective modes make a sizeable contribution to the viscosity that can equal or even outweigh the electronic contribution that is usually assumed dominant. We comment on how this finding carries over to systems beyond graphene and related Dirac materials

Molecular diffusion and slip boundary conditions at smooth surfaces with periodic and random nanoscale textures

The influence of periodic and random surface textures on the flow structure and effective slip length in Newtonian fluids is investigated by molecular dynamics (MD) simulations. We consider a situation where the typical pattern size is smaller than the channel height and the local boundary conditions at wetting and nonwetting regions are characterized by finite slip lengths. In case of anisotropic patterns, transverse flow profiles are reported for flows over alternating stripes of different wettability when the shear flow direction is misaligned with respect to the stripe orientation. The angular dependence of the effective slip length obtained from MD simulations is in good agreement with hydrodynamic predictions provided that the stripe width is larger than several molecular diameters. We found that the longitudinal component of the slip velocity along the shear flow direction is proportional to the interfacial diffusion coefficient of fluid monomers in that direction at equilibrium. In case of random textures, the effective slip length and the diffusion coefficient of fluid monomers in the first layer near the heterogeneous surface depend sensitively on the total area of wetting regions.Comment: 30 pages, 11 figure