Interface physics in microporous media : LDRD final report.

In recent years, the Lattice Boltzmann (LB) method has become a powerful numerical \ntool for simulating complex fluid flows and modeling physics and chemistry in \nfluids. Derived from the continuum Boltzmann equation used in statistical \nmechanics, the LB method has the advantage of describing non-equilibrium dynamics, \nespecially in fluid-flow applications involving interfacial dynamics and complex \nboundaries, without simplifying the physics. In addition, the parallel structure \ninherent in the LB method makes it extremely suitable for parallel computing. \nBecause of these features, the LB method affords the most comprehensive pore-scale \napproach to systematically investigate fundamental issues involving flow and \nreactive transport in porous media. In this paper, the state of the art of this \nmethod is discussed. Specifically, a multi-component LB model for simulating \nreactive transport in porous media at the pore scale is presented. In the model, a \nset of distribution functions is introduced to simulate fluid flow and solute \ntransport. The LB equation for flow recovers the correct pore-scale continuity and \nNavier-Stokes equations. The LB equations for solute transport are modified to \nrecover advection-diffusion equations for total concentrations at the pore scale. \nThe model takes into account advection, diffusion, homogeneous reactions among \nmultiple aqueous species, heterogeneous reactions between the aqueous solution and \nminerals, as well as changes in solid and pore geometry. Homogeneous reactions are \ndescribed through local equilibrium mass action relations. Mineral reactions are \ntreated kinetically through boundary conditions at the mineral surface. Simulation \nexamples presented include injection of carbon dioxide saturated brine into a \nlimestone rock with pore geometry derived from a thin section, crystal formation \nfrom a supersaturated solution without flow, and crystal formation during carbon \ndioxide sequestration in oceanic sediments.

A lattice Boltzmann model for the conjugate heat transfer

Pore-scale investigation on the effect of gas-liquid phase separation on reactive flow in a horizontal rough fracture using the lattice Boltzmann method

The pseudopotential lattice Boltzmann (LB) model is a widely used multiphase model in the LB community. In this model, an interaction force, which is usually implemented via a forcing scheme, is employed to mimic the molecular interactions that cause phase segregation. The forcing scheme is therefore expected to play an important role in the pseudoepotential LB model. In this paper, we aim to address some key issues about forcing schemes in the pseudopotential LB model. First, theoretical and numerical analyses will be made for Shan-Chen's forcing scheme [Shan and Chen, Phys. Rev. E 47, 1815 (1993)] and the exact-difference-method forcing scheme [Kupershtokh et al., Comput. Math. Appl. 58, 965 (2009)]. The nature of these two schemes and their recovered macroscopic equations will be shown. Second, through a theoretical analysis, we will reveal the physics behind the phenomenon that different forcing schemes exhibit different performances in the pseudopotential LB model. Moreover, based on the analysis, we will present an improved forcing scheme and numerically demonstrate that the improved scheme can be treated as an alternative approach to achieving thermodynamic consistency in the pseudopotential LB model.

Characterization of immiscible phase displacement in heterogeneous pore structures: Parallel multicomponent lattice Boltzmann simulation and experimental validation using three-dimensional printing technology

Simulation of two-phase fluid mixture flow in rectangular two-inlet cavity using lattice Boltzmann method

Numerical analyses and optimization of tubular thermochemical heat storage reactors using axisymmetric thermal lattice Boltzmann model

In this paper, we develop an efficient and alternative lattice Boltzmann (LB) model for simulating immiscible incompressible N-phase flows (N≥2) based on the Cahn-Hilliard phase field theory. In order to facilitate the design of LB model and reduce the calculation of the gradient term, the governing equations of the N-phase system are reformulated, and they satisfy the conservation of mass, momentum and the second law of thermodynamics. In the present model, (N-1) LB equations are employed to capture the interface, and another LB equation is used to solve the Navier-Stokes (N-S) equations, where a new distribution function for the total force is delicately designed to reduce the calculation of the gradient term. The developed model is first validated by two classical benchmark problems, including the tests of static droplets and the spreading of a liquid lens, the simulation results show that the current LB model is accurate and efficient for simulating incompressible N-phase fluid flows. To further demonstrate the capability of the LB model, two numerical simulations, including dynamics of droplet collision for four fluid phases and dynamics of droplets and interfaces for five fluid phases, are performed to test the developed model. The results show that the present model can successfully handle complex interactions among N (N≥2) immiscible incompressible flows.

Flows with chemical reactions in porous media are fundamental phenomena encountered in many natural, industrial, and scientific areas. For such flows, most existing studies use continuum assumptions and focus on volume-averaged properties on macroscopic scales. Considering the complex porous structures and fluid–solid interactions in realistic situations, this study develops a sophisticated lattice Boltzmann (LB) model for simulating reactive flows in porous media on the pore scale. In the present model, separate LB equations are built for multicomponent flows and chemical species evolutions, source terms are derived for heat and mass transfer, boundary schemes are formulated for surface reaction, and correction terms are introduced for temperature-dependent density. Thus, the present LB model offers a capability to capture pore-scale information of compressible/incompressible fluid motions, homogeneous reaction between miscible fluids, and heterogeneous reaction at the fluid–solid interface in porous media. Different scenarios of density fingering with homogeneous reaction are investigated, with effects of viscosity contrast being clarified. Furthermore, by introducing thermal flows, the solid coke combustion is modeled in porous media. During coke combustion, fluid viscosity is affected by heat and mass transfer, which results in unstable combustion fronts.

The present paper analyzes the typical unified lattice Boltzmann (LB) models for different convection-diffusion (CD) problems in multiphase systems. The CD problems in multiphase systems can be roughly classified into three groups: CD problems with a continuous scalar value and a continuous flux, a discontinuous scalar value and a continuous flux, a continuous scalar value and a discontinuous flux. The characteristics of the corresponding unified LB models for the three kinds of CD problems are analyzed and the equivalence between the LB models based on different perspectives or numerical schemes is revealed. Finally, a comprehensive multiphase LB model (CMLBM) capable of solving different isotropic and anisotropic CD problems in multiphase systems is proposed. Four typical CD problems in multiphase systems are calculated to validate the CMLBM; the results show that it performs well against the typical isotropic and anisotropic CD problems in multiphase systems.

Cavitation bubble collapse near rough solid wall is modeled by the multi-relaxation-time (MRT) pseudopotential lattice Boltzmann (LB) model. The modified forcing scheme, which can achieve LB model’s thermodynamic consistency by tuning a parameter related with the particle interaction range, is adopted to achieve desired stability and density ratio. The bubble collapse near rough solid wall was simulated by the improved MRT pseudopotential LB model. The mechanism of bubble collapse is studied by investigating the bubble profiles, pressure field and velocity field evolution. The eroding effects of collapsing bubble are analyzed in details. It is found that the process and the effect of the interaction between bubble collapse and rough solid wall are affected seriously by the geometry of solid boundary. At the same time, it demonstrates that the MRT pseudopotential LB model is a potential tool for the investigation of the interaction mechanism between the collapsing bubble and complex geometry boundary.

On the parallelization of the lattice Boltzmann method for turbomachinery applications

Surface tension plays a crucial role in governing interfacial dynamics during phase change phenomena spanning natural systems and industrial applications. The phase-field lattice Boltzmann (LB) method has emerged as a powerful approach for modeling phase change, particularly due to its inherent ability to capture interfacial tension effects in multiphase systems. However, there has been no three-dimensional phase-field LB method capable of simulating phase change initialed from a single-phase medium. In this study, we propose a phase-field-based LB method for modeling thermal phase change. A source term is derived to accurately describe phase change. A key distinguishing feature of our model is its capability to initiate phase change driven by the sensible heat of superheated or supercooled phases, thereby enabling the presence of superheated liquid and supercooled vapor. To validate the proposed model, we perform a series of benchmark tests using D3Q19 LB models with density ratios up to 1:1000. These include (i) a comparison between numerical results and analytical solutions of the one-dimensional Stefan problem and (ii) a quantitative evaluation of bubble departure diameter against the Fritz relation for bubble generation in a pure liquid phase under wall heating. The results demonstrate agreement with theoretical predictions, underscoring the accuracy and robustness of the proposed approach. This study extends the applicability of the LB method to scenarios requiring consideration of both surface tension and thermal phase change, offering a valuable tool for simulating complex multiphase systems.

A pseudopotential multicomponent lattice Boltzmann (LB) model that can account for the real buoyancy effect is proposed to simulate the mass transfer process around a rising bubble. The density profiles at the equilibrium state are determined based on the hydrostatic condition and the zero diffusion flux condition (the balance of chemical potential). Compared with the LB models using effective buoyancy force, the proposed model has three advantages: (1) avoiding the unrealistic distribution of gas components within the bubble due to the upward effective buoyancy force, (2) removing the undesirable diffusion process due to the application of effective buoyancy force, and (3) considering the effect of the pressure gradient on the change of bubble size. In addition, Henry's law, which can be automatically recovered from the multicomponent LB equation, is re-interpreted from the perspective of the balance of chemical potential. Simulation results showed that the diffusion flux non-uniformly distributes over the surface of a rising bubble. The diffusion zone primarily occurs at the top and the lateral side of a rising bubble, whereas the diffusion transport just below the rising bubble is much less significant than its counterpart above the rising bubble. Various bubble shapes and their corresponding diffusion zones have been obtained. Moreover, the correlation between the Sherwood number and the Peclet number derived from the simulation results is consistent with those from previous numerical results. Thus, the proposed LB model is capable of conducting a quantitative analysis of the mass transfer around a rising bubble.

Lattice Boltzmann model for incompressible flows through porous media with time-fractional effects