Boltzmann Model Research Articles

Macroscopic finite-difference scheme and modified equationsof the general propagation multiple-relaxation-time lattice Boltzmann model.

In this paper we first present the general propagation multiple-relaxation-time lattice Boltzmann (GPMRT-LB) model and obtain the corresponding macroscopic finite-difference (GPMFD) scheme on conservative moments. Then based on the Maxwell iteration method, we conduct the analysis on the truncation errors and modified equations(MEs) of the GPMRT-LB model and GPMFD scheme at both diffusive and acoustic scalings. For the nonlinear anisotropic convection-diffusion equation(NACDE) and Navier-Stokes equations(NSEs), we also derive the first- and second-order MEs of the GPMRT-LB model and GPMFD scheme. In particular, for the one-dimensional convection-diffusion equation(CDE) with the constant velocity and diffusion coefficient, we can develop a fourth-order GPMRT-LB (F-GPMRT-LB) model and the corresponding fourth-order GPMFD (F-GPMFD) scheme at the diffusive scaling. Finally, three benchmark problems, the Gauss hill problem, the CDE with nonlinear convection and diffusion terms, and the Taylor-Green vortex flow in two-dimensional space, are used to test the GPMRT-LB model and GPMFD scheme, and it is found that the numerical results not only are in good agreement with corresponding analytical solutions, but also have a second-order convergence rate in space. Additionally, a numerical study on one-dimensional CDE also demonstrates that the F-GPMRT-LB model and F-GPMFD scheme can achieve a fourth-order accuracy in space, which is consistent with our theoretical analysis.

A Block Triple-Relaxation-Time Lattice Boltzmann Method for Solid–Liquid Phase Change Problem

This study introduces a block triple-relaxation-time (B-TriRT) lattice Boltzmann model designed specifically for simulating melting phenomena within a rectangular cavity subject to intense heating from below, characterized by high Rayleigh (Ra) numbers (Ra=108). Through benchmark testing, it is demonstrated that the proposed B-TriRT approach markedly mitigates numerical diffusion along the phase interface. Furthermore, an examination of the heated region’s placement is conducted, revealing its significant impact on the rate of melting. Notably, findings suggest that optimal melting occurs most rapidly when the heated region is positioned centrally within the cavity.

Preparation of chitosan-hyaluronic acid microcapsules and its dynamic release behavior analysis in a 3D-printed microchannel system: Exploration and verification

This research focuses on the challenges of efficiently constructing drug carriers and evaluating their dynamic release in vitro simulation. By using pickering emulsion and layer-by-layer self-assembly methods. The microcapsules had tea tree oil as the core material, SiO2 nanoparticles as stabilizers, and chitosan and hyaluronic acid as shell materials. The microencapsulation mechanism, as well as the effects of core-shell mass ratio and stirring, were discussed. Specifically, a dynamic circulation simulation microchannel system was designed and manufactured based on 3D printing technology. In this simulation system, the release rate of microcapsules is accelerated and the trend changes, with its behavior aligning with the Boltzmann model. The study demonstrates the advantages of self-assembled inorganic-organic drug-loaded microcapsules in terms of controllable fabrication and ease of functional modification, and shows the potential of 3D printed cyclic microchannel systems in terms of operability and simulation fidelity in drug and physiological analysis.

Lattice Boltzmann modelling and study of droplet equatorial streaming in an electric field

Lattice Boltzmann modelling and study of droplet equatorial streaming in an electric field

Analysis of the Epidemic Curve of the Waves of COVID-19 Using Integration of Functions and Neural Networks in Peru

The coronavirus (COVID-19) pandemic continues to claim victims. According to the World Health Organization, in the 28 days leading up to 25 February 2024 alone, the number of deaths from COVID-19 was 7141. In this work, we aimed to model the waves of COVID-19 through artificial neural networks (ANNs) and the sigmoidal–Boltzmann model. The study variable was the global cumulative number of deaths according to days, based on the Peru dataset. Additionally, the variables were adapted to determine the correlation between social isolation measures and death rates, which constitutes a novel contribution. A quantitative methodology was used that implemented a non-experimental, longitudinal, and correlational design. The study was retrospective. The results show that the sigmoidal and ANN models were reasonably representative and could help to predict the spread of COVID-19 over the course of multiple waves. Furthermore, the results were precise, with a Pearson correlation coefficient greater than 0.999. The computational sigmoidal–Boltzmann model was also time-efficient. Moreover, the Spearman correlation between social isolation measures and death rates was 0.77, which is acceptable considering that the social isolation variable is qualitative. Finally, we concluded that social isolation measures had a significant effect on reducing deaths from COVID-19.

Three-dimensional lattice Boltzmann model with self-tuning equationof state for multiphase flows.

In this work, the recent lattice Boltzmann (LB) model with self-tuning equationof state (EOS) [Huang et al., Phys. Rev. E 99, 023303 (2019)2470-004510.1103/PhysRevE.99.023303] is extended to three dimensions for the simulation of multiphase flows, which is based on the standard three-dimensional 27-velocity lattice and multiple-relaxation-time collision operator. To achieve the self-tuning EOS, the equilibrium moment is devised by introducing a built-in variable, and the collision matrix is improved by introducing some velocity-dependent nondiagonal elements. Meanwhile, the additional cubic terms of velocity in recovering the Newtonian viscous stress are eliminated to enhance the numerical accuracy. For modeling multiphase flows, an attractive pairwise interaction force is introduced to mimic the long-range molecular interaction, and a consistent scheme is proposed to compensate for the ɛ^{3}-order discrete lattice effect. Thermodynamic consistency in a strict sense is established for the multiphase LB model with self-tuning EOS, and the wetting condition is also treated in a thermodynamically consistent manner. As a result, the contact angle, surface tension, and interface thickness can be independently adjusted in the present theoretical framework. Numerical tests are first performed to validate the multiphase LB model with self-tuning EOS and the theoretical analyses of bulk and surface thermodynamics. The collision of equal-sized droplets is then simulated to demonstrate the applicability and effectiveness of the present LB model for multiphase flows.

The Lattice Boltzmann Simulation of Free Convection Heat Transfer of a Carbon-Nanotube Nanofluid in a Triangular Cavity with a Solar Heater

In this paper, the flow and free convection heat transfer of a multi-walled carbon nanotube/water nanofluid in a triangular cavity with a solar heater is studied using the lattice Boltzmann method. The side walls of the cavity are cold and the bottom wall is partially heated by a solar heater, which have a non-uniform temperature distribution. It is assumed that the heating energy is provided by an absorber that is directly exposed to sunlight. Because of the limited variations of density, the Boussinesq approximation is used, which causes the coupling of hydrodynamic and thermal fields. For velocity and temperature distribution functions, a lattice Boltzmann model with two dimensions and nine directions is adopted. The effect of parameters, such as the Rayleigh number, the volume fraction of nanoparticles, and the position of solar heater, on the flow and heat fields is studied. The results show that, for all Rayleigh numbers studied, the Nusselt number increases as nanoparticles volume fraction increases. The addition of 4% nanoparticles causes the average Nusselt number to increase about 11% at low (Ra = 103) and moderate (Ra = 104) Rayleigh numbers and 217% at the high Rayleigh number (Ra = 105). Furthermore, it is shown that for a fixed Rayleigh number, heat transfer can be optimized by adjusting solar heater’s position. This study can provide a useful insight for utilizing solar heaters with non-uniform temperature distribution in triangular cavities.

Double distribution function-based lattice Boltzmann flux solver for simulation of compressible viscous flows

In this work, a double distribution function-based lattice Boltzmann flux solver (LBFS) is proposed for simulating compressible viscous flows. This approach utilizes the double distribution function compressible lattice Boltzmann model and employs Chapman–Enskog expansion analysis to connect the lattice Boltzmann equation (LBE) with the Navier–Stokes (N–S) equations. Unlike conventional computational fluid dynamics methods that compute inviscid and viscous fluxes separately, the present method simultaneously evaluates both types of fluxes at the cell interface by locally reconstructing the solution of the LBE. Recognizing the significance of considering the non-equilibrium part of distribution functions for viscous flows, a straightforward method is introduced to calculate this component. This facilitates the derivation of computational expressions for macroscopic conservative variables and fluxes in the N–S equations. To validate the accuracy and stability of the present numerical scheme, various benchmark problems, including shock tube problem, Couette flow, lid-driven cavity flow, and flow around the NACA0012 airfoil, are tested. The obtained numerical results are compared with analytical solutions or existing reference data, confirming the capability of the proposed LBFS to deliver accurate and stable numerical results for compressible flows. Moreover, this method demonstrates effectiveness in handling viscous flow problems on non-uniform grids and with curved boundaries.

Simulating dynamics of ellipsoidal particles using lattice Boltzmann method.

Anisotropic particles are often encountered in different fields of soft matter and complex fluids. In this work, we present an implementation of the coupled hydrodynamics of solid ellipsoidal particles and the surrounding fluid using the lattice Boltzmann method. A standard link-based mechanism is used to implement the solid-fluid boundary conditions. We develop an implicit method to update the position and orientation of the ellipsoid. This exploits the relations between the quaternion which describes the ellipsoid's orientation and the ellipsoid's angular velocity to obtain a stable and robust dynamic update. The proposed algorithm is validated by looking at four scenarios: (i) the steady translational velocity of a spheroid subject to an external force in different orientations, (ii) the drift of an inclined spheroid subject to an imposed force, (iii) three-dimensional rotational motions in a simple shear flow (Jeffrey's orbits), and (iv) developed fluid flows and self-propulsion exhibited by a spheroidal microswimmer. In all cases the comparison of numerical results shows good agreement with known analytical solutions, irrespective of the choice of the fluid properties, geometrical parameters, and lattice Boltzmann model, thus demonstrating the robustness of the proposed algorithm.

Variational solution to the lattice Boltzmann method for Couette flow.

Literature studies of the lattice Boltzmann method (LBM) demonstrate hydrodynamics beyond the continuum limit. This includes exact analytical solutions to the LBM, for the bulk velocity and shear stress of Couette flow under diffuse reflection at the walls through the solution of equivalent moment equations. We prove that the bulk velocity and shear stress of Couette flow with Maxwell-type boundary conditions at the walls, as specified by two-dimensional isothermal lattice Boltzmann models, are inherently linear in Mach number. Our finding enables a systematic variational approach to be formulated that exhibits superior computational efficiency than the previously reported moment method. Specifically, the number of partial differential equations(PDEs) in the variational method grows linearly with quadrature order while the number of moment method PDEs grows quadratically. The variational method directly yields a system of linear PDEs that provide exact analytical solutions to the LBM bulk velocity field and shear stress for Couette flow with Maxwell-type boundary conditions. It is anticipated that this variational approach will find utility in calculating analytical solutions for novel lattice Boltzmann quadrature schemes and other flows.

Water–ice phase transition in frozen soils: a mesoscopic numerical study based on lattice Boltzmann method

ABSTRACT The phenomenon of water–ice phase transition in frozen soils is the key to explaining the mechanism of frost heaving and thawing settlement disaster. However, numerical analysis of water–ice phase transitions in frozen soils at mesoscale is rarely reported. This study combines the modified Gibbs-Thomson equation and the enthalpy-based lattice Boltzmann model, and develops a mesoscale numerical method to simulate the water–ice phase transition in the local pores of saturated frozen soil during freezing and thawing process. In order to accurately simulate this process, a new η coefficient is proposed to modify the Gibbs-Thomson equation, which is unrelated to the type of soil sample and gradation characteristics. According to the particle size distribution curve, the two-dimensional random circle generation method is used to reconstruct the soil pore structure. The freezing and thawing processes are verified with the experimental data. A larger non-uniformity coefficient C u and curvature coefficient C c of the grain size distribution result in a lower degree of subcooling and lower residual water content of the soil during the freezing process. The new model provides an effective means to understand the water–ice phase transition in frozen soil at a mesoscopic scale.

Hydrophobic hypercrosslinked polymers prepared by secondary pore-forming method as excellent toluene adsorbents

In this work, inspired by molecular imprinting technology, we developed a secondary pore-forming method to chemically etch three hypercrosslinked polymers which are constructed from three novel hexapolar monomers containing imine groups, resulting in three novel hydrophobic porous hyper-crosslinked polymers (HCPs) pGly-TPA, pP-TPA and pBP-TPA. The structures were determined by FT-IR and solid-state 13C NMR spectroscopic techniques. The specific surface areas of pGly-TPA, pP-TPA and pBP-TPA are 694.1, 197.9 and 497.7 m2/g, respectively. All three porous polymers exhibit high hydrophobic properties with wetting angles of much greater than 90°. The breakthrough adsorption experiments revealed that the three prepared polymers exhibited significant adsorption capacity for toluene (322.05 mg/g for pGly-TPA, 114.43 mg/g for pP-TPA and 279.14 mg/g for pBP-TPA), but showed almost no adsorption for ethyl acetate, cyclohexane, and n-hexane, exhibiting certain molecular size and polarity selectivity. The adsorption behaviors of toluene on pGly-TPA, pP-TPA and pBP-TPA can be fit by the Boltzmann model and the Yoon-Nelson model, suggesting that the fixed bed has low mass transfer resistance. The adsorption rate is controlled by both external diffusion and intraparticle diffusion, as shown by the intraparticle diffusion model analysis. In addition, the adsorption capacity of toluene on pGly-TPA is almost unchanged under high humidity (70 %) or five adsorption–desorption processes, which demonstrates exceptional water-resistance and stability. This work is a reference for preparing novel hydrophobic HCPs using the secondary pore-forming method for removing VOCs from humid air.

Mesoscopic lattice Boltzmann modeling of dense gas flows in curvilinear geometries

Mesoscopic lattice Boltzmann modeling of dense gas flows in curvilinear geometries

Longitudinal transducer based membrane resonant ejector for high-viscosity and high-frequency micro-droplet jetting

Aiming at the requirement for high-precision on-demand droplet jetting of high-viscosity industrial inks, a longitudinal-transducer-based membrane resonant droplet ejector (LT-MRDE) is designed and fabricated in this work. The jetting and observing system of LT-MRDE is set up to quantitatively explore the variations of droplet volume and velocity with driving voltage. Moreover, the three-dimensional (3D) multi-relaxation-time (MRT) lattice Boltzmann (LB) model coupled immersed boundary (IB) is employed to elucidate the effects of driving voltage and liquid viscosity on droplet characteristics. Experimental results demonstrate that the LT-MRDE could stably eject the silicone oil with a viscosity of 100 mPa·s from ∼50 μm vibrating orifice. Furthermore, both the volume and velocity of droplet exhibit a proportionality to voltage and an inverse proportionality to viscosity. The optimal droplet volume and velocity of 100 mPa·s silicon oil are 67.27 pL and 9.07 m/s with the driving parameters of 75 Vpp/14.754 kHz. With high jetting frequency and controllable droplet volume, LT-MRDE provides a new alternative for on-demand precision jetting of high-viscosity industrial inks.

A study on the distribution and movement of water in unsaturated cement paste by a multi-component multi-phase lattice Boltzmann simulation

The distribution of water inside concrete is a crucial factor that determines its mechanical performance and durability. In contrast to experimental investigation, numerical models provide a new way to visualize and characterize the actual situation of water in unsaturated cementitious materials. However, the interactions between different components are quite complex and they are rarely considered so far. In this work, a multi-component multi-phase (MCMP) lattice Boltzmann model is developed to distribute moisture in partially saturated cement paste, in which the interactions between water and air are fully taken into account. The transport of water flow in unsaturated cement paste is modelled and the permeability is thus computed. The simulation results show a satisfactory agreement with experimental data, validating the proposed approach. The obtained permeability is found to decline at a decreased water saturation degree and this is attributed to a reduced number of transport paths for water flow. Moreover, as the contact angle increases from 80° to 100°, large pores become the preferred place for water to accumulate and the formed clusters are observed. According to the results, a strong correlation between pore structure (i.e., pore size and pore connectivity) and water permeability is found and discussed.

LBM modeling of three-dimensional mixed convection in CZ crystal growth on curvilinear coordinates system

A three-dimensional (3D) thermal lattice Boltzmann model of crystal growth is presented to study the magneto-hydrodynamics (MHD) mixed convection in the melt of Czochralski silicon single crystal growth in this paper. In order to solve the problem of lattice Boltzmann method’s difficulty in solving the flow of 3D cylindrical cavity, the 3D physical model of crystal growth is transformed from the Cartesian coordinate system to the Curvilinear coordinate system. And the irregular grids in the Cartesian coordinate system are transformed into regular grids in the Curvilinear coordinate system to facilitate the establishment of the Lattice Boltzmann model. Under the above operations, two coupled distribution functions are established to solve the governing equations. Two D3Q19 models are adopted to solve the melt velocity and temperature. And the 3D lattice Boltzmann modeling of crystal growth with cylinder boundary is realized by interpolation in Curvilinear coordinate system. The comparison with the experiment and other references proves that the proposed model and boundary treatment scheme is correct and it proposes a new way for studying the 3D crystal growth or other similar 3D cylindrical cavity simulations. Furthermore, the unstable melt flow for two cases are also simulated in this paper and the critical Reynolds number are also obtained. Results show that the introduction of the transverse magnetic field enhances the stability of the crystal growth system and increases the adjustable range of crystal rotation parameter. The obtained conclusion has an important reference for adjusting the process parameters during the CZ crystal growth.

Boltzmann Model Predicts Glycan Structures from Lectin Binding.

Glycans are complex oligosaccharides that are involved in many diseases and biological processes. Unfortunately, current methods for determining glycan composition and structure (glycan sequencing) are laborious and require a high level of expertise. Here, we assess the feasibility of sequencing glycans based on their lectin binding fingerprints. By training a Boltzmann model on lectin binding data, we predict the approximate structures of 88 ± 7% of N-glycans and 87 ± 13% of O-glycans in our test set. We show that our model generalizes well to the pharmaceutically relevant case of Chinese hamster ovary (CHO) cell glycans. We also analyze the motif specificity of a wide array of lectins and identify the most and least predictive lectins and glycan features. These results could help streamline glycoprotein research and be of use to anyone using lectins for glycobiology.

Homogenized color-gradient lattice Boltzmann model for immiscible two-phase flow in multiscale porous media

In this paper, a homogenized multiphase lattice Boltzmann (LB) model is established for parallelly simulating immiscible two-phase flow in both solid-free regions (pore scale) and porous areas (continuum scale). It combines the color-gradient multiphase model with the Darcy–Brinkman–Stokes method by adding a term that includes surface force and drag force of porous matrix to multiple-relaxation-time LB equation in moment space. Moreover, an improved algorithm is proposed to characterize and implement the apparent wettability in the locally homogenized porosity field. Validations and test cases are given to demonstrate the accuracy and robustness of this new model, as well as its applicability for trans-scale fluid simulation of transport and sorption behavior from porous (Darcy flow) area to free (Stokes flow) area. For practicality, the two-phase seepage flow in a composite rock structure with multiscale pores is simulated by this new model, and the effects of viscosity ratio and wettability on the displacement process are discussed.

Optimizing CO2 sequestration in Vapor Extraction Process: A Meso-Scale analysis of oil Viscosity, Permeability, and mobile oil orientation effects

Carbon dioxide (CO2) use in Vapor Extraction (VAPEX) has attracted attention for its potential to enhance oil recovery by altering oil density and viscosity, leading to convective-mixing flow in the VAPEX boundary layer. This study explores CO2 sequestration via dissolution into this layer, with a focus on the impact of oil viscosity, permeability, and mobile oil orientation. An isothermal lattice Boltzmann model, which accounts for the variable oil properties like viscosity and diffusion coefficient dependent on dissolved CO2 concentration, was developed for the analysis. Results show that reduced oil viscosity leads to accelerated growth of density fingers and an expanded area swept by CO2 dissolution. Similarly, heightened permeability and mobile oil angle contribute to these effects. This research provides novel insights into optimizing CO2 sequestration within the VAPEX process.

Equation-of-state-based lattice Boltzmann model of multicomponent adsorption onto fluid–fluid interfaces

In diffuse interface models, such as the lattice Boltzmann method (LBM), interfacial physics plays an important role. An example of an important interfacial phenomenon is adsorption onto a fluid–fluid interface. In the context of LBM, adsorption studies have traditionally only focused on adsorption onto a solid surface. The studies on adsorption onto fluid–fluid interfaces have been qualitative in nature, suffer from restrictions on the number of components, or are based on simple thermodynamic models designed for fully immiscible phases. Our recently published fugacity-based LBM model introduces a platform for the accurate modeling of multiphase fluids unrestricted by the number of components, and governed through accurate equations of state (Soomro and Ayala, 2023). In this study, we utilize the fugacity-based LBM to capture interfacial adsorption. This paper begins by simulating adsorption in a binary system with a flat interface, and shows that the amount of adsorption, quantified by relative adsorption measures, is in exact agreement with Gibbs theory. Next, the analysis is continued for a ternary system with two species adsorbing onto the interface. The binary and ternary simulations are then repeated for the case of a droplet and finally a five component case is presented. The study shows that the fugacity-based LBM can capture adsorption in full agreement with Gibbs adsorption theory. This provides a path for a generalized LBM model for adsorption, based on robust thermodynamic models for the fluids and unrestricted by the number of components, marking a significant contribution to the LBM literature.