Two-dimensional Lattice Boltzmann Research Articles

Quantifying surface wettability in textured surfaces using two-dimensional pseudo-potential multiphase lattice Boltzmann model

Surface wettability plays a critical role in microfluidic applications, enabling enhanced fluid flow control, minimizing sample waste, and improving efficiency across various fields, including drying technology, food processing, chemical manufacturing, and ­environmental engineering. This study presents a numerical investigation of surface wettability on textured surfaces utilizing a two-dimensional (2D) pseudo-potential multiphase lattice Boltzmann method (LBM) with a D2Q9 model. The analysis is conducted for a range of solid-fluid interaction parameters (Gads ), varying between −2.50 and −1.40. Initially, the equilibrium state of a water droplet on a flat surface is simulated for different interaction parameters to validate the accuracy of the numerical model. Subsequently, micropillars are introduced on the bottom wall of the surface with varying heights and spacings to create hydrophobic and superhydrophobic textures, resulting in enhanced contact angles. The wettability of these surfaces is analyzed by placing a water droplet with a radius of 30 lattice units at the center of a computational domain sized 200 × 200 lattice units. The findings reveal that increasing the interaction parameter on textured surfaces significantly reduces the contact area between the droplet and the solid surface due to the momentum redirection effect, thereby increasing surface surface wettability. Similarly, greater spacing between micropillars enhances surface surface wettability. The simulated contact angles for various interaction strengths have been qualitatively validated with previously reported results, confirming the robustness of the present numerical model.

Flow features induced by a rod-shaped microswimmer and its swimming efficiency: A two-dimensional numerical study

Abstract The swimming performance of rod-shaped microswimmers in a channel was numerically investigated using the two-dimensional lattice Boltzmann method (LBM). We considered variable-length squirmer rods, assembled from circular squirmer models with self-propulsion mechanisms, and analyzed the effects of the Reynolds number (Re), aspect ratio (ε), squirmer-type factor (β) and blockage ratio (κ) on swimming efficiency (η) and power expenditure (P). The results show no significant difference in power expenditure between pushers (microswimmers propelled from the tail) and pullers (microswimmers propelled from the head) at the low Reynolds numbers adopted in this study. However, the swimming efficiency of pushers surpasses that of pullers. Moreover, as the degree of channel blockage increases (i.e., κ increases), the squirmer rod consumes more energy while swimming, and its swimming efficiency also increases, which is clearly reflected when ε ≤ 3. Notably, squirmer rods with a larger aspect ratio ε and a β value approaching 0 can achieve high swimming efficiency with lower power expenditure. The advantages of self-propelled microswimmers are manifested when ε > 4 and β = ±1, where the squirmer rod consumes less energy than a passive rod driven by an external field. These findings underscore the potential for designing more efficient microswimmers by carefully considering the interactions between the microswimmer geometry, propulsion mechanism and fluid dynamic environment.

Research on sedimentation characteristics of squirmer in a power-law fluid.

Sedimentation characteristics of a squirmer in a power-law fluid within a vertical channel are studied numerically using the two-dimensional lattice Boltzmann method. The effects of swimming type (- 5 ≤ β ≤ 5), self-propelling strength (0.5 ≤ α ≤ 1.1), power-law indexes (0.5 ≤ n ≤ 1.5), and the density ratio of the squirmer to the fluid (γ = 1.01, 1.5 and 2.3) on the sedimentation of the squirmer are analyzed. Four settlement patterns are identified: steady falling in the center, downward along the wall, oscillating with large amplitude and oscillating around the centerline. The squirmer in the channel exhibits more fluctuations in shear-thinning (n < 1) and Newtonian (n = 1) fluids compared to shear-thickening fluids (n > 1). Additionally, a puller (β > 0) settles faster than a pusher (β < 0) in shear-thinning and Newtonian fluids. Puller generates flow towards their head and away from their tail, exhibiting small amplitude oscillations. Pushers exhibit higher amplitude oscillations throughout the channel, creating flow towards their tail and away from their head. At lower γ, the fluctuation of the squirmer is less pronounced compared to higher γ.

A novel framework of the lattice Boltzmann model for multilayer shallow water systems

This study proposes a novel framework of the lattice Boltzmann model for multilayer shallow water equations, considering the mass and momentum exchanges between layers (LABMSWE+). Compared with the original LABMSWE model consisting of N two-dimensional lattice Boltzmann method for shallow water equation (LABSWE) models, the new model includes 1+N LABSWE models. The singular LABSWE model with unit relaxation time is introduced to update the total water depth, and thus, the layer water depths can be obtained explicitly through the fixed layer ratios. The N-layer LABSWE models with the multiple-relaxation-time operator evolve the layer velocities. These two modules are coupled by the total water depth and depth-averaged velocities. The constructed model avoids the freely variable layer thicknesses, which is considered as the main source of the instability. In addition, the mass exchanges enable this model to simulate vertical circulation flows, which are beyond the application of the LABMSWE model. Several numerical tests are then conducted to validate the proposed model. The results show that it exactly satisfies the C-property. In addition, the central difference scheme is more stable and accurate than the upwind and nonequilibrium schemes in the computing of the mass exchanges. The numerical results have an excellent agreement with analytical solutions and reference data, while some unstable and nonphysical results are obtained by the original LABMSWE model. Moreover, the computational time is about 40%–60% of that for the MIKE3, a finite volume solver for the three-dimensional shallow water equations by the Danish Hydraulic Institute.

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.

A study on melting characteristics of micron aluminum particles by lattice Boltzmann method

In this article, a two-dimensional lattice Boltzmann model, utilizing enthalpy as a basis, has been constructed to explore the melting behavior of aluminum particles in the micron size range. The study investigates the impacts of several key factors such as particle size, Rayleigh number, Stefan number, and porosity on temperature distribution, liquid fraction, solid-liquid interface, and melting end time. The findings demonstrate that an increase in particle size stimulates the melting process, with a weakened effect observed as particle size continues to increase. Rayleigh number has a significant effect on natural convection and heat transfer, promoting the development of these processes. Additionally, Stefan number presents a noticeable impact on the melting process, with a more apparent effect in the range of low Stefan numbers. Finally, the increase of porosity proves to be a compelling factor in the promotion of the melting process.

An improved axisymmetric interfacial lattice Boltzmann flux solver for large-density-ratio multiphase flows

In this paper, an improved axisymmetric interfacial lattice Boltzmann flux solver abandoning the previous predictor-corrector scheme is proposed. Unlike the previous model starting from the two-dimensional standard lattice Boltzmann method (LBM), the present method is developed using the axisymmetric LBM, which directly incorporates the axisymmetric effects into the distribution functions. As a result, the proposed solver does not need the corrector step involving complicated space derivatives. It makes this method simpler and more computationally efficient. In the present solver, the resultant governing equation is globally resolved by the finite volume method, while the fluxes are reconstructed by local application of the axisymmetric LBM. Therefore, the inconsistency between the local reconstruction and the global governing equation can be eliminated because the global equation can be strictly derived from the axisymmetric LBM, which holds stronger physical basis than the previous method. Numerical experiments about the interface capturing and the multiphase flows are conducted to test the proposed model. Results show that the present method is superior to the fractional step solver in terms of the accuracy, stability, and computational efficiency. In addition, this solver has the capacity of simulating large-density-ratio and complex interfacial change.

Study of sedimentation characteristics of an elliptical squirmer in a vertical channel

Abstract We used a two-dimensional lattice Boltzmann method to simulate the sedimentation motion of an elliptical squirmer in a vertical channel, taking into account the case of a circular squirmer, aiming to more realistically simulate the swimming of microorganisms in nature. The study in this was divided into two phases. The first phase comprised the numerical calculations of an elliptical squirmer with an aspect ratio of c = 2.0 and revealed three typical motion modes: steady inclined motion, wall-attraction oscillation, and large-amplitude oscillation. It was found that the formation of these three motion modes and transitions between modes are related to the pressure distribution formed between the elliptical squirmer and wall. In addition, significant differences exist between the motions of elliptical and circular squirmers. The force generated by the interaction between the elliptical squirmer and wall does not all point towards its center of mass, resulting in an additional torque on the elliptical squirmer; this is not the situation for the circular squirmer. The second phase of the study simulated squirmers with different aspect ratios (c = 1.0, c = 3.0). It was found that for an elliptical squirmer with an aspect ratio c = 3.0, the large-amplitude oscillation mode (among the above three motion modes) no longer exists. By combining the motion modes of a circular squirmer in the channel, it can be observed that as the aspect ratio c increases, the squirmer’s head direction tends to be more vertical, which may reduce the drag force during swimming.

Passive particles driven by self-propelled particle: The wake effect

This work focuses on numerically studying hydrodynamic interaction between a passive particle and a self-propelled particle, termed a squirmer, by using a two-dimensional lattice Boltzmann method (LBM). It is found that the squirmer can capture a passive particle and propel it simultaneously, provided the passive particle is situated within the squirmer’s wake. Our research shows that the critical capture distance, which determines whether the particle is captured, primarily depends on the intensity of the squirmer’s dipolarity. The stronger dipolarity of squirmer results in an increased critical capture distance. Conversely, the Reynolds number is found to have minimal influence on this interaction. Interestingly, the passive particle, when driven by the squirmer’s wake, contributes to a reduction in the squirmer’s drag. This results in a mutual acceleration for both particles. Our findings can provide valuable perspectives for formulating the principles of reducing the drag of micro-swimmers and help to achieve the goal of using micro-swimmers to transport goods without physical tethers.

Three-dimensional reconstruction and optimization of porous fuel electrode in reversible solid oxide cells based on the Lattice Boltzmann method

A reversible solid oxide cell can work as a fuel cell (FC) or an electrolyzer cell (EC) with superior efficiency in a single device, which has the potential to become the core of energy conversion and storage. Since the redox reaction occurs at the three phase boundary in the porous electrode, the microstructure of which has a significant effect on the dynamic performance of the cell. Current research on porous electrodes mainly focuses on parametric and steady-state analysis but lacks studies on dynamic performance. In this study, we investigate the mass transfer process and dynamic performance of rSOC fuel electrodes by 3D reconstruction and artificial generation combined with a two-dimensional lattice Boltzmann method. The results show that the effective diffusion coefficients and cell performance of the XCT cross-sectional and random sphere method are much higher than those of the Gaussian filter and fiber rod structure. The change in H2 concentration is larger for switching from FC to EC compared to switching from EC to FC, but the transient steady-state difference and relaxation time of the voltage is smaller. These results can be used as a reference for the design and optimization of the porous electrodes in reversible solid oxide cells.

Simulation of flow past a squirmer confined in a channel at low Reynolds numbers

The two-dimensional lattice Boltzmann method was employed to numerically investigate the flow around a circular squirmer in a channel at low Reynolds numbers. The study thoroughly examined the impact of various factors on flow structures and drag coefficients (C d) of the squirmer, such as the Reynolds number (Re), self-propelled strength (α), squirmer-type factor (β), blockage ratio (B), and orientation angle (θ). Notably, despite the low Reynolds numbers, a change in the orientation angle θ resulted in a lift in the squirmer, consequently affecting its lift coefficient (C l). The simulation findings underscored that a pair of up-down backflow regions are generated on the squirmer’s surface. Interestingly, the locations of these backflow regions varied significantly between the pusher type (β< 0), the neutral squirmer (β= 0), and the puller type (β> 0). These variations were closely tied to the pressure and velocity distributions on the surfaces of the respective squirmers. Furthermore, an increase in α might induce the formation of a new pair of backflow regions near the channel walls and subsequently elevate the C d . On the other hand, alterations in Re did not affect the flow structures but created a negative correlation with C d. Overall, the study unveiled unique dynamic characteristics, offering a contrast to the extensively investigated case of flow past a cylinder.

Pore-Scale Investigation of Mass Transport in Compressed Cathode Gas Diffusion Layer of Proton Exchange Membrane Fuel Cells

Proton exchange membrane fuel cells (PEMFCs) are considered a promising energy source in the field of transport and distributed power generation. Fundamental research into their key components is needed to improve PEMFC performance and accelerate commercialization. Binder addition and compression induced by assembly pressure can significantly change the microstructure of the gas diffusion layer and affect mass transport. A two-dimensional multicomponent lattice Boltzmann (LB) model considering the cathode electrochemical reaction was developed, and a GDL was reconstructed numerically and considering a binder structure. The effects of the binder and compression on mass transport and electrochemical performance within the GDL were investigated. The results showed that an increase in binder volume fraction led to more chain-like structures and closed pores that were unfavorable for mass transport. Compression increased the mass transfer resistance of the GDL in the region under the rib, leading to a decrease in oxygen concentration and local current density.

Channel flow boiling on hybrid wettability surface with lattice Boltzmann method

Channel flow boiling on the hybrid wettability surface is studied numerically using a two-dimensional pseudo potential lattice Boltzmann method (LBM) coupled with a thermal phase transition model. Heat transfer performance between single and hybrid wettability surfaces is compared first, and it is shown that the heat flux on the hybrid surface is higher than that of its single wettability competitor. After analyzing 36 groups of numerical results, it is found that the impacts brought by contact angle and geometrical parameters of the hybrid surface on heat flux is complex. By fixing the hydrophilic contact angle, the heat flux increases first but then decreases with the increase of hydrophobic contact angle. However, the heat flux decreases monotonously with increasing the hydrophilic contact angle under a fixed hydrophobic contact angle. The 30°/120° hybrid wettability surface shows the best heat transfer performance due to its better three-phase contact line spreading and accelerated bubble departure frequency. Aside from the contact angle, the flow boiling heat transfer performance dominated by bubble dynamics is also closely related to the widths of hydrophilic/hydrophobic regions, and there exist optimal widths under various wall superheats. Finally, the pressure drop inside channel is investigated, and it is shown that the hybrid surface is favorable to reduce pressure drop fluctuation on the premise of providing high vapor yield.

Simulation of Rayleigh convection during dichloromethane absorption by water using lattice Boltzmann method

Developing dichloromethane (DCM) waste gas purification and absorption technology is consistent with the demand of the circular economy and contributes to the goals of achieving carbon peaking and carbon neutrality. In addition, Rayleigh convection generated during the absorption of DCM by water is of great significance for understanding the interfacial mass transfer mechanism and enhancing the mass transfer efficiency. Thus, the absorption process of DCM discrete diffusion sources was simulated using the two-dimensional lattice Boltzmann method (LBM) with external forces to visualize the effect of Rayleigh convection evolution law on the mass transfer of the absorption process in this study. The concentration and velocity distribution with single or multiple diffusion sources were respectively simulated at 298.15 K and 1.00 atm. The results show that the convection structure of the simulated plume is similar to that of comparable studies, and the convective structure on both sides suppresses the development of the intermediate convective structure when convection occurs. At a constant gas-phase concentration (CB,g), the more the number of diffusion sources, the faster the convective structures integration, and the rapid integration of convective structures is associated with the sharp increasing instantaneous mass transfer flux. Meanwhile, increasing the gas phase concentration can effectively shorten the convection onset time (tc), increase the instantaneous mass transfer flux (Nins,t), and enhance the mass transfer efficiency by calculating the simulated transfer mass data. Furthermore, the critical onset time of Rayleigh convection first lengthens and then shortens with the number of diffusion sources (n) increasing. And the more the number of diffusion sources, the more significant the final cumulative (Nt) absorption amounts are. The simulation results can provide theoretical guidance for enhancing the mass transfer efficiency in the DCM absorption process.

Lattice Boltzmann modelling of colloidal suspensions drying in porous media accounting for local nanoparticle effects

A two-dimensional (2-D) double-distribution lattice Boltzmann method (LBM) is implemented to study isothermal drying of a colloidal suspension considering local nanoparticle effects. The two LBMs solve isothermal two-phase flow and nanoparticle transport, respectively. The three local nanoparticle effects on the fluid dynamics considered in this paper are viscosity increase, surface tension drop and local drying rate reduction. The proposed model is first validated by the study of the drying of a 2-D suspended colloidal droplet for two different Péclet numbers, where the evolution of the diameter squared agrees well with experimental results. The model is further validated looking at drying of a colloid in a 2-D capillary tube with two open ends. Compared with experimental results, the best agreement in terms of deposition profile and drying time is obtained when considering all three nanoparticle effects. Afterwards, we apply the model to investigate the complicated drying of a colloidal suspension in a 2-D porous asphalt, considering all three local nanoparticle effects. The drying dynamics, resultant nanoparticle transport, accumulation and deposition are first analysed for a base case. Then a parametric study is conducted varying the initial nanoparticle concentration, porous medium contact angle, nanoparticle contact angle and nanoparticle diffusion coefficient. The influence of these parameters on drying dynamics, drying rate, deposition process and final deposition configurations is analysed in detail, together with the mutual influence of local nanoparticle behaviour. Finally, a unified relation between the average drying rate and the studied parameters is proposed and verified, covering the full parameter ranges of simulations.

Electric field inspired alternating surface wettability for enhancing pool boiling heat transfer performance: A lattice Boltzmann method study

Electric field and surfactants have been proven to potentially alter surface wettability on demand. In this work, alternating wettability inspired by an electric field has been used to enhance boiling heat transfer performance in terms of critical heat flux (CHF) over a rough surface by using two-dimensional lattice Boltzmann simulations. In alternating wettability, the surface wettability changes with time between hydrophobic and hydrophilic. The effects of the parameters, including alternating wettability time-period and wettability contrast on the boiling process have been revealed. The simulation results show that for the alternating wettability: when surface is hydrophobic bubble expansion is faster, and then wettability transition to hydrophilic quickly retracts three-phase contact line leading to faster bubble shrinking as compared to constantly hydrophobic and constantly hydrophilic surfaces. Furthermore, the rapid shrinking of the bubble tends to disintegrate vapor film on the surface at high wall superheats, resulting in a 53% enhancement in CHF compared to a constantly hydrophilic surface. The bubble departure takes much longer time for too small/large time-periods of alternating wettability. The CHF increases with time-period, becomes maximum at a certain value and then reduces. The CHF also increases with wettability contrast, becomes largest for hydrophilic and hydrophobic contact angles 55o and 107o, respectively, and decreases with further increase in wettability contrast due to high potential for vapor film formation.

Effects of Compression and Porosity Gradients on Two-Phase Behavior in Gas Diffusion Layer of Proton Exchange Membrane Fuel Cells

Water management within the gas diffusion layer (GDL) plays an important role in the performance of the proton exchange membrane fuel cell (PEMFC) and its reliability. The compression of the gas diffusion layer during fabrication and assembly has a significant impact on the mass transport, and the porosity gradient design of the gas diffusion layer is an essential way to improve water management. In this paper, the two-dimensional lattice Boltzmann method (LBM) is applied to investigate the two-phase behavior in gas diffusion layers with different porosity gradients under compression. Compression results in an increase in flow resistance below the ribs, prompting the appearance of the flow path of liquid water below the channel, and liquid water breaks through to the channel more quickly. GDLs with linear, multilayer, and inverted V-shaped porosity distributions with an overall porosity of 0.78 are generated to evaluate the effect of porosity gradients on the liquid water transport. The liquid water saturation values within the linear and multilayer GDLs are significantly reduced compared to that of the GDL with uniform porosity, but the liquid water within the inverted V-shaped GDL accumulates in the middle region and is more likely to cause flooding.

Two-dimensional stable lattice Boltzmann simulation of turbulent flow in wavy walled channel

In recent years, the lattice Boltzmann equation has developed into a promising technique for computational fluid dynamics (CFD). The lattice Boltzmann model (LBM) approach is derived from the Boltzmann equation and kinetic theory, as opposed to the standard CFD methods that are based on direct discretization of the Navier–Stokes equations. In this paper, Newtonian flow passing through a wavy walled channel has been examined for laminar to turbulent transition by using the LBM. The simple LBM for this problem becomes unstable as the Reynolds number increases and the laminar to turbulent transition begins. When Ehrenfest’s limiters are introduced in the LBM, the simulation becomes stable for higher Reynolds numbers. Two types of channel geometries are studied here, the channel walls of relatively small amplitude and channel walls of large amplitude. Our findings are that for large amplitude channel walls, flow becomes unsteady for lower Reynolds numbers as compared to that for small amplitude channel walls. For large amplitude walls, the vortices formed exhibit periodic shedding inside the channel furrows and remain there. For small amplitude walls, the vortex shedding starts downstream of the channel. The present LBM variant is able to simulate small amplitude channel flow for a Reynolds number Re = 800 and large amplitude channel flow for a Reynolds number R = 570.

Lattice Boltzmann study of droplet evaporation on a heated substrate under a uniform electric field

In this paper, a two-dimensional hybrid thermal lattice Boltzmann (LB) method coupled with the leaky dielectric model was firstly presented to study droplet evaporation on a heated substrate under the influence of an electric field. Contact angle hysteresis and Marangoni effects are included. The accuracy of this model is validated by simulation a static droplet evaporation and droplet deformation in the electric field. Then, the validated model is used to explore the effects of the electrical field on droplet evaporation, by varying the electric field strength and direction. The electric field is seen to change the droplet morphology, internal flow, heat transfer and thus evaporation time. The droplet is elongated along the direction of the electric field, and the contact angle is reduced. A pair of vortices is formed inside the droplet, which is consistent with the Marangoni flow direction, while the pair of vortices outside the droplet is oriented in the opposite direction to the internal one. For all droplets, the average heat flux to the evaporating is linearly related to the contact line length density. Additionally, it is discovered that applying a vertical electric field increases the evaporation time of a sessile droplet, while applying a horizontal electric field decreases it. Our research aids in achieving precise regulation of droplet evaporation and gives a better understanding of the influence of electric fields on droplet evaporation.

A curvilinear lattice Boltzmann scheme for thermal flows

Lattice Boltzmann schemes are known for their efficiency and low dissipation properties. However, the standard lattice Boltzmann method (LBM) is limited to Cartesian grids, and this approach can be troublesome when approximating thermal flows over curved walls. The present work proposes to solve the two-dimensional lattice Boltzmann equation under curvilinear coordinate transformation to simulate thermal flows with body-fitted grids. Several test cases are discussed, and the results are extensively compared with a very favourable outcome to the available numerical and experimental data, confirming the importance of the implemented methodology. Natural convection in a square cavity and a wavy cavity, as well as flow in a concentric cylindrical annulus are used for validation. Forced convection over a heated two-dimensional cylinder is also included.