Lattice Boltzmann Model Research Articles

Study on the evolution of heterogeneous double-cavity induced by near-wall and the fluctuation characteristics of load field

It is well known that the collapse of heterogeneous multi-cavity near the wall will induce the fluctuation of the load field. To address this problem, the Lattice Boltzmann Method (LBM) is applied to model the three-phase coupling between gas-liquid-solid. The objective is to investigate the evolution of heterogeneous double bubbles and the spatial-temporal distribution characteristics of wall loads induced near the wall. In this study, the pseudopotential Multi-Relaxation-Time Lattice Boltzmann Model (MRT-LBM) and the Carnahan-Starling Equation of State (C-S-EOS) with an extended format for the external force term are used. The effects of the distance of the bubble to the wall, the pressure differences between the inside and outside of the bubble, and the relative size of the bubble on the dynamic evolution and the load distribution characteristics of heterogeneous multi-bubbles near the wall are investigated in order to determine the influence of these factors. Under a two-dimensional pressure field, the collapse process of double cavitation bubbles is visualized. Through the flow field, the morphological changes of the cavitation bubble collapse near the wall are also described. Various parameters are found to have an influence on the evolution of double cavitation bubbles near the wall and the resulting load field. The study employs the Lattice Boltzmann Method and the Potential Model for the analysis of the heterogeneous bubble collapses in the near wall region.

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.

Lattice Boltzmann Model for a Class of Viscous Wave Equation

Lattice Boltzmann Model for a Class of Viscous Wave Equation

Lattice Boltzmann modeling of natural circulation loop with emphasis on non-Boussinesq mechanism

The natural circulation loop is crucial for the safe and stable operation of nuclear reactors and other applications. Traditional numerical algorithms, based on the Boussinesq approximation, have limitations when dealing with large temperature differences and density disparity, and they do not fully address fluid compressibility. This paper adopts the decoupled and stabilized lattice Boltzmann method (DSLBM) with a non-Boussinesq algorithm to study the natural circulation loop. The DSLBM provides a detailed flow description under large temperature and density differences, incorporating the pseudopotential multiphase model, temperature equation, and state equation, without relying on assumptions. The study examines the loop's performance under various temperature differences, central height differences, and heating source lengths, focusing on mass flow rate, driving head, and heating power. It reveals the energy performance, flow characteristics, and heat transfer properties of the loop, highlighting the physical mechanisms involved. Comparison with the empirical formulation of the incompressible equation from the theoretical aspect shows that when the temperature difference coefficient is lower than 0.15, the two methods are not much different from each other. When the temperature difference coefficient reaches 0.2, 0.3, and 0.4, the difference between the two methods is 9.47%, 19.11%, and 42.64%, respectively. Consequently, the Boussinesq approximation can be compensated by DSLBM, which proves the value of the application of the algorithm in exploiting the compressibility of fluids. The dimensionless fitting correlation with greater universality is obtained, which helps to predict the properties of the natural circulation loop with varying temperature differences, friction coefficients, and geometric structures. The research in this paper will lay the foundation for optimizing the system design of the natural circulation loop and improving energy utilization efficiency.

Axisymmetric phase-field-based lattice Boltzmann model for incompressible two-phase flow with phase change

In this work, a phase-field-based lattice Boltzmann equation (LBE) model for axisymmetric two-phase flow with phase change is proposed. Two sets of discrete particle distribution functions are employed to match the conserved Allen–Cahn equation and the hydrodynamic equations with phase change effect, respectively. Since phase change occurs at the interface, the divergence-free condition of the velocity field is no longer satisfied due to mass transfer, and the conserved Allen–Cahn equation needs to be equipped with a source term dependent on the phase change model. To deal with these, a novel source term in the hydrodynamic LBE is delicately designed to recover the correct target governing equations. Meanwhile, the LBE for the Allen–Cahn equation is modified with a discrete force term to model mass transfer. In particular, an additional correction term is added into the hydrodynamic LBE to reduce the spurious velocity and improve numerical stability. Several axisymmetric benchmark multiphase problems with phase change, including bubble growing in superheated liquid, D2 law, film boiling, bubble rising in superheated liquid under gravity, and droplet impact on a hot surface, have been conducted to test the performance of the proposed model. Numerical results agree well with analytical solutions and available published data in the literature.

A free-energy based multiple-distribution-function lattice Boltzmann method for multi-component and multi-phase flows

This study presents the development of a multiple-distribution-function lattice Boltzmann model (MDF-LBM) for the accurate simulation of multi-component and multi-phase flow. The model is based on the diffuse interface theory and free energy model, which enable the derivation of hydrodynamic equations for the system. These equations comprise a Cahn-Hilliard (CH) type mass balance equation, which accounts for cross diffusion terms for each species, and a momentum balance equation. By establishing a relationship between the total chemical potential and the general pressure, the momentum balance equation is reformulated in a potential form. This potential form, together with the CH type mass balance equation, is then utilized to construct the MDF-LBM as a coupled convection–diffusion system. Numerical simulations demonstrate that the proposed MDF-LBM accurately captures phase behavior and ensures mass conservation. Additionally, the calculated interface tension exhibits good agreement with experimental data obtained from laboratory studies.

A pore-scale lattice Boltzmann model for solute transport coupled with heterogeneous surface reactions and mineral dissolution

In this paper, we propose a pore-scale lattice Boltzmann model to simulate fluid flow coupled with heterogeneous surface reactions and mineral dissolution. The primary innovation lies in the transformation of surface reactions, originally treated as a boundary condition, into a volume-source term through dimensional augmentation within the framework of sharp liquid–solid interfaces. This significantly simplifies the implementation, particularly for reactions occurring in porous media with intricate geometric structures. Several benchmark tests were performed to validate the accuracy of this model, including a reaction–diffusion problem in a rectangular domain, a two-dimensional reaction and dissolution of a circular grain, as well as a three-dimensional calcite crystal dissolution in a micro-channel. All the obtained simulation results agree well with the reference solutions. In addition, a dissolution problem in a three-dimensional porous medium built with the sand pack is then investigated. Cases with different Péclet numbers (Pe) and Damköhler numbers (Da) were simulated, and five dissolution modes were obtained, which were finally summarized in a diagram of Pe and Da.

Lattice Boltzmann simulation of ion transport during the charging process of porous electrodes in randomly reconstructed seawater desalination batteries

The economics and desalination results of desalination cells are superior to those of other desalination technologies due to their unique electrochemical mechanisms. Nevertheless, there has been a paucity of research into the potential mechanisms of pore-scale ion removal during the operation of this specific type of battery. In this paper, the relationship between electrode microstructure and cell performance is investigated by establishing a lattice Boltzmann model and a high-fidelity two-dimensional electrode structure. The results demonstrate that the random morphology and irregular agglomeration of particles result in significant differences in electrode performance. During electrode deionization, the ion embedding process is faster in particles close to the main flow. In addition, sodium ions are inserted faster in small particles than in large particles. If the particles comprising the electrode exhibit a localized uneven distribution, it is advantageous to have a greater density of particles in the vicinity of the flow channel. The larger the reaction interface per unit area, the faster the interpolation rate of the particle, while the larger the total area, the larger the interpolation capacity of the particle.

Lattice Boltzmann Model Investigation of Simultaneous Imbibition/Evaporation in PEMFC Cathodic Catalyst Layer Using Reconstructed 3D Image Data from Transmission Electron Microscopy

Proton Exchange Membrane Fuel Cells (PEMFCs) are widely used and significant attention is directed towards optimizing of the cathode catalyst layer. The critical focus revolves around refining the multi-phase boundary of the electrically conducting carbon support, the ion-conducting ionomer, the catalyst particles as well as the pore space that can be either occupied by oxygen (feedstock) or water (product). Challenges related to mass transport limitations of oxygen towards these multiple-phase boundaries, also denoted as active sites, persist, especially when liquid water increasingly saturates the pore space (Fig. 1). Furthermore, the evaporated water additionally hinders oxygen transport in the gas phase1,2. This study focuses on the investigation of pore-scale transport mechanisms inside of the cathodic catalyst layer, taking into account the counter-current diffusion of oxygen and water vapor in the gas phase as well as the generation of liquid water that increasingly saturates the void space. For this purpose, a multi-phase and multi-component pore scale Lattice Boltzmann model (LBM), coupled to two-phase reaction, was implemented. The LBM is tailored based on previous works3,4, including the localized generation of water at constant current densities, the imbibition of the pore structure with water counter-currently to the diffusion of oxygen, and the simultaneous evaporation of water. An actual 3D cathode catalyst layer from a commercial membrane electrode assembly, reconstructed from transmission electron microscopy (TEM) image data, was employed. It was imaged using a source voltage of 200kV and a current of 2 nA. The scanned sample had an approximate total volume of 500 × 500 × 100 nm3. From this, a 3D domain of 138 × 138 × 58 nm3 was reconstructed for this study. A 2D cross-section of the reconstructed image is exemplarily shown in Fig. 1. The in-silico study of water and oxygen transport through the catalyst layer elaborates the relationship between the rates of water invasion and evaporation in dependence of current density and catalyst layer structure. The critical conditions for water flooding are evaluated for different process conditions. Fig. 1 Schematic representation of the cathode catalyst layer: The ionomer is represented in white; the carbon for electron connectivity is represented in gray; pore space for oxygen and water transport in yellow; the black circles represent the active sites, i.e., Pt-particles located at the multi-phase boundary of ionomer, carbon and oxygen-filled pores; the red circles represent the inactive sites, that have no connection to ion and/or oxygen transport pathways. References A. Suzuki et al., Int. J. Hydrogen Energy, 36, 2221–2229 (2011) https://www.sciencedirect.com/science/article/pii/S0360319910022913.M. El Hannach, M. Prat, and J. Pauchet, Int. J. Hydrogen Energy, 37, 18996–19006 (2012) https://www.sciencedirect.com/science/article/pii/S0360319912022069.S. Bhaskaran et al., Dry. Technol., 40, 735–747 (2022) https://doi.org/10.1080/07373937.2021.1898417.S. Bhaskaran et al., Int. J. Hydrogen Energy, 47, 31551–31565 (2022) https://www.sciencedirect.com/science/article/pii/S0360319922030932. Figure 1

Design and Characterization of Porous Electrodes for Redox Flow Batteries

The commercialization of redox flow batteries as large-scale energy storage systems depends on lowering the capital and operating costs which depend on achieving maximum power density. Optimizing electrode design parameters and flow field-electrode combinations is critical to minimize losses and maximize active material utilization. Modeling the current drawn from an electrode offers a means to interpret electrode structure based on the electrolyte distribution driven by internal design. However, direct imaging methods (such as in-situ fluorescence microscopy and X-ray tomography) and numerical methods for current to potential prediction (3D Lattice Boltzmann modeling) are specific to individual electrode structures and possess limited predictable value to obtain an ideal electrode design. In this work, we present an electrode impedance spectroscopy (EIS)-based approach for determining electrode design parameters and devise a general method for determination of effective diffusion layer thickness. Using COMSOL modeling we verified the development of slug flow behavior in highly randomized porous electrode systems, indicating that the mass transport properties are dictated by inter-fiber distance. An analytical model to predict current as a function of applied overpotential is presented which allows us to vary structural parameters of the porous electrodes to study the influence of surface area, inter-fiber distances and diffusion layer thickness on the RFB performance. This model is a highly flexible tool applicable to any electrochemical system using a porous electrode and identifies critical variables affecting electrode design to characterize optimal electrode structure to minimize mass transport losses and optimize operational parameters.

A chemical-potential multiphase lattice Boltzmann model with high Reynolds and Weber numbers

Numerical simulation of nonideal fluids is one of the most successful applications of the lattice Boltzmann method. The Chapman–Enskog (C–E) analysis reveals that the pressure tensor in the chemical-potential lattice Boltzmann model deviates from the standard one, and consequently, the surface tension cannot be effectively adjusted by the coefficient. In this paper, an additional term is constructed to modify the pressure tensor, while a scaling factor is utilized to prevent the expansion of the phase interface. The proposed model has thermodynamic consistency and is able to linearly adjust the surface tension without changing the interface width largely. Laplace's law and Galilean invariance are also verified. The present model has excellent dynamic stability at large liquid/gas density ratios and, thus, enables dynamic simulations with high Reynolds and Weber numbers.

Simulation of melting characteristics of thermal washing of the wax layer in the pipeline based on lattice Boltzmann method

ABSTRACT The escalation of transportation costs and the obstruction of pipelines due to wax deposition significantly impact the secure and efficient production of oil fields. The thermal washing method, characterized by its simplicity and cost-effectiveness, is widely employed for dewaxing crude oil gathering pipelines. The investigation of the melting mechanism of the wax layer during thermal washing is extremely important. In this paper, the two-zone composite model of multiphase flow-porous medium in the mushy zone is introduced into the solid-liquid phase change lattice Boltzmann model based on the enthalpy method, and the problem of circumferential inhomogeneity in the melting of the wax layer and the important influence of flow and heat transfer in the mushy zone on the thermal washing are systematically investigated. The demarcation point (γ tr) between the high and low liquid fraction zones is measured to be 0.81 by microscopic experiment. The impacts of varying γ tr and Ste numbers on wax melting at different circumferential locations are analyzed in detail. The results show that the melting efficiency of wax exhibits a nonlinear enhancement from − 90° to 90°. The melting efficiency of wax decreases with increasing γ tr for wax layers between 90° and − 45°. The melting efficiency of wax increases with higher Ste numbers at all angles. The Ste number increases from 0.42 to 5.0, and the melting efficiency of the wax layer at angles ranging from 90° to − 90° increases by factors of 2.16, 2.16, 2.20, 2.61, and 3.33 respectively. The growth of the Ste number improves the warming rate and shortens the generation time of convection at the center point of the wax layer. The research findings serve as a fundamental reference for formulating a rational and efficient thermal washing scheme.

Transport Instabilities of Hazardous Contaminants in a Microscale Soil Sample Under Thermal Flow of Supercritical CO2

This work reveals the transient dynamics of supercritical carbon dioxide (sCO2) under a joint heat and mass interactions with resident polycyclic aromatic hydrocarbons (PAHs) in sedimentary microporous media. A variant of Multiphase Color Fluid Lattice Boltzmann model is developed to simulate spatiotemporal evolution of sCO2 front with degradation of a 5 μm mass-film of resident PAHs. The injection conditions of sCO2 range from 305 K to 315 K, and from 8 MPa to 10 MPa, with a mass flow rate of 0.05–0.15 kg/min. It has been found in this study that the growth of clusters reveals a critical operating time to promote the solvation power of sCO2. However, the cluster of such contaminants is affected by a secondary degradation inside the pore throats of the microporous. The heat and mass coefficients are remarkably relied on the nature of the contaminants and their clustering/clogging processes inside the pores. Hence, the saturation amount of CO2 will jump from a prompt movement to a quick equilibrium state while facing the balanced phase of clustering/degradation of resident contaminants inside the microporous media.

Phase-field-based lattice Boltzmann method for two-phase flows with interfacial mass or heat transfer.

In this work, we develop a phase-field-based lattice Boltzmann (LB) method for a two-scalar model of the two-phase flows with interfacial mass or heat transfer. Through the Chapman-Enskog analysis, we show that the present LB method can correctly recover the governing equationsfor phase field, flow field, and concentration or temperature field. In particular, to derive the two-scalar equationsfor the mass or heat transfer, we propose a new LB model with an auxiliary source distribution function to describe the extra flux terms, and the discretizations of some derivative terms can be avoided. The accuracy and efficiency of the present LB method are also tested through several benchmark problems, and the influence of mass or heat transfer on the fluid viscosity is further considered by introducing an exponential relation. The numerical results show that the present LB method is suitable for the two-phase flows with interfacial mass or heat transfer.

Evaluation of the non-Newtonian lattice Boltzmann model coupled with off-grid bounce-back scheme: Wall shear stress distributions in Ostwald-de Waele fluids flow.

We present a comprehensive analysis of the non-Newtonian lattice Boltzmann method (LBM) when it is used to simulate the distribution of wall shear stress (WSS). We systematically identify sources of numerical errors associated with non-Newtonian rheological behavior of fluids in off-grid geometries. We implement the single relaxation time, Bhatnagar-Gross-Krook (BGK), and multiple relaxation time (MRT) collision operators and investigate flow in a two-dimensional channel aligned with lattice directions and off-grid Hagen-Poiseuille flow of Ostwald-de Waele (power-law) fluids. As for boundary conditions, we implement constant body force-driven and pressure-driven flows. These two boundary conditions have different numerical challenges, which include numerical stability, accuracy, mass conservation, and compressibility effects, which are inherent in the LBM method. Our results indicate that MRT, when the relaxation times are adequately tuned in the non-Newtonian case, significantly improves the WSS distribution accuracy and the numerical stability of the LBM. MRT also enhances the stability and accuracy for non-Newtonian fluids compared with the Newtonian case, meaning that it is questionable if a BGK collision operator is appropriate to use in a non-Newtonian case with off-grid boundaries. When analyzing the non-Newtonian LBM in the context of staircase walls and interpolated bounce-back (IBB) walls, a MRT collision operator with the appropriate choice of tunable relaxation times makes it possible to achieve numerically accurate results without a significant increase in grid resolution for matching to the analytical solution of WSS distributions. In analyzing the non-Newtonian flows, we show that the viscosity dependency of bounce-back walls in the BGK-LBM deviates from the results obtained under Newtonian assumptions. The power-law index further influences these discrepancies, and errors caused by the viscosity dependency of the bounce-back boundary conditions can be effectively mitigated by implementing the MRT procedure. Results show that non-Newtonian fluids, in contrast with the Newtonian assumption, encounter a greater mass imbalance when flowing through a periodic system with IBB walls. MRT can address this challenge, as it allows for independent adjustments of physical relaxation times and enhances mass conservation in the case of non-Newtonian fluids. In pressure-driven non-Newtonian flows, there is a significant impact of bulk viscosity. This aspect is often overlooked in Newtonian simulations but can significantly impact fluid adapting to rapid changes in local effective viscosity. One of our main conclusions is that the MRT collision operator with tuned relaxation times can effectively resolve numerical problems caused by non-Newtonian rheological properties and off-grid geometries. We also provide practical guidelines for selecting the most suitable simulation approach.

Lattice Boltzmann method for the linear complementarity problem arising from American option pricing

In this paper, a lattice Boltzmann method is proposed for solving the linear complementarity problem (LCP) arising in single and multi-asset American put option pricing. The LCP for American option is a variable coefficient parabolic model defined on an unbounded domain. Initially, using the far field estimate method and the penalty method respectively, the LCP could be reformulated into a nonlinear parabolic partial differential equation on a bounded domain. To construct a unified lattice Boltzmann model for the option pricing problems, the above transformation equations are rewritten into an equivalent divergence form. Then, through the incorporation of an amending function into the evolution equation, which assists in recovering the source term and eliminating the error term, the lattice Boltzmann model with spatial second-order accuracy is constructed. Finally, the present model is validated using numerical simulations, and the numerical results agree well with the option values obtained by existing methods, which indicates that the present lattice Boltzmann model is efficient for solving the American put option pricing problem.

Pore-scale study of CO2 desublimation and sublimation in a packed bed during cryogenic carbon capture

Cryogenic carbon capture (CCC) is an innovative technology to desublimate $\text {CO}_2$ out of industrial flue gases. A comprehensive understanding of $\text {CO}_2$ desublimation and sublimation is essential for widespread application of CCC, which is highly challenging due to the complex physics behind. In this work, a lattice Boltzmann (LB) model is proposed to study $\text {CO}_2$ desublimation and sublimation for different operating conditions, including the bed temperature (subcooling degree $\Delta T_s$ ), gas feed rate (Péclet number $Pe $ ) and bed porosity ( $\psi$ ). The $\text {CO}_2$ desublimation and sublimation properties are reproduced. Interactions between convective $\text {CO}_2$ supply and desublimation/sublimation intensity are analysed. In the single-grain case, $Pe $ is suggested to exceed a critical value $Pe _c$ at each $\Delta T_s$ to avoid the convection-limited regime. Beyond $Pe _c$ , the $\text {CO}_2$ capture rate ( $v_c$ ) grows monotonically with $\Delta T_s$ , indicating a desublimation-limited regime. In the packed bed case, multiple grains render the convective $\text {CO}_2$ supply insufficient and make CCC operate under the convection-limited mechanism. Besides, in small- $\Delta T_s$ and high- $Pe $ tests, $\text {CO}_2$ desublimation becomes insufficient compared with convective $\text {CO}_2$ supply, thus introducing the desublimation-limited regime with severe $\text {CO}_2$ capture capacity loss ( $\eta _d$ ). Moreover, large $\psi$ enhances gas mobility while decreasing cold grain volume. A moderate porosity $\psi _c$ is recommended for improving the $\text {CO}_2$ capture performance. By analysing $v_c$ and $\eta _d$ , regime diagrams are proposed in $\Delta T_s$ – $Pe $ space to show distributions of convection-limited and desublimation-limited regimes, thus suggesting optimal conditions for efficient $\text {CO}_2$ capture. This work develops a viable LB model to examine CCC under extensive operating conditions, contributing to facilitating its application.

Lattice Boltzmann simulation of plunging breakers

ABSTRACT In the present work, the conservative phase-field lattice Boltzmann model is applied to simulate plunging breakers in shallow waters. The solver is computationally efficient as it is explicit in time stepping and does not require a solution for the pressure Poisson equation. Nevertheless, the solver can simultaneously handle a large Reynolds number ( = 10 4 ) and a high-density ratio of 1000. Simulations are performed by varying initial steepness and dispersion parameters, which influence the nonlinearity degree of wave (or the growth speed of instability) and the oscillatory motion (limited by the bottom) on the breaking characteristics. Detailed analyses of kinematics, air entrainment, vorticity, and energy dissipation are presented.

Scale translation yields insights into gas adsorption under nanoconfinement

This work describes a scale-translating simulation framework to investigate gas adsorption behavior in nanoconfined pores. The framework combines molecular simulations (MSs), equation of state (EoS), and lattice Boltzmann (LB) simulations. MSs reveal the physics of methane adsorption in nano-sized pores, where input values of fugacity coefficients are optimized based on EoS predictions. Then, an LB free-energy model, which incorporates a viral EoS, upscales intermolecular forces and estimates adsorption behavior via a proposed fluid–wall interaction model. Armed with the values of the LB interaction parameter as a function of pressure, the LB model is used to predict fluid behavior in irregular nanopores, and the results are validated against reference MS data. The LB model is then used to study adsorption behavior at a continuum scale in representative organic shale nanopores based on finely characterized Vaca Muerta shale samples. The results show that methane adsorption could significantly increase contained fluids by 10%–25% in pores smaller than 20 nm. However, in larger pores (40 nm to 90 nm), adsorption's impact diminishes to 2%–3%, suggesting sorption's negligible role beyond a 40 nm pore size.

Droplet boiling on two-tier hierarchical micro-pillar array surface – Nucleate boiling regime

Although hierarchical structured surfaces have shown great potential in improving heat transfer performance of boiling, the mechanisms associated with structure configuration and structure size remain elusive. In this work, the nucleate boiling regime of droplet on single-tier micro-pillar array (SM) surfaces and three types of two-tier hierarchical micro-pillar array (THM) surfaces is investigated comprehensively using the lattice Boltzmann model. Effects brought by the primary pillar size and the secondary pillar configuration on the development of vapor confined in pillar gaps are emphatically discussed from bubble nucleation through vapor coalescence to vapor expansion. Boiling dynamic characteristics concerning droplet morphological evolution, liquid-vapor interfacial deformation and triple-phase contact line (TPCL) motion are elucidated by the distributions of vapor pressure, fluid temperature and substrate heat flux. It is most efficient for the secondary pillar to enhance boiling heat transfer performance when configured on the side of primary pillar and least efficient when configured on the top of primary pillar.