Lattice Boltzmann model for simulating flows with multiple phases and components

Reaction-limited evaporation for the color-gradient lattice Boltzmann model

We propose a reaction-limited evaporation model within the color-gradient lattice Boltzmann (LB) multicomponent framework to address the lack of intrinsic evaporation mechanisms. Unlike diffusion-driven approaches, our method directly enforces mass removal at the fluid interface in a reaction-limited manner while maintaining numerical stability. Using the inherent color-gradient magnitude and a single adjustable parameter, evaporation sites are chosen in a computationally efficient way with seamless mass exchange between the components, with no change to the core algorithm. Extensive validation across diverse interface geometries and evaporation flux magnitudes demonstrates high accuracy, with errors below 5% for unit density ratios. For density contrasts, the method remains robust in the limit of smaller evaporation flux magnitudes and density ratios. Our approach extends the applicability of the color-gradient LB model to scenarios involving reaction-limited evaporation, such as droplet evaporation on heated substrates, vacuum evaporation of molten metals, and drying processes in porous media.

Precisely Designed Hydrophilic Networks in Microporous Layer for High Performance of Proton Exchange Membrane Fuel Cells

Proton exchange membrane fuel cell (PEMFC) is considered the next promising generation of power devices for vehicles. The microporous layer (MPL) improves the performance through effective water management. In this study, local hydrophilic networks of nano- and macropores are formed in different MPLs. The measured internal contact angle to water confirms that Vulcan carbon black (VB) is helpful for the formation of hydrophilic pores. The MPL sample containing 10% VB (P1-H) exhibits the best performance under a wide range of humidities. Its peak power density reaches 1.51 W/cm2 under 60% relative humidity (RH) and drops only 1.99% under 80%RH. As shown in the three-dimensional simulation model, the hydrophilic nanopores preferentially serve as water reservoir regions to ensure a certain amount of water for membrane hydration and control the water droplet size at the interface. The ohmic resistance and mass transfer resistance of P1-H are reduced under a high current density. The MPL containing hydrophilic macropores (P3-H) displays a slight performance improvement. Despite enhanced air permeability, hydrophilic macropores directly drain water and result in membrane dehydration. The findings provide an optimized strategy for the precise design of MPL to achieve high performance and adaptation under a wide range of humidity.

Characterizing Dynamic Contact Angle during Gas-Liquid Imbibition in Microchannels by Lattice Boltzmann Method Modeling

Spontaneous imbibition in microchannels is a critical phenomenon in various industrial applications, such as enhanced oil recovery and microfluidic systems. One of the key factors influencing the imbibition process is the dynamic wetting effect, which governs the interaction between the liquid and solid surfaces. This paper improves the original pseudopotential model for interfluid forces by coupling it with the Peng-Robinson equation of state. The model's accuracy is verified through thermodynamic consistency checks, simulations of gas-liquid interfacial tensions, and testing of static equilibrium contact angles. Following model validation, we use it to simulate spontaneous gas-liquid imbibition in microchannels and investigate dynamic contact angle evolution during the process. The results demonstrate that (1) as the microchannel width increases, inertia forces become more significant during the initial imbibition stages, leading to a greater difference between the dynamic and static contact angles. (2) A decrease in fluid-solid interaction strength results in a larger gap between dynamic and static contact angles. (3) Higher interfacial tension strengthens the capillary forces, accelerating the imbibition rate and enlarging the difference between the dynamic and static contact angles. Furthermore, the dynamic contact angle data obtained from our simulations can be used to correct the traditional Lucas-Washburn equation. The corrected equation predicts imbibition distances that closely match the simulation results.

Formation of bijels stabilized by magnetic ellipsoidal particles in external magnetic fields

Bicontinuous interfacially-jammed emulsion gels (bijels) are increasingly used as emulsion templates for the fabrication of functional porous materials including membranes, electrodes, and biomaterials. Control over the domain size and structure is highly desirable in these applications. For bijels stabilized by spherical particles, particle size and volume fraction are the main parameters that determine the emulsion structure. Here, we investigate the use of ellipsoidal magnetic particles and study the effect of external magnetic fields on the formation of bijels. Using hybrid Lattice Boltzmann-molecular dynamics simulations, we analyze the effect of the magnetic field on emulsion dynamics and the structural properties of the resulting bijel. We find that the formation of bijels remains robust in the presence of magnetic fields, and that the domain size and tortuosity become anisotropic when ellipsoidal particles are used. We show that the magnetic fields lead to orientational ordering of the particles which in turn leads to alignment of the interfaces. The orientational order facilitates enhanced packing of particles in the interface which leads to different jamming times in the directions parallel and perpendicular to the field. Our results highlight the potential of magnetic particles for fabrication and processing of emulsion systems with tunable properties.

Impact of Wettability on CO2 Dynamic Dissolution in Three-Dimensional Porous Media: Pore-Scale Simulation Using the Lattice Boltzmann Method

Understanding the dissolution behavior of supercritical CO2 (scCO2) in porous media is crucial for efficient CO2 storage. However, the precise modeling of dynamic dissolution behavior at this pore scale remains a huge challenge, and the impact of wettability on this process still needs to be clarified. In this study, the influence of rock wettability on CO2 dynamic dissolution in the three-dimensional porous media is investigated using the lattice Boltzmann method (LBM). The LBM is coupled with scCO2-water two-phase flow, solute transport, and heterogeneous and homogeneous reactions. The size, number, and dissolution pattern of scCO2 bubbles during the dissolution process are observed under strongly water-wet, weakly water-wet, intermediate-wet, and mixed-wet conditions. The CO2(aq) concentration and pH are investigated, followed by a quantitative investigation of the impact of wettability on the specific interface area and the mass transfer coefficient. An empirical relationship between the specific interface area and scCO2 saturation is established. The findings reveal that under weakly water-wet and intermediate-wet conditions, the sizes of scCO2 clusters and monomers are small and mostly distributed at the dead end of the pores. In contrast, under strongly water-wet and mixed-wet conditions, the clusters are larger and interconnected, and distributed in the center of the pore. This results in a greater scCO2-water interface area, consequently enhancing the dissolution rate. Furthermore, a strong linear correlation is observed between scCO2 saturation and specific interface area. It is noted that as the hydrophilicity of the rock increases, the mass transfer coefficient initially rises and then declines.

Divergence of Critical Fluctuations on Approaching Catastrophic Phase Inversion in Turbulent Emulsions

Catastrophic phase inversion, the breakdown of a concentrated emulsion characterized by the most puzzling sudden feature, is crucial in numerous industrial applications. Here we combine well-controlled experiments and fully resolved numerical simulations to study the critical dynamics of catastrophic phase inversion in oil-water emulsions under turbulent flow as the phase-inversion volume fraction is approached. We reveal that the phase inversion is characterized by the critical power-law divergence of fluctuations in the global drag force. We determine the enhanced dynamical heterogeneity in the local droplet structures at approaching the phase inversion, and tightly connect it to the diverging drag fluctuations. Moreover, we show that near to the critical point the phase inversion is triggered as a stochastic process by large fluctuations at both large and small scales. Our findings pave the way to modeling the phase inversion process as an out-of-equilibrium critical-like phenomena.

Enhancement and Predictable Guidance of Coalescence-Induced Droplet Jumping on V-Shaped Superhydrophobic Surfaces with a Ridge

Coalescence-induced droplet jumping has attracted significant attention in recent years. However, achieving a high jumping velocity while predictably regulating the jumping direction of the merged droplets by simple superhydrophobic structures remains a challenge. In this work, a novel V-shaped superhydrophobic surface with a ridge is conceived for enhanced and predictably guided coalescence-induced droplet jumping. By conducting experiments and lattice Boltzmann simulations, it is found that the presence of a ridge in the V-shaped superhydrophobic surface can modify the fluid dynamics during the droplet coalescence process, resulting in a much higher droplet jumping velocity than that achieved by the V-shaped superhydrophobic surface without a ridge. The enhancement of the droplet jumping velocity is mainly attributed to the combined effect of the earlier and more sufficient impingement between the liquid bridge and the ridge, as well as the accelerated droplet contraction by redirecting the internal liquid flow toward the jumping direction. A high normalized jumping velocity of V j * ≈ 0.71 is achieved by the newly designed surface, with a 930% increase in the energy conversion efficiency in comparison with that on a flat surface. Moreover, adjusting the opening direction of the V-groove at different groove angles is found to be an effective method to regulate the droplet jumping direction and expand the range of the jumping angle. Particularly, the droplet jumping angle can be well predicted based on the rotational angle (ω) and the groove angle (α), i.e., θj,p ≈ 90° - 0.5α - ω.

Three-dimensional solidification modeling of various materials using the lattice Boltzmann method with an explicit enthalpy equation

Based on the mesoscopic scale, the lattice Boltzmann method (LBM) with an enthalpy-based model represented in the form of distribution functions is widely used in the liquid-solid phase transition process of energy storage materials due to its direct and relatively accurate characterization of the presence of latent heat of solidification. However, since the enthalpy distribution function itself contains the physical properties of the material, these properties are transferred along with the enthalpy distribution function during the streaming process. This leads to deviations between the enthalpy-based model when simulating the phase transition process of different materials mixed and the actual process. To address this issue, in this paper, we construct an enthalpy-based model for different types of materials. For multiple materials, various forms of enthalpy distribution functions are employed. This method still uses the form of enthalpy distribution functions for collisions and streaming processes among the same type of substance, while for heat transfer between different materials, it avoids the direct transfer of enthalpy distribution functions and instead applies a source term to the enthalpy distribution functions, characterizing the heat transfer between different materials through the energy change before and after mixing based on the temperature. To verify the accuracy of the method proposed in this paper, a detailed solidification model for two different materials is constructed using the example of water droplets solidifying in air, and the results are compared with experimental outcomes. The results of the simulation show that the model constructed in this paper is largely in line with the actual process.

Polyphenol-Derived Carbonaceous Frameworks with Multiscale Porosity for High-Power Electrochemical Applications

With the escalating global demand for electric vehicles and sustainable energy solutions, increasing focus is placed on developing electrochemical systems that offer fast charging and high-power output, primarily governed by mass transport. Accordingly, porous carbons have emerged as highly promising electrochemically active or supporting materials due to expansive surface areas, tunable pore structures, and superior electrical conductivity, accelerating surface reaction. Yet, while substantial research has been devoted to crafting various porous carbons to increase specific surface areas, the optimal utilization of the surfaces remains underexplored. This review emphasizes the critical role of the fluid dynamics within multiscale porous carbonaceous electrodes, leading to substantially enhanced pore utilization in electrochemical systems. It elaborates on strategies of using sacrificial templates for incorporating meso/macropores into microporous carbon matrix, while exploiting the unique properties of polyphenol moieties such as sustainable carbons derived from biomass, inherent adhesive/cohesive interactions with template materials, and facile complexation capabilities with diverse materials, thereby enabling adaptive structural modulations. Furthermore, it explores how multiscale pore configurations influence pore-utilization efficiency, demonstrating advantages of incorporating multiscale pores. Finally, synergistic impact on the high-power electrochemical systems is examined, attributed to improved fluid-dynamic behavior within the carbonaceous frameworks, providing insights for advancing next-generation high-power electrochemical applications.

Computational Fluid-Structure Interaction in Microfluidics

Micro elastofluidics is a transformative branch of microfluidics, leveraging the fluid-structure interaction (FSI) at the microscale to enhance the functionality and efficiency of various microdevices. This review paper elucidates the critical role of advanced computational FSI methods in the field of micro elastofluidics. By focusing on the interplay between fluid mechanics and structural responses, these computational methods facilitate the intricate design and optimisation of microdevices such as microvalves, micropumps, and micromixers, which rely on the precise control of fluidic and structural dynamics. In addition, these computational tools extend to the development of biomedical devices, enabling precise particle manipulation and enhancing therapeutic outcomes in cardiovascular applications. Furthermore, this paper addresses the current challenges in computational FSI and highlights the necessity for further development of tools to tackle complex, time-dependent models under microfluidic environments and varying conditions. Our review highlights the expanding potential of FSI in micro elastofluidics, offering a roadmap for future research and development in this promising area.

Emulsions in microfluidic channels with asymmetric boundary conditions and directional surface roughness: stress and rheology

The flow of emulsions in confined microfluidic channels is affected by surface roughness. Directional roughness effects have recently been reported in channels with asymmetric boundary conditions featuring a flat wall, and a wall textured with directional roughness, the latter promoting a change in the velocity profiles when the flow direction of emulsions is inverted [D. Filippi et al., Adv. Mater. Technol., 2023, 8, 2201748]. An operative protocol is needed to reconstruct the stress profile inside the channel from velocity data to shed light on the trigger of the directional response. To this aim, we performed lattice Boltzmann numerical simulations of the flow of model emulsions with a minimalist model of directional roughness in two dimensions: a confined microfluidic channel with one flat wall and the other patterned by right-angle triangular-shaped posts. Simulations are essential to develop a protocol based on mechanical arguments to reconstruct stress profiles. Hence, one can analyze data to relate directional effects in velocity profiles to different rheological responses close to the rough walls associated with opposite flow directions. We finally show the universality of this protocol by applying it to other realizations of directional roughness by considering experimental data on emulsions in a microfluidic channel featuring a flat wall and a wall textured by herringbone-shaped roughness.

Improved lattice Boltzmann model for immiscible multicomponent systems with high viscosity gradients at the interface

We propose alternative discretization schemes for improving the lattice Boltzmann pseudopotential model for incompressible multicomponent systems, with the purpose of modeling the flow of immiscible fluids with a large viscosity ratio. Compared to the original model of Shan-Chen [Phys. Rev. E 47, 1815 (1993)1063-651X10.1103/PhysRevE.47.1815], the present discretization schemes consider: (i) an explicit force term, (ii) a second-order discretization of the stream term, (iii) a moments-based model for the kinetic nonequilibrium distributions, and (iv) a high-order discretization of the spatial derivative terms. To verify the accuracy of the proposed model, the effects of varying the viscosity ratio as well as both fluid's viscosities on spurious currents and capillary number are investigated for the problems dealing with a static bubble, two-component Poiseuille flow, and immiscible fluid-fluid displacement. The resulting algorithm maintains the simplicity of the pseudopotential model while allowing an easy implementation for multicomponent systems. The results of the model herein proposed show improved control of the interface region and interfacial tension, relatively smaller magnitudes of spurious current values with increasing viscosity ratio, and also a significantly wider stability range with respect to the previously best results in the literature.

Droplet dynamics in homogeneous isotropic turbulence with the immersed boundary-lattice Boltzmann method

We develop a numerical method for simulating the dynamics of a droplet immersed in a generic time-dependent velocity gradient field. This approach is grounded on the hybrid coupling between the lattice Boltzmann (LB) method, employed for the flow simulation, and the immersed boundary (IB) method, utilized to couple the droplet with the surrounding fluid. We show how to enrich the numerical scheme with a mesh regularization technique, allowing droplets to sustain large deformations. The resulting methodology is adapted to simulate the dynamics of droplets in homogeneous and isotropic turbulence, with the characteristic size of the droplet being smaller than the characteristic Kolmogorov scale of the outer turbulent flow. We report statistical results for droplet deformation and orientation collected from an ensemble of turbulent trajectories, as well as comparisons with theoretical models in the limit of small deformation.

Simulating Two-Phase Seepage in Undisturbed Soil Based on Lattice Boltzmann Method and X-ray Computed Tomography Images

The two-phase seepage fluid (i.e., air and water) behaviors in undisturbed granite residual soil (U-GRS) have not been comprehensively studied due to a lack of accurate and representative models of its internal pore structure. By leveraging X-ray computed tomography (CT) along with the lattice Boltzmann method (LBM) enhanced by the Shan-Chen model, this study simulates the impact of internal pore characteristics of U-GRS on the water-gas two-phase seepage flow behaviors. Our findings reveal that the fluid demonstrates a preference for larger and straighter channels for seepage, and as seepage progresses, the volume fraction of the water/gas phases exhibits an initial increase/decrease trend, eventually stabilizing. The results show the dependence of two-phase seepage velocity on porosity, while the local seepage velocity is influenced by the distribution and complexity of the pore structure. This emphasizes the need to consider pore distribution and connectivity when studying two-phase flow in undisturbed soil. It is observed that the residual gas phase persists within the pore space, primarily localized at the pore margins and dead spaces. Furthermore, the study identifies that hydrophobic walls repel adjacent fluids, thereby accelerating fluid movement, whereas hydrophilic walls attract fluids, inducing a viscous effect that decelerates fluid flow. Consequently, the two-phase flow rate is found to increase with then-enhanced hydrophobicity. The apex of the water-phase volume fraction is observed under hydrophobic wall conditions, reaching up to 96.40%, with the residual gas-phase constituting 3.60%. The hydrophilic wall retains more residual gas-phase volume fraction than the neutral wall, followed by the hydrophobic wall. Conclusively, the investigations using X-ray CT and LBM demonstrate that the pore structure characteristics and the wettability of the pore walls significantly influence the two-phase seepage process.

Three-dimensional lattice Boltzmann model with self-tuning equation of state for multiphase flows

In this work, the recent lattice Boltzmann (LB) model with self-tuning equation of 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.

Metastable and unstable hydrodynamics in multiphase lattice Boltzmann

Metastability in liquids is at the foundation of complex phase transformation dynamics such as nucleation and cavitation. Intermolecular interaction details, beyond the equation of state, and thermal hydrodynamic fluctuations play a crucial role. However, most numerical approaches suffer from a slow time and space convergence, thus hindering the convergence to the hydrodynamic limit. This work shows that the Shan-Chen lattice Boltzmann model has the unique capability of simulating the hydrodynamics of the metastable state. The structure factor of density fluctuations is theoretically obtained and numerically verified to a high precision, for all simulated wave vectors, reduced temperatures, and pressures, deep into the metastable region. Such remarkable agreement between the theory and simulations leverages the exact implementation at the lattice level of the mechanical equilibrium condition. The static structure factor is found to consistently diverge as the temperature approaches the critical point or the density approaches the spinodal line at a subcritical temperature. Theoretically predicted critical exponents are observed in both cases. Finally, the phase separation in the unstable branch follows the same pattern, i.e., the generation of interfaces with different topology, as observed in molecular dynamics simulations.

Hybrid lattice-Boltzmann-finite-difference approach for the simulation of micro-phase-change-material slurry in convective flow

In this paper, we present a hybrid numerical scheme that couples the lattice Boltzmann method (LBM) with the finite difference method (FDM) to model micro-phase-change-material (MPCM) suspensions in a minichannel. Within this framework, the LBM was employed to solve the continuity, momentum, and energy equations for the fluid domain, while a Lagrangian scheme replicates the motion of MPCM particles. The LBM is coupled with an FDM solver which operates under the lumped capacitance assumption to address the phase-change phenomena within the microparticles. This hybrid coupling eliminates the necessity for any specific treatment in handling phase transitions and tracking phase interfaces. The proposed method is first evaluated on classic particle cases, demonstrating its ability to achieve four-way coupling. Furthermore, the current model effectively adapted viscosity changes when integrating the microparticles, obviating the need for homogenous viscosity models. Subsequently, the potential of this approach is demonstrated by examining the influence of the near-wall thermal interaction of MPCM particles considering three scenarios based on particle density: light (ρ_{p}<ρ_{f}), neutrally buoyant (ρ_{p}≈ρ_{f}), and dense (ρ_{p}>ρ_{f}) microparticles. The hybrid approach further revealed insights into the impact of the volume fraction on the heat transfer coefficient as well as on the overall heat transfer coefficient and performance index from a Lagrangian perspective.

Validating the Transition Criteria from the Cassie-Baxter to the Wenzel State for Periodically Pillared Surfaces with Lattice Boltzmann Simulations

Microfabrication techniques allow the development and production of artificial superhydrophobic surfaces that possess a precisely controlled roughness at the micrometer level, typically achieved through the arrangement of micropillar structures in periodic patterns. In this work, we analyze the stability and energy barrier of droplets in the Cassie-Baxter (CB) state on such periodic patterns. In addition, we further develop a transition criterion using the CB equation and derive an improved version which allows predicting for which pillar geometries, equilibrium contact angles, and droplet volumes the CB state switches from a metastable to an unstable state. This enables a comparison with existing experiments and three-dimensional multiphase Lattice Boltzmann simulations for different pillar distances, two contact angles, and two droplet volumes, where a good agreement has been found.

Color-gradient-based phase-field equation for multiphase flow

In this paper, the underlying problem with the color-gradient (CG) method in handling density-contrast fluids is explored. It is shown that the CG method is not fluid invariant. Based on nondimensionalizing the CG method, a phase-field interface-capturing model is proposed which tackles the difficulty of handling density-contrast fluids. The proposed formulation is developed for incompressible, immiscible two-fluid flows without phase-change phenomena, and a solver based on the lattice Boltzmann method is proposed. Coupled with an available robust hydrodynamic solver, a binary fluid flow package that handles fluid flows with high density and viscosity contrasts is presented. The macroscopic and lattice Boltzmann equivalents of the formulation, which make the physical interpretation of it easier, are presented. In contrast to existing color-gradient models where the interface-capturing equations are coupled with the hydrodynamic ones and include the surface tension forces, the proposed formulation is in the same spirit as the other phase-field models such as the Cahn-Hilliard and the Allen-Cahn equations and is solely employed to capture the interface advected due to a flow velocity. As such, similarly to other phase-field models, a so-called mobility parameter comes into play. In contrast, the mobility is not related to the density field but a constant coefficient. This leads to a formulation that avoids individual speed of sound for the different fluids. On the lattice Boltzmann solver side, two separate distribution functions are adopted to solve the formulation, and another one is employed to solve the Navier-Stokes equations, yielding a total of three equations. Two series of numerical tests are conducted to validate the accuracy and stability of the model, where we compare simulated results with available analytical and numerical solutions, and good agreement is observed. In the first set the interfacial evolution equations are assessed, while in the second set the hydrodynamic effects are taken into account.

Evolution dynamics of thin liquid structures investigated using a phase-field model

Liquid structures of thin-films and torus droplets are omnipresent in daily lives. The morphological evolution of liquid structures suspending in another immiscible fluid and sitting on a solid substrate is investigated by using three-dimensional (3D) phase-field (PF) simulations. Here, we address the evolution dynamics by scrutinizing the interplay of surface energy, kinetic energy, and viscous dissipation, which is characterized by Reynolds number Re and Weber number We. We observe special droplet breakup phenomena by varying Re and We. In addition, we gain the essential physical insights into controlling the droplet formation resulting from the morphological evolution of the liquid structures by characterizing the top and side profiles under different circumstances. We find that the shape evolution of the liquid structures is intimately related to the initial shape, Re, We as well as the intrinsic wettability of the substrate. Furthermore, it is revealed that the evolution dynamics are determined by the competition between the coalescence phenomenology and the hydrodynamic instability of the liquid structures. For the coalescence phenomenology, the liquid structure merges onto itself, while the hydrodynamic instability leads to the breakup of the liquid structure. Last but not least, we investigate the influence of wall relaxation on the breakup outcome of torus droplets on substrates with different contact angles. We shed light on how the key parameters including the initial shape, Re, We, wettability, and wall relaxation influence the droplet dynamics and droplet formation. These findings are anticipated to contribute insights into droplet-based systems, potentially impacting areas like ink-jet printing, drug delivery systems, and microfluidic devices, where the interplay of surface energy, kinetic energy, and viscous dissipation plays a crucial role.

Phase-field lattice Boltzmann model with singular mobility for quasi-incompressible two-phase flows

In this paper, a lattice Boltzmann for quasi-incompressible two-phase flows is proposed based on the Cahn-Hilliard phase-field theory, which can be viewed as an improved model of a previous one [Yang and Guo, Phys. Rev. E 93, 043303 (2016)2470-004510.1103/PhysRevE.93.043303]. The model is composed of two LBE's, one for the Cahn-Hilliard equation (CHE) with a singular mobility, and the other for the quasi-incompressible Navier-Stokes equations (qINSE). Particularly, the LBE for the CHE uses an equilibrium distribution function containing a free parameter associated with the gradient of chemical potential, such that the variable (and even zero) mobility can be handled. In addition, the LBE for the qINSE uses an equilibrium distribution function containing another free parameter associated with the local shear rate, such that the large viscosity ratio problems can be handled. Several tests are first carried out to test the capability of the proposed LBE for the CHE in capturing phase interface, and the results demonstrate that the proposed model outperforms the original LBE model in terms of accuracy and stability. Furthermore, by coupling the hydrodynamic equations, the tests of double-stationary droplets and droplets falling problems indicate that the proposed model can reduce numerical dissipation and produce physically acceptable results at large time scales. The results of droplets falling and phase separation of binary fluid problems show that the present model can handle two-phase flows with large viscosity ratio up to the magnitude of 10^{4}.

A ternary mixture model with dynamic boundary conditions

The influence of short-range interactions between a multi-phase, multi-component mixture and a solid wall in confined geometries is crucial in life sciences and engineering. In this work, we extend the Cahn-Hilliard model with dynamic boundary conditions from a binary to a ternary mixture, employing the Onsager principle, which accounts for the cross-coupling between forces and fluxes in both the bulk and surface. Moreover, we have developed a linear, second-order and unconditionally energy-stable numerical scheme for solving the governing equations by utilizing the invariant energy quadratization method. This efficient solver allows us to explore the impacts of wall-mixture interactions and dynamic boundary conditions on phenomena like spontaneous phase separation, coarsening processes and the wettability of droplets on surfaces. We observe that wall-mixture interactions influence not only surface phenomena, such as droplet contact angles, but also patterns deep within the bulk. Additionally, the relaxation rates control the droplet spreading on surfaces. Furthermore, the cross-coupling relaxation rates in the bulk significantly affect coarsening patterns. Our work establishes a comprehensive framework for studying multi-component mixtures in confined geometries.

Self-consistent force scheme in the spectral multiple-relaxation-time lattice Boltzmann model

In the present work, the force term is first derived in the spectral multiple-relaxation-time high-order lattice Boltzmann model. The force term in the Boltzmann equation is expanded in the Hermite temperature rescaled central moment space (RCM), instead of the Hermite raw moment space (RM). The contribution of nonequilibrium RCM moments beyond second order are neglected. For the collision operator in the RCM space, each order of the force term can be incorporated directly. Through the transformation between the RCM space and the RM space, the force term for practical numerical implementation in the RM space can be derived. It can be demonstrated that the present force scheme is self-consistent for the isothermal flow and compressible thermal flow with adjustable Prandtl number via the numerical experiments.

Droplet Boiling on Micro-Pillar Array Surface ─ Transition Boiling Regime

Droplet boiling on the heating surface is a representative phenomenon in two-phase spray cooling under low volumetric fluxes. In particular, droplet boiling in the transition boiling regime holds the advantages of avoiding heat transfer deterioration in a film boiling regime and achieving comparable high heat transfer capacity in a nucleate boiling regime. While it is known to consist of intermittent liquid contact with the surface and surface dryout, quantifying the ensuing transient heat transfer performance and droplet behavior is very illusive. In this study, droplet boiling in the transition boiling regime on a micropillar array surface is investigated systematically, using the lattice Boltzmann model built up in the lab. The major contents discussed include the transient behaviors of the droplet, motion of the liquid bridge, and pinning/depinning of the three-phase contact line (TPCL), as well as the corresponding heat transfer performance. The evolution of a vapor film pierced by micropillars is analyzed from the views of morphological change and pressure distribution. The thickness of the vapor film is determined by the vapor generation rate dominated by the contact area and effective thermal conductivity, and the vapor escape rate by the permeability. The low permeability under a large pillar side length is responsible for the pressure buildup below the droplet, thus facilitating droplet rebound. The competition between capillary pressure and vapor film pressure dominates the trigger mode of the droplet rebound, i.e., fracture of the liquid bridge or filament and depinning of TPCL. The micropillar array surface is optimized to pursue the best cooling performance by assessing the impact from micropillar geometric dimensions on droplet contact time and area.

Generalized equilibria for color-gradient lattice Boltzmann model based on higher-order Hermite polynomials: A simplified implementation with central moments

We propose generalized equilibria of a three-dimensional color-gradient lattice Boltzmann model for two-component two-phase flows using higher-order Hermite polynomials. Although the resulting equilibrium distribution function, which includes a sixth-order term on the velocity, is computationally cumbersome, its equilibrium central moments (CMs) are velocity-independent and have a simplified form. Numerical experiments show that our approach, as in Wen et al. [Phys. Rev. E 100, 023301 (2019)2470-004510.1103/PhysRevE.100.023301] who consider terms up to third order, improves the Galilean invariance compared to that of the conventional approach. Dynamic problems can be solved with high accuracy at a density ratio of 10; however, the accuracy is still limited to a density ratio of 1000. For lower density ratios, the generalized equilibria benefit from the CM-based multiple-relaxation-time model, especially at very high Reynolds numbers, significantly improving the numerical stability.

Theoretical and numerical study on the well-balanced regularized lattice Boltzmann model for two-phase flow

In the multiphase flow simulations based on the lattice Boltzmann equation (LBE), the spurious velocity near the interface and the inconsistent density properties are frequently observed. In this paper, a well-balanced regularized lattice Boltzmann (WB-RLB) model with Hermite expansion up to third order is developed for two-phase flows. To this end, the equilibrium distribution function and the modified force term proposed by Guo [Phys. Fluids 33, 031709 (2021)1070-663110.1063/5.0041446] are directly introduced into the regularization of the transformed distribution functions when considering the LBE with trapezoidal integral. First, to give a detailed comparison of the well-balanced lattice Boltzmann equation (WB-LBE), WB-RLB, and second-order mixed difference scheme (SOMDS) proposed by Lee and Fischer [Phys. Rev. E 74, 046709 (2006)1539-375510.1103/PhysRevE.74.046709], the theoretical analyses on the force balance of LBE with two different gradient operators, isotropic central scheme (ICS) and SOMDS, as well as the numerical simulations of the stationary droplet are carried out. The force analysis shows that SOMDS can achieve a higher accuracy than ICS for the force balance, which has been validated in the simulations of stationary droplet cases. For the stationary droplet cases, all three models (WB-LBE, WB-RLB, and SOMDS) can capture the physical equilibrium state even at a large density ratio of 1000. Also, the numerical investigations of the WB-RLB model with third-order expansion (WB-RLB3) demonstrate that adjusting the relaxation parameters of the third-order moment can further improve the accuracy and stability of the WB-RLB model. Then, both the droplet coalescence and the phase separation cases are investigated with considering the effect of different interface thickness, which demonstrates that the performance of the WB-RLB for the two-phase dynamic problems is still quite well, and it exhibits better numerical stability when compared with the WB-LBE. In addition, the contact angle problem is investigated by the present WB-RLB model; the numerical results show that the predicted values of the contact angles agree well with the analytical solutions, but the well-balance property is not validated, especially near the three-phase junction. Overall, the present WB-RLB model exhibits excellent numerical accuracy and stability for both static and dynamic interface problems.

Unrestricted component count in multiphase lattice Boltzmann: A fugacity-based approach

Studies of multiphase fluids utilizing the lattice Boltzmann method (LBM) are typically severely restricted by the number of components or chemical species being modeled. This restriction is particularly pronounced for multiphase systems exhibiting partial miscibility and significant interfacial mass exchange, which is a common occurrence in realistic multiphase systems. Modeling such systems becomes increasingly complex as the number of chemical species increases due to the increased role of molecular interactions and the types of thermodynamic behavior that become possible. The recently introduced fugacity-based LBM [Soomro et al., Phys. Rev. E 107, 015304 (2023)2470-004510.1103/PhysRevE.107.015304] has provided a thermodynamically consistent modeling platform for multicomponent, partially miscible LBM simulations. However, until now, this fugacity-based LB model had lacked a comprehensive demonstration of its ability to accurately reproduce thermodynamic behavior beyond binary mixtures and to remove any restrictions in a number of components for multiphase LBM. In this paper we closely explore these fugacity-based LBM capabilities by showcasing comprehensive, thermodynamically consistent simulations of multiphase mixtures of up to ten chemical components. The paper begins by validating the model against the Young-Laplace equation for a droplet composed of three components. The model is then applied to study mixtures with a range of component numbers from one to six, showing agreement with rigorous thermodynamic predictions and demonstrating linear scaling of computational time with the number of components. We further investigate ternary systems in detail by exploring a wide range of temperature, pressure, and overall composition conditions to produce various characteristic ternary diagrams. In addition, the model is shown to be unrestricted in the number of phases as demonstrated through simulations of a three-component three-phase equilibrium case. The paper concludes by demonstrating simulations of a ten-component, realistic hydrocarbon mixture, achieving excellent agreement with thermodynamics for both flat interface vapor-liquid equilibrium and curved interface spinodal decomposition cases. This study represents a significant expansion of the scope and capabilities of multiphase LBM simulations that encompass multiphase systems of keen interest in engineering.

Accurate and Wide-Voltage-Range Modeling of Electrowetting with a Lattice Boltzmann Approach

The lattice Boltzmann method (LBM) has been widely used in multi-phase fluid mechanics and is known to be more computationally efficient than the traditional method of numerically solving Navier-Stokes and Cahn-Hilliard equations. Electrowetting is an important component of interfacial sciences, in which the liquid-liquid and solid-liquid interfaces are tuned by electrostatics. Modeling electrowetting using the LBM can be categorized into surface and bulk methods. By modifying the surface tension scalar, the surface method easily reproduces the fundamental Young-Lippmann (YL) equation at low voltages but fails to capture contact angle saturation at high voltages. With fully coupled hydrodynamics and electrostatics in the form of spatially dependent matrices, the bulk method can successfully show contact angle saturation, but it is often unable to reproduce the YL equation due to its intrinsic inaccuracies. The inaccuracies are mainly due to the fact that while the hydrodynamics are all described by continuous physical quantities in the framework of diffusive interfaces, the interfacial electrostatics are governed by discontinuous electric fields caused by sheet charge density. In this paper, we show that accurately modeling electrowetting using the LBM is non-trivial. Additional modeling work, especially the treatment of interfacial electric fields, is needed to recover the fundamental YL equation at low voltages and predict contact angle saturation at high voltages, with a systematic model validation over key parameters and applications.

Cell-free layer development and spatial organization of healthy and rigid red blood cells in a microfluidic bifurcation

Bifurcations and branches in the microcirculation dramatically affect blood flow as they determine the spatiotemporal organization of red blood cells (RBCs). Such changes in vessel geometries can further influence the formation of a cell-free layer (CFL) close to the vessel walls. Biophysical cell properties, such as their deformability, which is impaired in various diseases, are often thought to impact blood flow and affect the distribution of flowing RBCs. This study investigates the flow behavior of healthy and artificially hardened RBCs in a bifurcating microfluidic T-junction. We determine the RBC distribution across the channel width at multiple positions before and after the bifurcation. Thus, we reveal distinct focusing profiles in the feeding mother channel for rigid and healthy RBCs that dramatically impact the cell organization in the successive daughter channels. Moreover, we experimentally show how the characteristic asymmetric CFLs in the daughter vessels develop along their flow direction. Complimentary numerical simulations indicate that the buildup of the CFL is faster for healthy than for rigid RBCs. Our results provide fundamental knowledge to understand the partitioning of rigid RBC as a model of cells with pathologically impaired deformability in complex in vitro networks.

Phase-field lattice Boltzmann equation for wettable particle fluid dynamics

In this paper a phase-field based lattice Boltzmann equation (LBE) is developed to simulate wettable particles fluid dynamics together with the smoothed-profile method (SPM). In this model the evolution of a fluid-fluid interface is captured by the conservative Allen-Cahn equation (CACE) LBE, and the flow field is solved by a classical incompressible LBE. The solid particle is represent by SPM, and the fluid-solid interaction force is calculated by direct force method. Some benchmark tests including a single wettable particle trapped at the fluid-fluid interface without gravity, capillary interactions between two wettable particles under gravity, and sinking of a horizontal cylinder through an air-water interface are carried out to validate present CACE LBE for fluid-fluid-solid flows. Raft sinking of multiple horizontal cylinders (up to five cylinders) through an air-water interface is further investigated with the present CACE LBE, and a nontrivial dynamics with an unusual nonmonotonic motion of the multiple cylinders is observed in the vertical plane. Numerical results show that the predictions by the present LBE are in good agreement with theoretical solutions and experimental data.

Particle-based mesoscopic model for phase separation in a binary fluid mixture

A mesoscopic simulation model to study the phase separation in a binary fluid mixture in three dimensions (3D) is presented here by augmenting the existing particle-based multiparticle collision dynamics (MPCD) algorithm. The approach describes the nonideal equation of the fluid state by incorporating the excluded-volume interaction between the two components within the framework of stochastic collision, which depends on the local fluid composition and velocity. Calculating the nonideal contribution to the pressure both from simulation and analytics shows the model to be thermodynamically consistent. A phase diagram to explore the range of parameters that give rise to phase separation in the model is investigated. The interfacial width and phase growth obtained from the model agree with the literature for a wide range of temperatures and parameters.

Coupled Lattice Boltzmann Modeling Framework for Pore-Scale Fluid Flow and Reactive Transport

In this paper, we propose a modeling framework for pore-scale fluid flow and reactive transport based on a coupled lattice Boltzmann model (LBM). We develop a modeling interface to integrate the LBM modeling code parallel lattice Boltzmann solver and the PHREEQC reaction solver using multiple flow and reaction cell mapping schemes. The major advantage of the proposed workflow is the high modeling flexibility obtained by coupling the geochemical model with the LBM fluid flow model. Consequently, the model is capable of executing one or more complex reactions within desired cells while preserving the high data communication efficiency between the two codes. Meanwhile, the developed mapping mechanism enables the flow, diffusion, and reactions in complex pore-scale geometries. We validate the coupled code in a series of benchmark numerical experiments, including 2D single-phase Poiseuille flow and diffusion, 2D reactive transport with calcite dissolution, as well as surface complexation reactions. The simulation results show good agreement with analytical solutions, experimental data, and multiple other simulation codes. In addition, we design an AI-based optimization workflow and implement it on the surface complexation model to enable increased capacity of the coupled modeling framework. Compared to the manual tuning results proposed in the literature, our workflow demonstrates fast and reliable model optimization results without incorporating pre-existing domain knowledge.

Electrowetting lattice Boltzmann method for micro- and nano-droplet manipulations

Electrowetting has become a widely used tool for manipulating tiny amounts of liquids on surfaces. This paper proposes an electrowetting lattice Boltzmann method for manipulating micro-nano droplets. The hydrodynamics with the nonideal effect is modeled by the chemical-potential multiphase model, in which the phase transition and equilibrium are directly driven by chemical potential. For electrostatics, droplets in the micro-nano scale cannot be considered as equipotential as macroscopic droplets due to the Debye screening effect. Therefore, we linearly discretize the continuous Poisson-Boltzmann equation in a Cartesian coordinate system, and the electric potential distribution is stabilized by iterative computations. The electric potential distribution of droplets at different scales suggests that the electric field can still penetrate micro-nano droplets even with the screening effect. The accuracy of the numerical method is verified by simulating the static equilibrium of the droplet under the applied voltage, and the results show the apparent contact angles agree very well with the Lippmann-Young equation. The microscopic contact angles present some obvious deviations due to the sharp decrease of electric field strength near the three-phase contact point. These are consistent with previously reported experimental and theoretical analyses. Then, the droplet migrations on different electrode structures are simulated, and the results show that droplet speed can be stabilized more quickly due to the more uniform force on the droplet in the closed symmetric electrode structure. Finally, the electrowetting multiphase model is applied to study the lateral rebound of droplets impacting on the electrically heterogeneous surface. The electrostatic force prevents the droplets from contracting on the side which is applied voltage, resulting in the lateral rebound and transport toward the side.

Toward learning Lattice Boltzmann collision operators

In this work, we explore the possibility of learning from data collision operators for the Lattice Boltzmann Method using a deep learning approach. We compare a hierarchy of designs of the neural network (NN) collision operator and evaluate the performance of the resulting LBM method in reproducing time dynamics of several canonical flows. In the current study, as a first attempt to address the learning problem, the data were generated by a single relaxation time BGK operator. We demonstrate that vanilla NN architecture has very limited accuracy. On the other hand, by embedding physical properties, such as conservation laws and symmetries, it is possible to dramatically increase the accuracy by several orders of magnitude and correctly reproduce the short and long time dynamics of standard fluid flows.

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.

Improved partially saturated method for the lattice Boltzmann pseudopotential multicomponent flows

This paper extends the partially saturated method (PSM), used for curved or complex walls, to the lattice Boltzmann (LB) pseudopotential multicomponent model and adapts the wetting boundary condition to model the contact angle. The pseudopotential model is widely used for various complex flow simulations due to its simplicity. To simulate the wetting phenomenon within this model, the mesoscopic interaction force between the boundary fluid and solid nodes is used to mimic the microscopic adhesive force between the fluid and the solid wall, and the bounce-back (BB) method is normally adopted to achieve the no-slip boundary condition. In this paper, the pseudopotential interaction forces are computed with eighth-order isotropy since fourth-order isotropy leads to the condensation of the dissolved component on curved walls. Due to the staircase approximation of curved walls in the BB method, the contact angle is sensitive to the shape of corners on curved walls. Furthermore, the staircase approximation makes the movement of the wetting droplet on curved walls not smooth. To solve this problem, the curved boundary method may be used, but due to the interpolation or extrapolation process, most curved boundary conditions suffer from massive mass leakage when applied to the LB pseudopotential model. Through three test cases, it is found that the improved PSM scheme is mass conservative, that nearly identical static contact angles are observed on flat and curved walls under the same wetting condition, and that the movement of a wetting droplet on curved and inclined walls is smoother compared to the usual BB method. The present method is expected to be a promising tool for modeling flows in porous media and in microfluidic channels.

Contact Angle Measurement on Curved Wetting Surfaces in Multiphase Lattice Boltzmann Method

Contact angle is an essential physical quantity that characterizes the wettability of a substrate. Although it is widely used in the studies of surface wetting, capillary phenomena, and moving contact lines, the contact angle measurements in simulations and experiments are still complicated and time-consuming. In this paper, we present an efficient scheme for the measurement of contact angle on curved wetting surfaces in lattice Boltzmann simulations. The measuring results are in excellent agreement with the theoretical predictions without considering the gravity effect. A series of simulations with various drop sizes and surface curvatures confirm that the present scheme is grid-independent. Then, the scheme is verified in gravitational environments by simulating the deformations of sessile and pendent droplets on the curved wetting surface. The numerical results are highly consistent with experimental observations and support the theoretical analysis that the microscopic contact angle is independent of gravity. Furthermore, the method utilizes only the microscopic geometry of the contact angle and does not depend on the droplet profile; therefore, it can be applied to nonaxisymmetric shapes or moving contact lines. The scheme is applied to capture the dynamic contact angle hysteresis on homogeneous or chemically heterogeneous curved surfaces. Importantly, the accurate contact angle measurement enables the dynamic mechanical analysis of moving contact lines. The present measurement is simple and efficient and can be extended to implementations in various multiphase lattice Boltzmann models.

Diffuse interface model for a single-component liquid-vapor system

We elucidate the theoretical relationships among fundamental physical concepts that are involved in the diffuse interface modeling for an isothermal single-component liquid-vapor system, which cover both the equation of state (EOS) and the surface tension force. As an example, a flat surface at equilibrium is discussed both theoretically and numerically by using two different approaches. Particularly, the force structure in the transition region is clearly presented, which demonstrates that the capillary contributions due to the density gradients can suppress the mechanical instability of the thermodynamic pressure and lead to constant hydrodynamic pressure (and chemical potential). Then, by comparing with the van der Waals (vdW) EOS for a flat interface at equilibrium, it is shown that applying the double-well approximation can give qualitative predictions for relatively high density ratio (ρ_{l}/ρ_{g}=7.784) and satisfactory results for relatively low density ratio (ρ_{l}/ρ_{g}=1.774). The main cause for this observation is attributed to the nonlinear variation of the generalized coefficient function in the double-well formulation at different density ratios. In addition, for the latter case, we simulate a droplet impact on a hydrophilic wall by using a recently proposed well-balanced discrete unified gas kinetic scheme (WB-DUGKS), which justifies the applicability of the double-well approximation to complex interfacial dynamics in the low-density-ratio limit. Furthermore, the reason for the inconsistency between the coefficients of the mean-field force expressions in the existing literature is explained.

Equation-of-state-dependent surface free-energy density for wettability in lattice Boltzmann method

In thermodynamic theory, the liquid-vapor fluids can be described by a single multiphase equation of state and the surface wettability is usually characterized by the surface free-energy density. In this work, we propose an equation-of-state-dependent surface free-energy density for the wettability of the liquid-vapor fluids on a solid surface, which can lead to a simple closed-form analytical expression for the contact angle. Meanwhile, the thermodynamically derived equilibrium condition is equivalent to the geometric formulation of the contact angle. To numerically validate the present surface free-energy density, the mesoscopic multiphase lattice Boltzmann model with self-tuning equation of state, which is strictly consistent with thermodynamic theory, is employed, and the two-dimensional wetting condition treatment is extended to the three-dimensional situation with flat and curved surfaces. Two- and three-dimensional lattice Boltzmann simulations of static droplets on flat and curved surfaces are first performed, and the obtained contact angles agree well with the closed-form analytical expression. Then, the three-dimensional lattice Boltzmann simulation of a moving droplet on an inclined wall, which is vertically and sinusoidally oscillated, is carried out. The dynamic contact angles well satisfy the Cox-Voinov law. The droplet movement regimes are consistent with previous experiments and two-dimensional simulations. The dependence of the droplet overall velocity with respect to the dimensionless oscillation strength is also discussed in detail.

Interaction between a rising bubble and a stationary droplet immersed in a liquid pool using a ternary conservative phase-field lattice Boltzmann method

When a stationary bubble and a stationary droplet immersed in a liquid pool are brought into contact, they form a bubble-droplet aggregate. Its equilibrium morphology and stability largely depend on the combination of different components' surface tensions, known as the "spreading factor." In this study, we look at the interaction between a rising bubble and a stationary droplet to better understand the dynamics of coalescence and rising and morphological changes for the bubble-droplet aggregate. A systematic study is conducted on the interaction processes with various bubble sizes and spreading factors in two dimensions. The current simulation framework consists of the ternary conservative phase-field lattice Boltzmann method (LBM) for interface tracking and the velocity-pressure LBM for hydrodynamics, which is validated by benchmark cases such as the liquid lens and parasitic currents around a static droplet with several popular surface tension formulations. We further test our LBM for the morphology changes of two droplets initially in contact with various spreading factors and depict the final morphologies in a phase diagram. The separated, partially engulfed, and completely engulfed morphologies can be replicated by systematically altering the sign of the spreading factors. The rising bubble and stationary droplet interaction are simulated based on the final morphologies obtained under stationary conditions by imposing an imaginary buoyancy force on the rising bubble. The results indicate that the bubble-droplet aggregate with double emulsion morphology can minimize the distortion of the bubble-droplet aggregate and achieve a greater terminal velocity than the aggregate with partially engulfed morphology.

Numerical Modeling Using Immersed Boundary-Lattice Boltzmann Method and Experiments for Particle Manipulation under Standing Surface Acoustic Waves

In this work, we employed the Immersed Boundary-Lattice Boltzmann Method (IB-LBM) to simulate the motion of a microparticle in a microchannel under the influence of a standing surface acoustic wave (SSAW). To capture the response of the target microparticle in a straight channel under the effect of the SSAW, in-house code was built in C language. The SSAW creates pressure nodes and anti-nodes inside the microchannel. Here, the target particle was forced to traverse toward the pressure node. A mapping mechanism was developed to accurately apply the physical acoustic force field in the numerical simulation. First, benchmarking studies were conducted to compare the numerical results in the IB-LBM with the available analytical, numerical, and experimental results. Next, several parametric studies were carried out in which the particle types, sizes, compressibility coefficients, and densities were varied. When the SSAW is applied, the microparticles (with a positive acoustic contrast factor) move toward the pressure node locations during their motion in the microchannel. Hence, their steady-state locations are controlled by adjusting the pressure nodes to the desired locations, such as the centerline or near the microchannel sidewalls. Moreover, the geometric parameters, such as radius, density, and compressibility of the particles affect their transient response, and the particles ultimately settle at the pressure nodes. To validate the numerical work, a microfluidic device was fabricated in-house in the cleanroom using lithographic techniques. Experiments were performed, and the target particle was moved either to the centerline or sidewalls of the channel, depending on the location of the pressure node. The steady-state placements obtained in the computational model and experiments exhibit excellent agreement and are reported.

Thermal and Postural Effects on Fluid Mixing and Irrigation Patterns for Intraventricular Hemorrhage Treatment

Intraventricular hemorrhage is characterized by blood leaking into the cerebral ventricles and mixing with cerebrospinal fluid. A standard treatment method involves inserting a passive drainage catheter, known as an external ventricular drain (EVD), into the ventricle. EVDs have common adverse complications, including the occlusion of the catheter, that may lead to permanent neural damage or even mortality. In order to prevent such complications, a novel dual-lumen catheter (IRRAflow®) utilizing an active fluid exchange mechanism has been recently developed. However, the fluid dynamics of the exchange system have not been investigated. In this study, convective flow in a three-dimensional cerebral lateral ventricle with an inserted catheter is evaluated using an in-house lattice-Boltzmann-based fluid-solid interaction solver. Different treatment conditions are simulated, including injection temperature and patient position. Thermal and gravitational effects on medication distribution are studied using a dye simulator based on a recently-introduced (pseudo)spectral convection-diffusion equation solver. The effects of injection temperature and patient position on catheter performance are presented and discussed in terms of hematoma irrigation, vortical structures, mixing, and medication volume distribution. Results suggest that cold-temperature injections can increase catheter efficacy in terms of dye distribution and irrigation potential, both of which can be further guided by patient positioning.

Direct 0D-3D coupling of a lattice Boltzmann methodology for fluid-structure aortic flow simulations

This work introduces a numerical approach and implementation for the direct coupling of arbitrary complex ordinary differential equation- (ODE-)governed zero-dimensional (0D) boundary conditions to three-dimensional (3D) lattice Boltzmann-based fluid-structure systems for hemodynamics studies. In particular, a most complex configuration is treated by considering a dynamic left ventricle- (LV-)elastance heart model which is governed by (and applied as) a nonlinear, non-stationary hybrid ODE-Dirichlet system. Other ODE-based boundary conditions, such as lumped parameter Windkessel models for truncated vasculature, are also considered. Performance studies of the complete 0D-3D solver, including its treatment of the lattice Boltzmann fluid equations and elastodynamics equations as well as their interactions, is conducted through a variety of benchmark and convergence studies that demonstrate the ability of the coupled 0D-3D methodology in generating physiological pressure and flow waveforms-ultimately enabling the exploration of various physical and physiological parameters for hemodynamics studies of the coupled LV-arterial system. The methods proposed in this paper can be easily applied to other ODE-based boundary conditions as well as to other fluid problems that are modeled by 3D lattice Boltzmann equations and that require direct coupling of dynamic 0D boundary conditions.

Fugacity-based lattice Boltzmann method for multicomponent multiphase systems

The free-energy model can extend the lattice Boltzmann method to multiphase systems. However, there is a lack of models capable of simulating multicomponent multiphase fluids with partial miscibility. In addition, existing models cannot be generalized to honor thermodynamic information provided by any multicomponent equation of state of choice. In this paper, we introduce a free-energy lattice Boltzmann model where the forcing term is determined by the fugacity of the species, the thermodynamic property that connects species partial pressure to chemical potential calculations. By doing so, we are able to carry out multicomponent multiphase simulations of partially miscible fluids and generalize the methodology for use with any multicomponent equation of state of interest. We test this fugacity-based lattice Boltzmann method for the cases of vapor-liquid equilibrium for two- and three-component mixtures in various temperature and pressure conditions. We demonstrate that the model is able to reliably reproduce phase densities and compositions as predicted by multicomponent thermodynamics and can reproduce different characteristic pressure-composition and temperature-composition envelopes with a high degree of accuracy. We also demonstrate that the model can offer accurate predictions under dynamic conditions.

Equations of state in multiphase lattice Boltzmann method revisited

The single-component multiphase fluids can be described by a single equation of state (EOS), and various EOSs have been employed in the multiphase lattice Boltzmann (LB) method. In this work, we revisit five commonly used EOSs, including the van der Waals EOS, the Redlich-Kwong EOS, the Redlich-Kwong-Soave EOS, the Peng-Robinson EOS, and the Carnahan-Starling EOS. The recent multiphase LB model with self-tuning EOS is employed because of its thermodynamic consistency in a strict sense and clear physical picture at the microscopic level. First, the way to incorporate these multiphase EOSs is proposed. Two scaling factors are introduced to independently adjust the surface tension and interface thickness, and the lattice sound speed is EOS-dependent to ensure the numerical stability. Then, numerical tests are conducted to validate the incorporations of these EOSs and compare their numerical performances. The surface tension and interface thickness are set to the same values for different EOSs in the comparisons. The liquid and gas densities, surface tension, and interface thickness by the LB simulation agree well with the thermodynamic results. The maximum density ratios achieved with different EOSs are at the same level and could be very close to each other when the interface thickness is relatively small. The effects of multiphase EOS, density ratio, and dimensionless relaxation time on the spurious current are discussed in detail. It is interesting to find the van der Waals EOS shows the best numerical performance in reducing the spurious current.

Discontinuous dewetting dynamics of highly viscous droplets on chemically heterogeneous substrates

HYPOTHESIS

Droplet spreading on heterogeneous (chemical/structural) surfaces has revealed local disturbances that affect the advancing contact line. With droplet dewetting being less studied, we hypothesize that a receding droplet can be perturbed by localized heterogeneity which leads to irregular and discontinuous dewetting of the substrate.

EXPERIMENTS

The sessile drop method was used to study droplet dewetting at a wettability boundary. One-half of a hydrophilic surface was hydrophobically modified with either i) methyloctyldichlorosilane or ii) clustered macromolecules. A Lattice Boltzmann method (LBM) simulation was also developed to determine the effect of contact angle hysteresis and boundary conditions on the droplet dynamics.

FINDINGS

The two surface treatments were optimized to produce comparable water wetting characteristics. With a negative Gibbs free energy on the hydrophilic-half, the oil droplet receded to the hydrophobic-half. On the silanized surface, the droplet was pinned and the resultant droplet shape was a distorted spherical cap, having receded uniformly on the unmodified surface. Modifying the surface with clustered macromolecules, the droplet receded slightly to form a spherical cap. However, droplet recession was non-uniform and daughter droplets formed near the wettability boundary. The LBM simulation revealed that daughter droplets formed when θR > 164°, with the final droplet shape accurately described by imposing a diffuse wettability boundary condition.

Mechanistic Insight into Wettability Enhancement of Lithium-Ion Batteries Using a Ceramic-Coated Layer

The crucial issue of wettability in high-energy-density lithium-ion batteries (LIBs) has not been comprehensively addressed to date. To overcome the challenge, state-of-the-art LIBs employing a ceramic-coated separator improves the safety- and wettability-related aspects of LIBs. Here, we present a mechanistic study of the effects of a ceramic-coated layer (CCL) on electrode wettability and report the optimal position of the CCL in LIBs. The electrolyte wetting was investigated using the multiphase lattice Boltzmann method and electrochemical impedance spectroscopy for capturing the electrolyte-transport dynamics in porous electrodes and impedance spectra in pouch-type LIBs, respectively. Results indicate that the CCL caused the velocity vector to transport the electrolyte further, resulting in an increase in the wetting rate. Moreover, the location of the CCL considerably affected the wettability of the LIBs. This study provides mechanical insight into the design and fabrication of high-performance LIBs by incorporating CCLs.