Lattice Boltzmann model for simulating flows with multiple phases and components

Quasi-Isotropic Cycles and Nonsingular Bounces in a Mixmaster Cosmology

A Bianchi type-IX mixmaster spacetime is the most general spatially homogeneous solution of Einstein's equations and it can represent the space-averaged universe. We introduce two novel mechanisms resulting in a mixmaster universe with nonsingular bounces that are quasi-isotropic. Matter with a nonlinear equation of state allows these bounces. Using a negative anisotropic stress successfully isotropizes this universe and mitigates the well-known mixmaster chaotic behavior. The Universe can be an eternal mixmaster spacetime, going through an infinite series of quasi-isotropic cycles separated by bounces.

Implementation of contact angles in pseudopotential lattice Boltzmann simulations with curved boundaries

The pseudopotential multiphase lattice Boltzmann (LB) model is a very popular model in the LB community for simulating multiphase flows. When the multiphase modeling involves a solid boundary, a numerical scheme is required to simulate the contact angle at the solid boundary. In this work, we aim at investigating the implementation of contact angles in the pseudopotential LB simulations with curved boundaries. In the pseudopotential LB model, the contact angle is usually realized by employing a solid-fluid interaction or specifying a constant virtual wall density. However, it is shown that the solid-fluid interaction scheme yields very large spurious currents in the simulations involving curved boundaries, while the virtual-density scheme produces an unphysical thick mass-transfer layer near the solid boundary although it gives much smaller spurious currents. We also extend the geometric-formulation scheme in the phase-field method to the pseudopotential LB model. Nevertheless, in comparison with the solid-fluid interaction scheme and the virtual-density scheme, the geometric-formulation scheme is relatively difficult to implement for curved boundaries and cannot be directly applied to three-dimensional space. By analyzing the features of these three schemes, we propose an improved virtual-density scheme to implement contact angles in the pseudopotential LB simulations with curved boundaries, which does not suffer from a thick mass-transfer layer near the solid boundary and retains the advantages of the original virtual-density scheme, i.e., simplicity, easiness for implementation, and low spurious currents.

Simulation of circulating tumor cell transport and adhesion in cell suspensions in microfluidic devices

Understanding cell transport and adhesion dynamics under flow is important for many biotransport problems. We investigated the influence of cell size, ligand coating density, micropost size, and intercellular collisions on circulating tumor cell adhesion and transport in microfluidic devices. The cells were modeled as coarse-grained cell membranes and the adhesion was modeled as pairwise interacting potentials, while the fluid was solved using the lattice Boltzmann method. The coupling between the cell and the fluid was achieved through the immersed boundary method. The cell showed transient rolling adhesion in high shear regions and firm adhesion in low shear regions. The adhesive force for rolling cells on a micropost was increasing before the cell reached the crest of the post and then decreasing afterward. The adhesive strength for cells increases with ligand coating density. Cell trajectories in a microfluidic device with a shifted post design were studied as well. At low concentrations, the majority of the cells follow streamlines closely. However, the intercellular collision and collision from red blood cells impacted the cell trajectories. An L 2 norm of | e | was defined to characterize the difference between the cell trajectories and the associated streamlines. It was shown that | e | L 2 increases with micropost sizes and cell concentrations.

Origin of spurious oscillations in lattice Boltzmann simulations of oscillatory noncontinuum gas flows

Oscillatory noncontinuum gas flows at the micro and nanoscales are characterized by two dimensionless groups: a dimensionless molecular length scale, the Knudsen number Kn, and a dimensionless frequency θ, relating the oscillatory frequency to the molecular collision frequency. In a recent study [Shi et al., Phys. Rev. E 89, 033305 (2014)10.1103/PhysRevE.89.033305], the accuracy of the lattice Boltzmann (LB) method for simulating these flows at moderate-to-large Kn and θ was examined. In these cases, the LB method exhibits spurious numerical oscillations that cannot be removed through the use of discrete particle velocities drawn from higher-order Gauss-Hermite quadrature. Here, we identify the origin of these spurious effects and formulate a method to minimize their presence. This proposed method splits the linearized Boltzmann Bhatnagar-Gross-Krook (BGK) equation into two equations: (1) a homogeneous "gain-free equation" that can be solved directly, containing terms responsible for the spurious oscillations; and (2) an inhomogeneous "remainder equation" with homogeneous boundary conditions (i.e., stationary boundaries) that is solved using the conventional LB algorithm. This proposed "splitting method" is validated using published high-accuracy numerical solutions to the linearized Boltzmann BGK equation where excellent agreement is observed.

Phase-field-based lattice Boltzmann model for liquid-gas-solid flow

Based on phase-field theory, we develop a lattice Boltzmann (LB) model for liquid-gas-solid flow from multiphase and particle dynamics algorithms. A modified bounce-back method is developed for the velocity-based LB approach. A curved boundary treatment with second-order accuracy based on velocity interpolation is developed. We propose a predictor-corrector scheme algorithm for specifying the three-phase contact angle on curved boundaries within the framework of structured Cartesian grids. In order to make the algorithm more stable, we combine the implicit particle velocity update scheme and the Galilean invariant momentum exchange method. The proposed method is validated through several single- and multicomponent fluid test cases. It was found the surface tension force associated with the interface acting on the solid structures can be captured. We simulate the sinking of a circular cylinder due to gravity, the numerical results agree well with the experimental data. Finally, we apply the method to the self-assembly process of multiple floating cylinders on water surface.

Mesoscale simulation of soft particles with tunable contact angle in multicomponent fluids

Soft particles at fluid interfaces play an important role in many aspects of our daily life, such as the food industry, paints and coatings, and medical applications. Analytical methods are not capable of describing the emergent effects of the complex dynamics of suspensions of many soft particles, whereas experiments typically either only capture bulk properties or require invasive methods. Computational methods are therefore a great tool to complement experimental work. However, an efficient and versatile numerical method is needed to model dense suspensions of many soft particles. In this article we propose a method to simulate soft particles in a multicomponent fluid, both at and near fluid-fluid interfaces, based on the lattice Boltzmann method, and characterize the error stemming from the fluid-structure coupling for the particle equilibrium shape when adsorbed onto a fluid-fluid interface. Furthermore, we characterize the influence of the preferential contact angle of the particle surface and the particle softness on the vertical displacement of the center of mass relative to the fluid interface. Finally, we demonstrate the capability of our model by simulating a soft capsule adsorbing onto a fluid-fluid interface with a shear flow parallel to the interface, and the covering of a droplet suspended in another fluid by soft particles with different wettability.

The effect of the liquid layer thickness on the dissolution of immersed surface droplets

Droplets on a liquid-immersed solid surface are key elements in many applications, such as high-throughput chemical analysis and droplet-templated porous materials. Such surface droplets dissolve when the surrounding liquid is undersaturated and the dissolution process is usually treated analogous to a sessile droplet evaporating in air. Typically, theoretical models predict the mass loss rate of dissolving droplets as a function of droplet geometrical factors (radius, constant angle), and droplet material properties (diffusion constant and densities), where the thickness of the surrounding liquid layer is neglected. Here, we investigate, both numerically and theoretically, the effect of the liquid layer thickness on the dissolution of surface droplets. We perform 3D lattice Boltzmann simulations and obtain the density distribution and time evolution of droplet height during dissolution. Moreover, we find that the dissolution slows down and the lifetime linearly increases with increasing the liquid layer thickness. We propose a theoretical model based on a quasistatic diffusion equation which agrees quantitatively with simulation results for thick liquid layers. Our results offer insight to the fundamental understanding of dissolving surface droplets and can provide valuable guidelines for the design of devices where the droplet lifetime is of importance.

Improved three-dimensional color-gradient lattice Boltzmann model for immiscible two-phase flows

In this paper, an improved three-dimensional color-gradient lattice Boltzmann (LB) model is proposed for simulating immiscible two-phase flows. Compared with the previous three-dimensional color-gradient LB models, which suffer from the lack of Galilean invariance and considerable numerical errors in many cases owing to the error terms in the recovered macroscopic equations, the present model eliminates the error terms and therefore improves the numerical accuracy and enhances the Galilean invariance. To validate the proposed model, numerical simulations are performed. First, the test of a moving droplet in a uniform flow field is employed to verify the Galilean invariance of the improved model. Subsequently, numerical simulations are carried out for the layered two-phase flow and three-dimensional Rayleigh-Taylor instability. It is shown that, using the improved model, the numerical accuracy can be significantly improved in comparison with the color-gradient LB model without the improvements. Finally, the capability of the improved color-gradient LB model for simulating dynamic two-phase flows at a relatively large density ratio is demonstrated via the simulation of droplet impact on a solid surface.

Lattice Boltzmann method for contact-line motion of binary fluids with high density ratio

Within the phase-field framework, we present an accurate and robust lattice Boltzmann (LB) method for simulating contact-line motion of immiscible binary fluids on the solid substrate. The most striking advantage of this method lies in that it enables us to handle two-phase flows with mass conservation and a high density contrast of 1000, which is often unavailable in the existing multiphase LB models. To simulate binary fluid flows, the present method utilizes two LB evolution equations, which are respectively used to solve the conservative Allen-Cahn equation for interface capturing, and the incompressible Navier-Stokes equations for hydrodynamic properties. Besides, to account for the substrate wettability, two popular contact angle models including the cubic surface-energy model and the geometrical one are incorporated into the present method, and their performances are numerically evaluated over a wide range of contact angles. The contact-angle hysteresis effect, which is inherent to a rough or chemically inhomogeneous substrate, is also introduced in the present LB approach through the strategy proposed by Ding and Spelt [J. Fluid Mech. 599, 341 (2008)10.1017/S0022112008000190]. The present method is first validated by simulating droplet spreading and capillary intrusion on the ideal or smooth pipes. It is found that the cubic surface-energy and geometrical wetting schemes both offer considerable accuracy for predicting a static contact angle within its middle region, while the former is more stable at extremely small contact angles. Besides, it is shown that the geometrical wetting scheme enables us to obtain better accuracy for predicting dynamic contact points in capillary pipe. Then we use the present LB method to simulate the droplet shearing processes on a nonideal substrate with contact angle hysteresis. The geometrical wetting model is found to be capable of reproducing four typical motion modes of contact line, while the surface-energy wetting scheme fails to predict the hysteresis behaviors in some cases. At last, a complex contact-line dynamic problem of three-dimensional microscale droplet impact on a wettable solid is simulated, and it is found that the numerical results for droplet shapes agree well with the experimental data.

Mixed bounce-back boundary scheme of the general propagation lattice Boltzmann method for advection-diffusion equations

In this work, a mixed bounce-back boundary scheme of general propagation lattice Boltzmann (GPLB) model is proposed for isotropic advection-diffusion equations (ADEs) with Robin boundary condition, and a detailed asymptotic analysis is also conducted to show that the present boundary scheme for the straight walls has a second-order accuracy in space. In addition, several numerical examples, including the Helmholtz equation in a square domain, the diffusion equation with sinusoidal concentration gradient, one-dimensional transient ADE with Robin boundary and an ADE with a source term, are also considered. The results indicate that the numerical solutions agree well with the analytical ones, and the convergence rate is close to 2.0. Furthermore, through adjusting the two parameters in the GPLB model properly, the present boundary scheme can be more accurate than some existing lattice Boltzmann boundary schemes.

Droplet Misalignment Limit for Inkjet Printing into Cavities on Textured Surfaces

The control of droplets deposited onto textured surfaces is of great importance for both engineering and medical applications. This research investigates the dynamics of a single droplet deposited into a confined space and its final equilibrium morphology, with emphasis given to droplet deposition under print head misalignment, the effect of nonuniform wettability, and deposition of droplets with varying sizes. A multiphase pseudopotential lattice Boltzmann methodology is used to simulate the process of deposition. The print quality is characterized in terms of a parameter referred to as the wetted fraction, which describes the proportion of the cavity that is wetted by the droplet. Our results show how single and multiple axis misalignment affect the final equilibrium morphology, and it was found for comparable configurations that multiaxis misalignment resulted in a higher wetted fraction. Investigations into wettabilities of the substrate and cavity wall revealed how larger ratios of the contact angles between the two enhance the ability for the droplet to self-align within the cavity. Additionally, a range of uniform wettabilities between the substrate and cavity were found, which mitigate against misalignment. Investigations into varying droplet sizes relative to the cavity revealed how misalignment can be compensated for with larger droplets, and limits for filling a cavity with a single drop are defined. Finally, we explore the deposition with misalignment into closely positioned cavities where it is found that the spacing between cavities is a key factor in determining the maximum permissible misalignment.

Hybrid Wettability-Induced Heat Transfer Enhancement for Condensation with NonCondensable Gas

Heat transfer enhancement in dropwise condensation is widely investigated on a superhydrophobic surface with the advances in surface engineering, but the influence of a large amount of noncondensable gas (NCG) has not been clarified. In this work, the condensation heat transfer with a large amount of NCG is investigated by developing a multiphase lattice Boltzmann model for a multicomponent system. First, the condensation of a single droplet on a hydrophobic surface with NCG is simulated, demonstrating the capacity of the present model to capture the behaviors of different components during phase change and predict the significant influence of even a small fraction of the NCG on heat transfer. Then, solid surfaces with mixed wettability are built by introducing a fraction of hydrophilic parts to enhance heat transfer. It is found that there exists an optimized proportion which could maximize the condensation heat transfer efficiency corresponding to a specific mass fraction of NCG. Furthermore, the mechanism of this optimized proportion is revealed by examining the dynamic behaviors of condensation in a typical case, as a balance between a promotion of the nucleation rate and a put off of transition to filmwise condensation.

Lattice Boltzmann methods and active fluids

We review the state of the art of active fluids with particular attention to hydrodynamic continuous models and to the use of Lattice Boltzmann Methods (LBM) in this field. We present the thermodynamics of active fluids, in terms of liquid crystals modelling adapted to describe large-scale organization of active systems, as well as other effective phenomenological models. We discuss how LBM can be implemented to solve the hydrodynamics of active matter, starting from the case of a simple fluid, for which we explicitly recover the continuous equations by means of Chapman-Enskog expansion. Going beyond this simple case, we summarize how LBM can be used to treat complex and active fluids. We then review recent developments concerning some relevant topics in active matter that have been studied by means of LBM: spontaneous flow, self-propelled droplets, active emulsions, rheology, active turbulence, and active colloids.

Multiple-time-scaling lattice Boltzmann method for the convection diffusion equation

A multiple-time-scaling (MTS) strategy that decouples the time discretization in different domains and enables flexible time-step coarsening, refinement, and stretching in the lattice Boltzmann method (LBM) for the convection diffusion equation is developed. The key in the multiple-time scaling is the satisfaction of physical interface conditions without nested iterations in each time step by implementing appropriate interface schemes for the distribution functions in the LBM. The applicability and second-order accuracy of the MTS-LBM approach is demonstrated with two numerical tests. Our approach greatly expands the avenue and expedites the progress of applying the LBM for modeling complex flows and transport phenomena involving multiphases and multicomponents with large property ratios.

Interaction pressure tensor on high-order lattice Boltzmann models for nonideal fluids

In this work we address the application of pseudopotentials directly on high-order lattice Boltzmann models. We derive a general expression for the pressure tensor on high-order lattices considering all nonideal interactions, including intra- and intermolecular interactions, following the discrete lattice theory introduced by X. Shan [Phys. Rev. E 77, 066702 (2008)PLEEE81539-375510.1103/PhysRevE.77.066702]. From the derived expression, a generalized continuum approximation, truncated at fourth-order isotropy, is obtained that is readily applicable to high-order lattices. With this, we demonstrate that high-order lattice models with pseudopotentials can satisfy thermodynamic consistency. The derived generalized expression and continuum approximation are validated for the case of a flat interface and compared against the standard definition available from the literature. The generalized expression is also shown to accurately reproduce the Laplace experiment for a variety of high-order lattice structures. This work sets the preliminary steps towards the application of high-order lattice models for simulating nonideal fluid mixtures.

Lattice Boltzmann simulations of nonequilibrium fluctuations in a nonideal binary mixture

In recent years the lattice Boltzmann (LB) methodology has been fruitfully extended to include the effects of thermal fluctuations. So far, all studied cases pertain to equilibrium fluctuations, i.e., fluctuations with respect to an equilibrium background state. In this paper we take a step further and present results of fluctuating LB simulations of a binary mixture confined between two parallel walls in the presence of a constant concentration gradient in the wall-to-wall direction. This is a paradigmatic setup for the study of nonequilibrium (NE) fluctuations, i.e., fluctuations with respect to a nonequilibrium state. We analyze the dependence of the structure factors for the hydrodynamical fields on the wave vector q in both the directions parallel and perpendicular to the walls, highlighting the long-range (∼|q|^{-4}) nature of correlations in the NE framework. Results at the small scales (high wave numbers) quantitatively agree with the predictions of fluctuating hydrodynamics without fitting parameters. At larger scales (low wave numbers), however, results show finite-size effects induced by confinement and call for further studies aimed at controlling boundary conditions in the fluctuating LB framework as well as compressibility effects. Moreover, in the presence of a nonideal equation of state of the mixture, we also observe that the (spatially homogeneous) average pressure changes, due to a genuinely new contribution triggered by NE fluctuations. These NE pressure effects are studied at changing the system size and the concentration gradient. Taken all together, we argue that the results of this article are useful and instrumental to boost the applicability of the fluctuating LB methodology in the framework of NE fluctuations, possibly in conjunction with experiments.

Phase-field-theory-based lattice Boltzmann equation method for N immiscible incompressible fluids

From the phase field theory, we develop a lattice Boltzmann equation (LBE) method for N (N≥2) immiscible incompressible fluids, and the Cahn-Hilliard equation, which could capture the interfaces between different phases, is also solved by LBE for an N-phase system. In this model, the interface force of N immiscible incompressible fluids is incorporated by chemical potential form, and the fluid-fluid surface tensions could be directly calculated and independently tuned. Numerical simulations including two stationary droplets, spreading of a liquid lens with and without gravity and two immiscible liquid lenses, and phase separation are conducted to validate the present LBE, and numerical results show that the predictions by LBE agree well with the analytical solutions and other numerical results.

Phase-field method based on discrete unified gas-kinetic scheme for large-density-ratio two-phase flows

In this paper, a phase-field method under the framework of discrete unified gas-kinetic scheme (DUGKS) for incompressible multiphase fluid flows is proposed. Two kinetic models are constructed to solve the conservative Allen-Cahn equation that accounts for the interface behavior and the incompressible hydrodynamic equations that govern the flow field, respectively. With a truncated equilibrium distribution function as well as a temporal derivative added to the source term, the macroscopic governing equations can be exactly recovered from the kinetic models through the Chapman-Enskog analysis. Calculation of source terms involving high-order derivatives existed in the quasi-incompressible model is simplified. A series of benchmark cases including four interface-capturing tests and four binary flow tests are carried out. Results compared to that of the lattice Boltzmann method (LBM) have been obtained. A convergence rate of second order can be guaranteed in the test of interface diagonal translation. The capability of the present method to track the interface that undergoes a severe deformation has been verified. Stationary bubble and spinodal decomposition problems, both with a density ratio as high as 1000, are conducted and reliable solutions have been provided. The layered Poiseuille flow with a large viscosity ratio is simulated and numerical results agree well with the analytical solutions. Variation of positions of the bubble front and spike tip during the evolution of Rayleigh-Taylor instability has been predicted precisely. However, the detailed depiction of complicated interface patterns appearing during the evolution process is failed, which is mainly caused by the relatively large numerical dissipation of DUGKS compared to that of LBM. A high-order DUGKS is needed to overcome this problem.

Separate-phase model and its lattice Boltzmann algorithm for liquid-vapor two-phase flows in porous media

In this article, we formulate a set of the separate-phase governing equations at the representative-elementary-volume scale and develop its double-distribution function lattice Boltzmann (LB) algorithm to describe liquid-vapor two-phase flows with or without phase change in porous media. Different from those previous studies, the mathematical description in this article involves the Darcy force, viscous force, and pressure gradient, and the resulting LB simulations can well describe two-phase flows and mass transfer throughout porous media under the compounding effects of these forces. The LB algorithm was validated by simulating single-phase flows in porous media. Its results are in good agreement with those available analytical solutions. We also applied it to model water flows through a semi-infinite porous region bounded by a heated solid wall, where liquid-vapor phase change takes place. The numerical simulations recover the previous results in the limit of the zero Darcy number. Significantly, it reveals much richer two-phase flow and mass transfer characteristics in porous media adjacent to solid walls. The separate-phase model and its lattice Boltzmann algorithm in this article are effective means to gain more profound and clearer understandings of complex two-phase transport processes in a porous system.

Hydrodynamic behavior of the pseudopotential lattice Boltzmann method for interfacial flows

The lattice Boltzmann method (LBM) is routinely employed in the simulation of complex multiphase flows comprising bulk phases separated by nonideal interfaces. The LBM is intrinsically mesoscale with a hydrodynamic equivalence popularly set by the Chapman-Enskog analysis, requiring that fields slowly vary in space and time. The latter assumptions become questionable close to interfaces where the method is also known to be affected by spurious nonhydrodynamical contributions. This calls for quantitative hydrodynamical checks. In this paper, we analyze the hydrodynamic behavior of the LBM pseudopotential models for the problem of the breakup of a liquid ligament triggered by the Plateau-Rayleigh instability. Simulations are performed at fixed interface thickness, while increasing the ligament radius, i.e., in the "sharp interface" limit. The influence of different LBM collision operators is also assessed. We find that different distributions of spurious currents along the interface may change the outcome of the pseudopotential model simulations quite sensibly, which suggests that a proper fine-tuning of pseudopotential models in time-dependent problems is needed before the utilization in concrete applications. Taken all together, we argue that the results of the proposed paper provide a valuable insight for engineering pseudopotential model applications involving the hydrodynamics of liquid jets.

Curvature dynamics and long-range effects on fluid-fluid interfaces with colloids

We investigate the dynamics of a phase-separating binary fluid, containing colloidal dumbbells anchored to the fluid-fluid interface. Extensive lattice Boltzmann-immersed boundary method simulations reveal that the presence of soft dumbbells can significantly affect the curvature dynamics of the interface between phase-separating fluids, even though the coarsening dynamics is left nearly unchanged. In addition, our results show that the curvature dynamics exhibits distinct non-local effects, which might be exploited for the design of new soft mesoscale materials. We point out that the inspection of the statistical dynamics of the curvature can disclose new insights into local inhomogeneities of the binary fluid configuration, as a function of the volume fraction and aspect ratio of the dumbbells.

Lattice Boltzmann model with self-tuning equation of state for multiphase flows

A lattice Boltzmann (LB) model for multiphase flows is developed that complies with the thermodynamic foundations of kinetic theory. By directly devising the collision term for the LB equation at the discrete level, a self-tuning equation of state is achieved, which can be interpreted as the incorporation of short-range molecular interaction. A pairwise interaction force is introduced to mimic the long-range molecular interaction, which is responsible for interfacial dynamics. The derived pressure tensor is naturally consistent with thermodynamic theory, and surface tension and interface thickness can be independently prescribed. Numerical tests, including static and dynamic cases, are carried out to validate the present model and good results are obtained. As a further application, head-on collision of equal-sized droplets is simulated and the elusive "bouncing" regime is successfully reproduced.

Entropy production in thermal phase separation: a kinetic-theory approach

Entropy production during the process of thermal phase-separation of multiphase flows is investigated by means of a discrete Boltzmann kinetic model. The entropy production rate is found to increase during the spinodal decomposition stage and to decrease during the domain growth stage, attaining its maximum at the crossover between the two. Such behaviour provides a natural criterion to identify and discriminate between the two regimes. Furthermore, the effects of heat conductivity, viscosity and surface tension on the entropy production rate are investigated by systematically probing the interplay between non-equilibrium energy and momentum fluxes. It is found that the entropy production rate due to energy fluxes is an increasing function of the Prandtl number, while the momentum fluxes exhibit an opposite trend. On the other hand, both contributions show an increasing trend with surface tension. The present analysis inscribes within the general framework of non-equilibrium thermodynamics and consequently it is expected to be relevant to a broad class of soft-flowing systems far from mechanical and thermal equilibrium.

Pore-scale characteristics of multiphase flow in heterogeneous porous media using the lattice Boltzmann method

This study provides a pore-scale investigation of two-phase flow dynamics during primary drainage in a realistic heterogeneous rock sample. Using the lattice Boltzmann (LB) method, a series of three-dimensional (3D) immiscible displacement simulations are conducted and three typical flow patterns are identified and mapped on the capillary number (Ca)-viscosity ratio(M) phase diagram. We then investigate the effect of the viscosity ratio and capillary number on fluid saturation patterns and displacement stability in Tuscaloosa sandstone, which is taken from the Cranfield site. The dependence of the evolution of saturation, location of the displacement front, 3D displacement patterns and length of the center of mass of the invading fluid on the viscosity ratio and capillary number have been delineated. To gain a quantitative insight into the characteristics of the invasion morphology in 3D porous media, the fractal dimension D_f of the non-wetting phase displacement patterns during drainage has been computed for various viscosity ratios and capillary numbers. The logarithmic dependence of D_f on invading phase saturation appears to be the same for various capillary numbers and viscosity ratios and follows a universal relation.

Comparison of the lattice-Boltzmann model with the finite-difference time-domain method for electrodynamics

A three-dimensional lattice-Boltzmann model (LBM) for the simulation of the Maxwell equations is presented. The inclusion of media follows an extension of a special limit described in the literature which is applicable to this LBM and does not harm the stability of simulations. The focus of the present study lies on the properties of numerical accuracy and stability of the LBM in comparison to the standard finite-difference time-domain (FDTD) method based on Yee's method. Typical examples, often investigated in the context of numerical simulations, are considered. These include the propagation of electrodynamic (EM) fields in one- and three-dimensional systems. Results of this simulations are compared to the ones of their theoretical predictions. Further on, long-time simulations are done in systems with periodic boundary conditions to check if the total energy is conserved. To investigate the effect of the numeric impedance, the propagation of an EM pulse is monitored spatially and temporarily in a two-dimensional system. The simulation results indicate, in contrast to the one obtained from the FDTD method, that the presented LBM does fulfill the expected energy conservation and is not effected by the numerical impedance. This LBM therefore represents a valuable alternative for the simulation of EM problems like long-time simulations by avoiding intrinsic properties the FDTD method suffers from.

Lattice Boltzmann simulation of immiscible three-phase flows with contact-line dynamics

A multiphase lattice Boltzmann method is developed to simulate immiscible three-phase flows with contact-line dynamics. In this method, the immiscible three-phase flow is modeled by a multiple-relaxation-time color-gradient model, which not only allows for a full range of interfacial tensions but also can produce viscosity-independent results especially when the fluid-surface interactions are considered. To achieve the desired contact angles, a weighted contact angle model is utilized to obtain a relatively smooth transition of contact angle for each fluid, which is enforced through a geometrical wetting condition. This method is first validated by simulations of a Janus droplet resting on a surface for various contact angles and fluid properties and dynamic capillary filling of ternary fluids with different viscosity ratios. It is then used to simulate a Janus droplet on a substrate subject to Poiseuille flow. Results show that the droplet may undergo three typical modes, namely, two stable deformation modes and breakup mode, which depend not only on the inlet velocity but also on the fluid viscosity. The terminal velocity of moving droplet increases linearly with the inlet velocity in both stable modes only when three fluids do not differ much in their viscosities.

How antagonistic salts cause nematic ordering and behave like diblock copolymers

We present simulation results and an explanatory theory on how antagonistic salts affect the spinodal decomposition of binary fluid mixtures. We find that spinodal decomposition is arrested and complex structures form only when electrostatic ion-ion interactions are small. In this case, the fluid and ion concentrations couple and the charge field can be approximated as a polynomial function of the relative fluid concentrations alone. When the solvation energy associated with transferring an ion from one fluid phase to the other is of the order of a few k_BT, the coupled fluid and charge fields evolve according to the Ohta-Kawasaki free energy functional. This allows us to accurately predict structure sizes and reduce the parameter space to two dimensionless numbers. The lamellar structures induced by the presence of the antagonistic salt in our simulations exhibit a high degree of nematic ordering and the growth of ordered domains over time follows a power law. This power law carries a time exponent proportional to the salt concentration. We qualitatively reproduce and interpret neutron scattering data from previous experiments of similar systems. The dissolution of structures at high salt concentrations observed in these experiments agrees with our simulations, and we explain it as the result of a vanishing surface tension due to electrostatic contributions. We conclude by presenting 3D results showing the same morphologies as predicted by the Ohta-Kawasaki model as a function of volume fraction and suggesting that our findings from 2D systems remain valid in 3D.

Liquid membrane catalytic model of hydrolyzing cellulose into 5-hydroxymethylfurfural based on the lattice Boltzmann method

Conversion of cellulose to 5-hydroxymethylfurfural (HMF) is an important means of biomass utilization.

A Comparative Study of Multiphase Lattice Boltzmann Methods for Bubble-Dendrite Interaction during Solidification of Alloys

This paper presents a comparative study between the pseudopotential Shan-Chen model and the phase field multiphase lattice Boltzmann method for simulating bubble dynamics during dendritic solidification of binary alloys. The Shan-Chen method is an efficient lattice Boltzmann multiphase method despite having some limitations, including the generation of large spurious currents. The phase field model solves the Cahn-Hilliard equation in addition to the Navier-Stokes equation to track the interface between phases. The phase field method is more accurate than the Shan-Chen model for simulation of fluids with a high-density ratio since it generates an acceptable small spurious current, though at the expense of higher computational costs. For the simulations in this article, the multiphase lattice Boltzmann model was coupled with the cellular automata and finite difference methods to solve temperature and concentration fields. The simulated results were presented and compared regarding the ability of each model to simulate phenomena at a microscale resolution, such as Marangoni convection, the magnitude of spurious current, and the computational costs. It is shown that although Shan-Chen methods can replicate some qualitative features of bubble-dendrite interaction, the generated spurious current is unacceptably large, particularly for practical values of the density ratio between fluid and gas phases. This occurs even after implementation of several enhancements to the original Shan-Chen method. This serious limitation makes the Shan-Chen models unsuitable to simulate fluid flow phenomena, such as Marangoni convection, because the large spurious currents mask completely the physical flow.

Electrokinetic droplet transport from electroosmosis to electrophoresis

Droplet transport in microfluidic channels by electrically induced flows often entails the simultaneous presence of electroosmosis and electrophoresis. Here we make use of coupled lattice-Boltzmann/molecular dynamics simulations to compute the mobility of a droplet in a microchannel under the effect of an external electric field. By varying the droplet solvation free energy of the counterions released at the channel walls, we observe the continuous transition between the electroosmotic and electrophoretic regime. We show that it is possible to describe the mobility of a droplet in a unified, consistent way, by combining the theoretical description of the electroosmotic flow with, in this case, the Hückel limit of electrophoresis, modified in order to take into account the Hadamard-Rybczynski droplet drag.