Lattice Boltzmann model for simulating flows with multiple phases and components

Prediction of immiscible two-phase flow properties in a two-dimensional Berea sandstone using the pore-scale lattice Boltzmann simulation

Immiscible two-phase flow in porous media is commonly encountered in industrial processes and environmental issues, such as enhanced oil recovery and the migration of fluids in an unsaturated zone. To deepen the current understanding of its underlying mechanism, this work focuses on the factors that influence the relative permeability and specific interfacial length of a two-phase flow in porous media, i.e., fluid saturation, viscosity ratio and contact angle. The lattice Boltzmann color-gradient model is adopted for pore-scale investigations, and the main findings are obtained as follows. Firstly, the relative permeability of each fluid increases as its saturation increases. The specific interfacial length first increases and then decreases as the saturation of the wetting fluid increases, and reaches a maximum when the permeabilities of both fluids are equal. Secondly, as the viscosity ratio of wetting to non-wetting fluids increases, the relative permeability of the wetting fluid will increase while that of the non-wetting fluid will decrease. The specific interfacial length will increase with increasing the viscosity difference between fluids. Finally, as the contact angle (measured from the wetting fluid) increases, the relative permeability of the wetting fluid overall increases while that of the non-wetting fluid decreases. Increasing contact angle always leads to a decrease in the specific interfacial length.

Theoretical investigation of heterogeneous wettability in porous media using NMR

It is highly important to understand the heterogeneous wettability properties of porous media for enhanced oil recovery (EOR). However, wettability measurements are still challenging in directly investigating the wettability of porous media. In this paper, we propose a multidimensional nuclear magnetic resonance (NMR) method and the concept of apparent contact angles to characterize the heterogeneous wettability of porous media. The apparent contact angle, which is determined by both the wetting surface coverage and the local wettability (wetting contact angles of each homogeneous wetting regions or wetting patches), is first introduced as an indicator of the heterogeneous wettability of porous media using the NMR method. For homogeneously wetting patches, the relaxation time ratio T1/T2 is employed to probe the local wettabiity of wetting patches. The T2 - D is introduced to obtain the wetting surface coverage using the effective relaxivity. Numerical simulations are conducted to validate this method.

On the effects of surface corrugation on the hydrodynamic performance of cylindrical rigid structures

In this work, we perform fully three-dimensional numerical simulations of the flow field surrounding cylindrical structures characterized by different types of corrugated surface. The simulations are carried out using the Lattice Boltzmann Method (LBM), considering a flow regime with a Reynolds number [Formula: see text]. The fluid-dynamic wake structure and stability are investigated by means of PSD analyses of the velocity components and by visual inspection of the vortical coherent structure evolution. Moreover, the energy dissipation of the flow is assessed by considering an equivalent discharge coefficient [Formula: see text], which measures the total pressure losses of the flow moving around the various layout under investigation. Outcomes from our study demonstrate that the helical ridges augment energy dissipation, but might also have a role in the passive control of the characteristic frequencies of the unsteady wake flow.

Effects of thermal fluctuations in the fragmentation of a nanoligament

We study the effects of thermally induced capillary waves in the fragmentation of a liquid ligament into multiple nanodroplets. Our numerical implementation is based on a fluctuating lattice Boltzmann (LB) model for nonideal multicomponent fluids, including nonequilibrium stochastic fluxes mimicking the effects of molecular forces at the nanoscales. We quantitatively analyze the statistical distribution of the breakup times and the droplet volumes after the fragmentation process at changing the two relevant length scales of the problem, i.e., the thermal length scale and the ligament size. The robustness of the observed findings is also corroborated by quantitative comparisons with the predictions of sharp interface hydrodynamics. Beyond the practical importance of our findings for nanofluidic engineering devices, our study also explores a novel application of LB in the realm of nanofluidic phenomena.

Thermal lattice Boltzmann method for multiphase flows

An alternative method to simulate heat transport in the multiphase lattice Boltzmann (LB) method is proposed. To solve the energy transport equation when phase boundaries are present, the method of a passive scalar is considerably modified. The internal energy is represented by an additional set of distribution functions, which evolve according to an LB-like equation simulating the transport of a passive scalar. Parasitic heat diffusion near boundaries with a large density gradient is suppressed by using special "pseudoforces" which prevent the spreading of energy. The compression work and heat diffusion are calculated by finite differences. A new method to take into account the latent heat of a phase transition Q(T) is realized. The latent heat is released or absorbed continuously inside a thin transition layer in a certain range of density, ρ_{1}<ρ<ρ_{2}. This allows one to avoid interface tracking. Several tests were carried out concerning all aspects of the processes. It is shown that the Galilean invariance and the scaling of the thermal conduction process hold, as well as the correct dependence of the sound speed on the heat capacity ratio. The method proposed has low scheme diffusion of the internal energy, and it can be applied to modeling a wide range of multiphase flows with heat and mass transfer even for high density ratios of liquid and vapor phases.

Single-component multiphase lattice Boltzmann simulation of free bubble and crevice heterogeneous cavitation nucleation

This work serves as an important extension of previous work on cavitation simulation [Sukop and Or, Phys. Rev. E 71, 046703 (2005)10.1103/PhysRevE.71.046703]. A modified Shan-Chen single-component multiphase lattice Boltzmann method is used to simulate two different heterogeneous cavitation nucleation mechanisms, the free gas bubble model and the crevice nucleation model. Improvements include the use of a real-gas equation of state, a redefined effective mass function, and the exact difference method forcing scheme. As a result, much larger density ratios, better thermodynamic consistency, and improved numerical accuracy are achieved. In addition, the crevice nucleation model is numerically investigated using the lattice Boltzmann method. The simulations show excellent qualitative and quantitative agreement with the heterogeneous nucleation theories.

Mass conservative lattice Boltzmann scheme for a three-dimensional diffuse interface model with Peng-Robinson equation of state

Peng-Robinson (P-R) equation of state (EOS) has been widely used in the petroleum industry for hydrocarbon fluids. In this work, a three-dimensional diffuse interface model with P-R EOS for two-phase fluid system is solved by the lattice Boltzmann (LB) method. In this diffuse interface model, an Allen-Cahn (A-C) type phase equation with strong nonlinear source term is derived. Using the multiscale Chapman-Enskog analysis, the A-C type phase equation can be recovered from the proposed LB method. Besides, a Lagrange multiplier is introduced based on the mesoscopic character of the LB scheme so that total mass of the hydrocarbon system is preserved. Three-dimensional numerical simulations of realistic hydrocarbon components, such as isobutane and propane, are implemented to illustrate the effectiveness of the proposed mass conservative LB scheme. Numerical results reach a better agreement with laboratory data compared to previous results of two-dimensional numerical simulations.

Fluid flow simulations meet high-speed video: Computer vision comparison of droplet dynamics

HYPOTHESIS

While multiphase flows, particularly droplet dynamics, are ordinary in nature as well as in industrial processes, their mathematical and computational modelling continue to pose challenging research tasks - patent approaches for tackling them are yet to be found. The lack of analytical flow field solutions for non-trivial droplet dynamics hinders validation of computer simulations and, hence, their application in research problems. High-speed videos and computer vision algorithms can provide a viable approach to validate simulations directly against experiments.

EXPERIMENTS

Droplets of water (or glycerol-water mixtures) impacting on both hydrophobic and superhydrophobic surfaces were imaged with a high-speed camera. The corresponding configurations were simulated using a lattice-Boltzmann multiphase scheme. Video frames from experiments and simulations were compared, by means of computer vision, over entire droplet impact events.

FINDINGS

The proposed experimental validation procedure provides a detailed, dynamic one-on-one comparison of a droplet impact. The procedure relies on high-speed video recording of the experiments, computer vision, and on a software package for the analyzation routines. The procedure is able to quantitatively validate computer simulations against experiments and it is widely applicable to multiphase flow systems in general.

Modeling thermal inkjet and cell printing process using modified pseudopotential and thermal lattice Boltzmann methods

Pseudopotential lattice Boltzmann methods (LBMs) can simulate a phase transition in high-density ratio multiphase flow systems. If coupled with thermal LBMs through equation of state, they can be used to study instantaneous phase transition phenomena with a high-temperature gradient where only one set of formulations in an LBM system can handle liquid, vapor, phase transition, and heat transport. However, at lower temperatures an unrealistic spurious current at the interface introduces instability and limits its application in real flow system. In this study, we proposed new modifications to the LBM system to minimize a spurious current which enables us to study nucleation dynamic at room temperature. To demonstrate the capabilities of this approach, the thermal ejection process is modeled as one example of a complex flow system. In an inkjet printer, a thermal pulse instantly heats up the liquid in a microfluidic chamber and nucleates bubble vapor providing the pressure pulse necessary to eject droplets at high speed. Our modified method can present a more realistic model of the explosive vaporization process since it can also capture a high-temperature/density gradient at nucleation region. Thermal inkjet technology has been successfully applied for printing cells, but cells are susceptible to mechanical damage or death as they squeeze out of the nozzle head. To study cell deformation, a spring network model, representing cells, is connected to the LBM through the immersed boundary method. Looking into strain and stress distribution of a cell membrane at its most deformed state, it is found that a high stretching rate effectively increases the rupture tension. In other words, membrane deformation energy is released through creation of multiple smaller nanopores rather than big pores. Overall, concurrently simulating multiphase flow, phase transition, heat transfer, and cell deformation in one unified LB platform, we are able to provide a better insight into the bubble dynamic and cell mechanical damage during the printing process.

Three-dimensional cascaded lattice Boltzmann method: Improved implementation and consistent forcing scheme

The cascaded or central-moment-based lattice Boltzmann method (CLBM) proposed in [Phys. Rev. E 73, 066705 (2006)PLEEE81539-375510.1103/PhysRevE.73.066705] possesses very good numerical stability. However, two constraints exist in three-dimensional (3D) CLBM simulations. First, the conventional implementation for 3D CLBM involves cumbersome operations and requires much higher computational cost compared to the single-relaxation-time (SRT) LBM. Second, it is a challenge to accurately incorporate a general force field into the 3D CLBM. In this paper, we present an improved method to implement CLBM in 3D. The main strategy is to adopt a simplified central moment set and carry out the central-moment-based collision operator based on a general multi-relaxation-time (GMRT) framework. Next, the recently proposed consistent forcing scheme for CLBM [Fei and Luo, Phys. Rev. E 96, 053307 (2017)2470-004510.1103/PhysRevE.96.053307] is extended to incorporate a general force field into 3D CLBM. Compared with the recently developed nonorthogonal CLBM [Rosis, Phys. Rev. E 95, 013310 (2017)2470-004510.1103/PhysRevE.95.013310], our implementation is proved to reduce the computational cost significantly. The inconsistency of adopting the discrete equilibrium distribution functions in the nonorthogonal CLBM is analyzed and validated. The 3D CLBM developed here in conjunction with the consistent forcing scheme is verified through numerical simulations of several canonical force-driven flows, highlighting very good properties in terms of accuracy, convergence, and consistency with the nonslip rule. Finally, the techniques developed here for 3D CLBM can be applied to make the implementation and execution of 3D MRT-LBM more efficient.

Lattice Boltzmann simulation of droplet dynamics on granular surfaces with variable wettability

Soil-composing particles undergo wettability changes, impacting hydraulic and mechanical processes such as erosion and landslides. Such processes evolve at very small scales, typically at the particle level. Here we capture the evolution of liquid interfaces in a single particle and several particles with the lattice Boltzmann (LB) method. The paper presents a three-dimensional LB study on the droplet dynamics on a layer of uniformly packed spherical particles with varying size and intrinsic contact angle (CA) aimed at mimicking conditions comparable to those of real soils. The numerical droplet is initialized close to the granular surface and deposited by gravity. Three spreading and infiltration behaviors were identified: a droplet with a stable apparent CA, a droplet with a metastable apparent CA before infiltration, and immediate infiltration. The results showed that the formation of a droplet with a stable or metastable spherical-cap shape depends on the particle size and the intrinsic CA. Furthermore, the initial wetted zone expansion was found to be governed by inertial effects with its behavior characterized by a power law. Finally, the apparent CA, which is closely related to the intrinsic CA, was found to be influenced by the particle size due to a significant portion of the droplet being embedded into the granular surface for the larger particles and reducing the apparent CA. This paper provides a basis for future research targeting the behavior of droplet interaction with granular surfaces with variable intrinsic CAs (from wettable to superhydrophobic) such as soils and other granular materials for industrial applications. The numerical approach implemented can also be extended to model other dynamic processes for a droplet, such as evaporation, high-velocity impacting, and lateral sliding.

Color-gradient lattice Boltzmann model with nonorthogonal central moments: Hydrodynamic melt-jet breakup simulations

We develop a lattice Boltzmann (LB) model for immiscible two-phase flow simulations with central moments (CMs). This successfully combines a three-dimensional nonorthogonal CM-based LB scheme [De Rosis, Phys. Rev. E 95, 013310 (2017)2470-004510.1103/PhysRevE.95.013310] with our previous color-gradient LB model [Saito, Abe, and Koyama, Phys. Rev. E 96, 013317 (2017)2470-004510.1103/PhysRevE.96.013317]. Hydrodynamic melt-jet breakup simulations show that the proposed model is significantly more stable, even for flow with extremely high Reynolds numbers, up to O(10^{6}). This enables us to investigate the phenomena expected under actual reactor conditions.

Numerical simulation of bubble growth on and departure from the heated surface by an improved lattice Boltzmann model

Based on the phase change model developed by lattice Boltzmann method (LBM), an improved source term which is responsible for phase change is proposed. The computation of the latent heat is taken into consideration to avoid the error and instability caused by the equation of state (EOS). Periodic bubble growth and departure from a heated surface during the boiling process is investigated based on the newly developed lattice Boltzmann model. Effects of gravity, contact angel and superheat on bubble departure diameter and release period under constant wall temperature conditions are illustrated. The three-phase contact line movements of the vapor bubble and the wall heat flux are also described. The results reflect the dynamic features and the influencing mechanism of bubble in boiling period, and this research lays the foundation of further studies on thermal-hydraulics and safety analysis by LBM.

Ternary Free-Energy Entropic Lattice Boltzmann Model with a High Density Ratio

A thermodynamically consistent free energy model for fluid flows comprised of one gas and two liquid components is presented and implemented using the entropic lattice Boltzmann scheme. The model allows a high density ratio, up to the order of O(10^{3}), between the liquid and gas phases, and a broad range of surface tension ratios, covering partial wetting states where Neumann triangles are formed, and full wetting states where complete encapsulation of one of the fluid components is observed. We further demonstrate that we can capture the bouncing, adhesive, and insertive regimes for the binary collisions between immiscible droplets suspended in air. Our approach opens up a vast range of multiphase flow applications involving one gas and several liquid components.

General propagation lattice Boltzmann model for nonlinear advection-diffusion equations

In this paper, a general propagation lattice Boltzmann model is proposed for nonlinear advection-diffusion equations (NADEs), and the Chapman-Enskog analysis shows that the NADEs with variable coefficients can be recovered correctly from the present model. We also perform some simulations of the linear advection-diffusion equation, nonlinear heat conduction equation, NADEs with anisotropic diffusion, and variable coefficients to test the present model, and find that the numerical results agree well with the corresponding analytical solutions. Moreover, it is also shown that by properly adjusting the two free parameters introduced into the propagation step, the present model could be more stable and more accurate than the standard lattice Bhatnagar-Gross-Krook model.

From Dot to Ring: The Role of Friction in the Deposition Pattern of a Drying Colloidal Suspension Droplet

The deposition of particles on a substrate by drying a colloidal suspension droplet is at the core of applications ranging from traditional printing on paper to printable electronics or photovoltaic devices. The self-pinning induced by the accumulation of particles at the contact line plays an important role in the formation of a deposit. In this article, we investigate, both numerically and theoretically, the effect of friction between the particles and the substrate on the deposition pattern. Without friction, the contact line shows a stick-slip behavior and a dotlike deposit is left after the droplet is evaporated. By increasing the friction force, we observe a transition from a dotlike to a ringlike deposit. We propose a theoretical model to predict the effective radius of the particle deposit as a function of the friction force. Our theoretical model predicts a critical friction force when self-pinning happens and the effective radius of deposit increases with increasing friction force, confirmed by our simulation results. Our results can find implications for developing active control strategies for the deposition of drying droplets.

Eliminating cubic terms in the pseudopotential lattice Boltzmann model for multiphase flow

It is well recognized that there exist additional cubic terms of velocity in the lattice Boltzmann (LB) model based on the standard lattice. In this work, elimination of these cubic terms in the pseudopotential LB model for multiphase flow is investigated, where the force term and density gradient are considered. By retaining high-order (≥3) Hermite terms in the equilibrium distribution function and the discrete force term, as well as introducing correction terms in the LB equation, the additional cubic terms of velocity are entirely eliminated. With this technique, the computational simplicity of the pseudopotential LB model is well maintained. Numerical tests, including stationary and moving flat and circular interface problems, are carried out to show the effects of such cubic terms on the simulation of multiphase flow. It is found that the elimination of additional cubic terms is beneficial to reduce the numerical error, especially when the velocity is relatively large. Numerical results also suggest that these cubic terms mainly take effect in the interfacial region and that the density-gradient-related cubic terms are more important than the other cubic terms for multiphase flow.

Lattice Boltzmann simulations of liquid CO2 displacing water in a 2D heterogeneous micromodel at reservoir pressure conditions

We employed the color-fluid lattice Boltzmann multiphase model to simulate liquid CO₂ displacing water documented in experiments in a 2D heterogeneous micromodel at reservoir pressure conditions. The main purpose is to investigate whether lattice Boltzmann simulation can reproduce the CO₂ invasion patterns observed in these experiments for a range of capillary numbers. Although the viscosity ratio used in the simulation matches the experimental conditions, the viscosity of the fluids in the simulation is higher than that of the actual fluids used in the experiments. Doing so is required to enhance numerical stability, and is a common strategy employed in the literature when using the lattice Boltzmann method to simulate CO₂ displacing water. The simulations reproduce qualitatively similar trends of changes in invasion patterns as the capillary number is increased. However, the development of secondary CO₂ pathways, a key feature of the invasion patterns in the simulations and experiments, is found to occur at a much higher capillary number in the simulations compared with the experiments. Additional numerical simulations were conducted to investigate the effect of the absolute value of viscosity on the invasion patterns while maintaining the viscosity ratio and capillary number fixed. These results indicate that the use of a high viscosity (which significantly reduces the inertial effect in the simulations) suppresses the development of secondary CO₂ pathways, leading to a different fluid distribution compared with corresponding experiments at the same capillary number. Therefore, inertial effects are not negligible in drainage process with liquid CO₂ and water despite the low Reynolds number based on the average velocity, as the local velocity can be much higher due to Haines jump events. These higher velocities, coupled with the low viscosity of CO₂, further amplifies the inertial effect. Therefore, we conclude that caution should be taken when using proxy fluids that only rely on the capillary number and viscosity ratio in both experiment and simulation.

Numerical simulation of three-component multiphase flows at high density and viscosity ratios using lattice Boltzmann methods

In this paper, we propose a multiphase lattice Boltzmann model for numerical simulation of ternary flows at high density and viscosity ratios free from spurious velocities. The proposed scheme, which is based on the phase-field modeling, employs the Cahn-Hilliard theory to track the interfaces among three different fluid components. Several benchmarks, such as the spreading of a liquid lens, binary droplets, and head-on collision of two droplets in binary- and ternary-fluid systems, are conducted to assess the reliability and accuracy of the model. The proposed model can successfully simulate both partial and total spreadings while reducing the parasitic currents to the machine precision.

A parallel fluid-solid coupling model using LAMMPS and Palabos based on the immersed boundary method

The study of viscous fluid flow coupled with rigid or deformable solids has many applications in biological and engineering problems, e.g., blood cell transport, drug delivery, and particulate flow. We developed a partitioned approach to solve this coupled Multiphysics problem. The fluid motion was solved by Palabos (Parallel Lattice Boltzmann Solver), while the solid displacement and deformation was simulated by LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). The coupling was achieved through the immersed boundary method (IBM). The code modeled both rigid and deformable solids exposed to flow. The code was validated with the Jeffery orbits of an ellipsoid particle in shear flow, red blood cell stretching test, and effective blood viscosity flowing in tubes. It demonstrated essentially linear scaling from 512 to 8192 cores for both strong and weak scaling cases. The computing time for the coupling increased with the solid fraction. An example of the fluid-solid coupling was given for flexible filaments (drug carriers) transport in a flowing blood cell suspensions, highlighting the advantages and capabilities of the developed code.

Regularized lattice Boltzmann model for immiscible two-phase flows with power-law rheology

In this work, a regularized lattice Boltzmann color-gradient model is developed for the simulation of immiscible two-phase flows with power-law rheology. This model is as simple as the Bhatnagar-Gross-Krook (BGK) color-gradient model except that an additional regularization step is introduced prior to the collision step. In the regularization step, the pseudo-inverse method is adopted as an alternative solution for the nonequilibrium part of the total distribution function, and it can be easily extended to other discrete velocity models no matter whether a forcing term is considered or not. The obtained expressions for the nonequilibrium part are merely related to macroscopic variables and velocity gradients that can be evaluated locally. Several numerical examples, including the single-phase and two-phase layered power-law fluid flows between two parallel plates, and the droplet deformation and breakup in a simple shear flow, are conducted to test the capability and accuracy of the proposed color-gradient model. Results show that the present model is more stable and accurate than the BGK color-gradient model for power-law fluids with a wide range of power-law indices. Compared to its multiple-relaxation-time counterpart, the present model can increase the computing efficiency by around 15%, while keeping the same accuracy and stability. Also, the present model is found to be capable of reasonably predicting the critical capillary number of droplet breakup.

Phase-field-based lattice Boltzmann modeling of large-density-ratio two-phase flows

In this paper, we present a simple and accurate lattice Boltzmann (LB) model for immiscible two-phase flows, which is able to deal with large density contrasts. This model utilizes two LB equations, one of which is used to solve the conservative Allen-Cahn equation, and the other is adopted to solve the incompressible Navier-Stokes equations. A forcing distribution function is elaborately designed in the LB equation for the Navier-Stokes equations, which make it much simpler than the existing LB models. In addition, the proposed model can achieve superior numerical accuracy compared with previous Allen-Cahn type of LB models. Several benchmark two-phase problems, including static droplet, layered Poiseuille flow, and spinodal decomposition are simulated to validate the present LB model. It is found that the present model can achieve relatively small spurious velocity in the LB community, and the obtained numerical results also show good agreement with the analytical solutions or some available results. Lastly, we use the present model to investigate the droplet impact on a thin liquid film with a large density ratio of 1000 and the Reynolds number ranging from 20 to 500. The fascinating phenomena of droplet splashing is successfully reproduced by the present model and the numerically predicted spreading radius exhibits to obey the power law reported in the literature.

Entropic lattice Boltzmann model for charged leaky dielectric multiphase fluids in electrified jets

We present a lattice Boltzmann model for charged leaky dielectric multiphase fluids in the context of electrified jet simulations, which are of interest for a number of production technologies including electrospinning. The role of nonlinear rheology on the dynamics of electrified jets is considered by exploiting the Carreau model for pseudoplastic fluids. We report exploratory simulations of charged droplets at rest and under a constant electric field, and we provide results for charged jet formation under electrospinning conditions.

Transition point prediction in a multicomponent lattice Boltzmann model: Forcing scheme dependencies

Pseudopotential-based lattice Boltzmann models are widely used for numerical simulations of multiphase flows. In the special case of multicomponent systems, the overall dynamics are characterized by the conservation equations for mass and momentum as well as an additional advection diffusion equation for each component. In the present study, we investigate how the latter is affected by the forcing scheme, i.e., by the way the underlying interparticle forces are incorporated into the lattice Boltzmann equation. By comparing two model formulations for pure multicomponent systems, namely the standard model [X. Shan and G. D. Doolen, J. Stat. Phys. 81, 379 (1995)JSTPBS0022-471510.1007/BF02179985] and the explicit forcing model [M. L. Porter et al., Phys. Rev. E 86, 036701 (2012)PLEEE81539-375510.1103/PhysRevE.86.036701], we reveal that the diffusion characteristics drastically change. We derive a generalized, potential function-dependent expression for the transition point from the miscible to the immiscible regime and demonstrate that it is shifted between the models. The theoretical predictions for both the transition point and the mutual diffusion coefficient are validated in simulations of static droplets and decaying sinusoidal concentration waves, respectively. To show the universality of our analysis, two common and one new potential function are investigated. As the shift in the diffusion characteristics directly affects the interfacial properties, we additionally show that phenomena related to the interfacial tension such as the modeling of contact angles are influenced as well.

Lattice Boltzmann simulations of droplet dynamics in time-dependent flows

We study the deformation and dynamics of droplets in time-dependent flows using 3D numerical simulations of two immiscible fluids based on the lattice Boltzmann model (LBM). Analytical models are available in the literature, which assume the droplet shape to be an ellipsoid at all times (P.L. Maffettone, M. Minale, J. Non-Newton. Fluid Mech 78, 227 (1998); M. Minale, Rheol. Acta 47, 667 (2008)). Beyond the practical importance of using a mesoscale simulation to assess "ab initio" the robustness and limitations of such theoretical models, our simulations are also key to discuss --in controlled situations-- some relevant phenomenology related to the interplay between the flow time scales and the droplet time scales regarding the "transparency" transition for high enough shear frequencies for an external oscillating flow. This work may be regarded as a step forward to discuss extensions towards a novel DNS approach, describing the mesoscale physics of small droplets subjected to a generic hydrodynamical strain field, possibly mimicking the effect of a realistic turbulent flow on dilute droplet suspensions.

Mesoscopic modelling and simulation of soft matter

The deformability of soft condensed matter often requires modelling of hydrodynamical aspects to gain quantitative understanding. This, however, requires specialised methods that can resolve the multiscale nature of soft matter systems. We review a number of the most popular simulation methods that have emerged, such as Langevin dynamics, dissipative particle dynamics, multi-particle collision dynamics, sometimes also referred to as stochastic rotation dynamics, and the lattice-Boltzmann method. We conclude this review with a short glance at current compute architectures for high-performance computing and community codes for soft matter simulation.

Improved thermal lattice Boltzmann model for simulation of liquid-vapor phase change

In this paper, an improved thermal lattice Boltzmann (LB) model is proposed for simulating liquid-vapor phase change, which is aimed at improving an existing thermal LB model for liquid-vapor phase change [S. Gong and P. Cheng, Int. J. Heat Mass Transfer 55, 4923 (2012)10.1016/j.ijheatmasstransfer.2012.04.037]. First, we emphasize that the replacement of ∇·(λ∇T)/∇·(λ∇T)ρc_{V}ρc_{V} with ∇·(χ∇T) is an inappropriate treatment for diffuse interface modeling of liquid-vapor phase change. Furthermore, the error terms ∂_{t_{0}}(Tv)+∇·(Tvv), which exist in the macroscopic temperature equation recovered from the previous model, are eliminated in the present model through a way that is consistent with the philosophy of the LB method. Moreover, the discrete effect of the source term is also eliminated in the present model. Numerical simulations are performed for droplet evaporation and bubble nucleation to validate the capability of the model for simulating liquid-vapor phase change. It is shown that the numerical results of the improved model agree well with those of a finite-difference scheme. Meanwhile, it is found that the replacement of ∇·(λ∇T)/∇·(λ∇T)ρc_{V}ρc_{V} with ∇·(χ∇T) leads to significant numerical errors and the error terms in the recovered macroscopic temperature equation also result in considerable errors.

Direct Assembly of Magnetic Janus Particles at a Droplet Interface

Self-assembly of nanoparticles at fluid-fluid interfaces is a promising route to fabricate functional materials from the bottom-up. However, directing and controlling particles into highly tunable and predictable structures, while essential, is a challenge. We present a liquid interface assisted approach to fabricate nanoparticle structures with tunable properties. To demonstrate its feasibility, we study magnetic Janus particles adsorbed at the interface of a spherical droplet placed on a substrate. With an external magnetic field turned on, a single particle moves to the location where its position vector relative to the droplet center is parallel to the direction of the applied field. Multiple magnetic Janus particles arrange into reconfigurable hexagonal lattice structures and can be directed to assemble at desirable locations on the droplet interface by simply varying the magnetic field direction. We develop an interface energy model to explain our observations, finding excellent agreement. Finally, we demonstrate that the external magnetic field allows one to tune the particle deposition pattern obtained when the droplet evaporates. Our results have implications for the fabrication of varied nanostructures on substrates for use in nanodevices, organic electronics, or advanced display, printing, and coating applications.

Consistent forcing scheme in the cascaded lattice Boltzmann method

In this paper, we give an alternative derivation for the cascaded lattice Boltzmann method (CLBM) within a general multiple-relaxation-time (MRT) framework by introducing a shift matrix. When the shift matrix is a unit matrix, the CLBM degrades into an MRT LBM. Based on this, a consistent forcing scheme is developed for the CLBM. The consistency of the nonslip rule, the second-order convergence rate in space, and the property of isotropy for the consistent forcing scheme is demonstrated through numerical simulations of several canonical problems. Several existing forcing schemes previously used in the CLBM are also examined. The study clarifies the relation between MRT LBM and CLBM under a general framework.

Improved locality of the phase-field lattice-Boltzmann model for immiscible fluids at high density ratios

Based on phase-field theory, we introduce a robust lattice-Boltzmann equation for modeling immiscible multiphase flows at large density and viscosity contrasts. Our approach is built by modifying the method proposed by Zu and He [Phys. Rev. E 87, 043301 (2013)PLEEE81539-375510.1103/PhysRevE.87.043301] in such a way as to improve efficiency and numerical stability. In particular, we employ a different interface-tracking equation based on the so-called conservative phase-field model, a simplified equilibrium distribution that decouples pressure and velocity calculations, and a local scheme based on the hydrodynamic distribution functions for calculation of the stress tensor. In addition to two distribution functions for interface tracking and recovery of hydrodynamic properties, the only nonlocal variable in the proposed model is the phase field. Moreover, within our framework there is no need to use biased or mixed difference stencils for numerical stability and accuracy at high density ratios. This not only simplifies the implementation and efficiency of the model, but also leads to a model that is better suited to parallel implementation on distributed-memory machines. Several benchmark cases are considered to assess the efficacy of the proposed model, including the layered Poiseuille flow in a rectangular channel, Rayleigh-Taylor instability, and the rise of a Taylor bubble in a duct. The numerical results are in good agreement with available numerical and experimental data.