Generalized three-dimensional lattice Boltzmann color-gradient method for immiscible two-phase pore-scale imbibition and drainage in porous media

Lattice Boltzmann simulation of deformable fluid-filled bodies: progress and perspectives

With the rapid development of studies involving droplet microfluidics, drug delivery, cell detection, and microparticle synthesis, among others, many scientists have invested significant efforts to model the flow of these fluid-filled bodies. Motivated by the intricate coupling between hydrodynamics and the interactions of fluid-filled bodies, several methods have been developed. The objective of this review is to present a compact foundation of the methods used in the literature in the context of lattice Boltzmann methods. For hydrodynamics, we focus on the lattice Boltzmann method due to its specific ability to treat time- and spatial-dependent boundary conditions and to incorporate new physical models in a computationally efficient way. We split the existing methods into two groups with regard to the interfacial boundary: fluid-structure and fluid-fluid methods. The fluid-structure methods are characterised by the coupling between fluid dynamics and mechanics of the flowing body, often used in applications involving membranes and similar flexible solid boundaries. We further divide fluid-structure-based methods into two subcategories, those which treat the fluid-structure boundary as a continuum medium and those that treat it as a discrete collection of individual springs and particles. Next, we discuss the fluid-fluid methods, particularly useful for the simulations of fluid-fluid interfaces. We focus on models for immiscible droplets and their interaction in a suspending fluid and describe benchmark tests to validate the models for fluid-filled bodies.

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.

Lightweight lattice Boltzmann

A regularized version of the lattice Boltzmann method for efficient simulation of soft materials is introduced. Unlike standard approaches, this method reconstructs the distribution functions from available hydrodynamic variables (density, momentum, and pressure tensor) without storing the full set of discrete populations. This scheme shows significantly lower memory requirements and data access costs. A series of benchmark tests of relevance to soft matter, such as collisions of fluid droplets, is discussed to validate the method. The results can be of particular interest for high-performance simulations of soft matter systems on future exascale computers.

Pore-scale modeling of two-phase flow: A comparison of the generalized network model to direct numerical simulation

Despite recent advances in pore-scale modeling of two-phase flow through porous media, the relative strengths and limitations of various modeling approaches have been largely unexplored. In this work, two-phase flow simulations from the generalized network model (GNM) [Phys. Rev. E 96, 013312 (2017)2470-004510.1103/PhysRevE.96.013312; Phys. Rev. E 97, 023308 (2018)2470-004510.1103/PhysRevE.97.023308] are compared with a recently developed lattice-Boltzmann model (LBM) [Adv. Water Resour. 116, 56 (2018)0309-170810.1016/j.advwatres.2018.03.014; J. Colloid Interface Sci. 576, 486 (2020)0021-979710.1016/j.jcis.2020.03.074] for drainage and waterflooding in two samples-a synthetic beadpack and a micro-CT imaged Bentheimer sandstone-under water-wet, mixed-wet, and oil-wet conditions. Macroscopic capillary pressure analysis reveals good agreement between the two models, and with experiments, at intermediate saturations but shows large discrepancy at the end-points. At a resolution of 10 grid blocks per average throat, the LBM is unable to capture the effect of layer flow which manifests as abnormally large initial water and residual oil saturations. Critically, pore-by-pore analysis shows that the absence of layer flow limits displacement to invasion-percolation in mixed-wet systems. The GNM is able to capture the effect of layers, and exhibits predictions closer to experimental observations in water and mixed-wet Bentheimer sandstones. Overall, a workflow for the comparison of pore-network models with direct numerical simulation of multiphase flow is presented. The GNM is shown to be an attractive option for cost and time-effective predictions of two-phase flow, and the importance of small-scale flow features in the accurate representation of pore-scale physics is highlighted.

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.

Color-gradient lattice Boltzmann model for immiscible fluids with density contrast

We present a color-gradient-based lattice Boltzmann model for immiscible fluids with a large density contrast. The model employs the velocity-based equilibrium distribution function, initially proposed for the phase-field-based model by Zu and He [Phys. Rev. E 87, 043301 (2013)1539-375510.1103/PhysRevE.87.043301], with a modification necessary to satisfy the kinematic condition at the interface. Different from the existing color-gradient models, the present model allows to specify interface mobility that is independent of the fluid density ratio. Further, we provide a unified framework, which uses the recursive representation of the lattice Boltzmann equation, to derive the governing equations of the system. The emergent color dynamics thus obtained, through an analysis of the segregation operator, is shown to obey the locally conservative Allen-Cahn equation. We use a series of benchmarks, which include a stationary drop, a layered Poiseuille flow, translation of a drop under a forced velocity field, the Rayleigh-Taylor instability, and the capillary intrusion test to demonstrate the model's ability in dealing with complex flow problems.

Validation and application of the lattice Boltzmann algorithm for a turbulent immiscible Rayleigh-Taylor system

We develop a multicomponent lattice Boltzmann (LB) model for the two-dimensional Rayleigh-Taylor turbulence with a Shan-Chen pseudopotential implemented on GPUs. In the immiscible case, this method is able to accurately overcome the inherent numerical complexity caused by the complicated structure of the interface that appears in the fully developed turbulent regime. The accuracy of the LB model is tested both for early and late stages of instability. For the developed turbulent motion, we analyse the balance between different terms describing variations of the kinetic and potential energies. Then we analyse the role of the interface in the energy balance and also the effects of the vorticity induced by the interface in the energy dissipation. Statistical properties are compared for miscible and immiscible flows. Our results can also be considered as a first validation step to extend the application of LB model to three-dimensional immiscible Rayleigh-Taylor turbulence. This article is part of the theme issue 'Progress in mesoscale methods for fluid dynamics simulation'.

Enhanced single-node lattice Boltzmann boundary condition for fluid flows

We propose a procedure to implement Dirichlet velocity boundary conditions for complex shapes that use data from a single node only, in the context of the lattice Boltzmann method. Two ideas are at the base of this approach. The first is to generalize the geometrical description of boundary conditions combining bounce-back rule with interpolations. The second is to enhance them by limiting the interpolation extension to the proximity of the boundary. Despite its local nature, the resulting method exhibits second-order convergence for the velocity field and shows similar or better accuracy than the well-established Bouzidi's scheme for curved walls [M. Bouzidi, M. Firdaouss, and P. Lallemand, Phys. Fluids 13, 3452 (2001)]PHFLE61070-663110.1063/1.1399290. Among the infinite number of possibilities, we identify several meaningful variants of the method, discerned by their approximation of the second-order nonequilibrium terms and their interpolation coefficients. For each one, we provide two parametrized versions that produce viscosity independent accuracy at steady state. The method proves to be suitable to simulate moving rigid objects or surfaces moving following either the rigid body dynamics or a prescribed kinematic. Also, it applies uniformly and without modifications in the whole domain for any shape, including corners, narrow gaps, or any other singular geometry.

Optimal surface-tension isotropy in the Rothman-Keller color-gradient lattice Boltzmann method for multiphase flow

The Rothman-Keller color-gradient (CG) lattice Boltzmann method is a popular method to simulate two-phase flow because of its ability to deal with fluids with large viscosity contrasts and a wide range of interfacial tensions. Two fluids are labeled red and blue, and the gradient in the color difference is used to compute the effect of interfacial tension. It is well known that finite-difference errors in the color-gradient calculation lead to anisotropy of interfacial tension and errors such as spurious currents. Here, we investigate the accuracy of the CG calculation for interfaces between fluids with several radii of curvature and find that the standard CG calculations lead to significant inaccuracy. Specifically, we observe significant anisotropy of the color gradient of order 7% for high curvature of an interface such as when a pinchout occurs. We derive a second order accurate color gradient and find that the diagonal nearest neighbors can be weighted differently than in the usual color-gradient calculation such that anisotropy is minimized to a fraction of a percent. The optimal weights that minimize anisotropy for the smallest radius of curvature interface are found to be w=(0.298,0.284,0.275) for diagonal nearest neighbors for the cases of the interface smoothing parameter β=(0.5,0.7,0.99), somewhat higher than the w=0.25 value derived by Leclaire et al. [Leclaire, Reggio, and Trepanier, Computers and Fluids 48, 98 (2011)CPFLBI0045-793010.1016/j.compfluid.2011.04.001] based on obtaining isotropic errors to second order. We find that use of these optimal w values yields over a factor of 10 decrease in anisotropy and over a factor of 30 decrease in mean anisotropy relative to using the standard w=1 value. And we find a factor of about 2 decrease in the anisotropic error and up to factor 15 decrease in mean anisotropic error relative to the choice of w=0.25 for small radius of curvature interfaces. The improved CG calculations will allow the method to be more reliably applied to studies of phenomenology and pore scale processes such as viscous and capillary fingering, and droplet formation where surface-tension isotropy of narrow fingers and small droplets plays a crucial role in correctly capturing phenomenology. We present an example illustrating how different phenomena can be captured using the improved color-gradient method. Namely, we present simulations of a wetting fluid invading a fluid filled pipe where the viscosity ratio of fluids is unity in which droplets form at the transition to fingering using the improved CG calculations that are not captured using the standard CG calculations. We present an explanation of why this is so which relates to anisotropy of the surface tension, which inhibits the pinchouts needed to form droplets.

Mesoscale modelling of droplets' self-assembly in microfluidic channels

A recently proposed mesoscale approach for the simulation of multicomponent flows with near-contact interactions is employed to investigate the early stage formation and clustering statistics of soft flowing crystals in microfluidic channels. Specifically, we first demonstrate the ability of the aforementioned mesoscale model to accurately reproduce main mechanisms leading to the formation of two basic droplet patterns (triangular and hexagonal), in close agreement with experimental evidence. Next, we quantitatively evaluate the device-scale clustering efficiency of the crystal formation process by introducing a new orientational order parameter, based on the Delaunay triangulation and Voronoi diagrams analysis of the droplet patterns. The mesoscale computational approach employed in this work proves to be an efficient tool to shed new light on the complex dynamics of dense emulsions, from short-scale thin-film hydrodynamics, all the way up to global structure formation and statistics of the resulting droplets ensembles.

Tracking droplets in soft granular flows with deep learning techniques

The state-of-the-art deep learning-based object recognition YOLO algorithm and object tracking DeepSORT algorithm are combined to analyze digital images from fluid dynamic simulations of multi-core emulsions and soft flowing crystals and to track moving droplets within these complex flows. The YOLO network was trained to recognize the droplets with synthetically prepared data, thereby bypassing the labor-intensive data acquisition process. In both applications, the trained YOLO + DeepSORT procedure performs with high accuracy on the real data from the fluid simulations, with low error levels in the inferred trajectories of the droplets and independently computed ground truth. Moreover, using commonly used desktop GPUs, the developed application is capable of analyzing data at speeds that exceed the typical image acquisition rates of digital cameras (30 fps), opening the interesting prospect of realizing a low-cost and practical tool to study systems with many moving objects, mostly but not exclusively, biological ones. Besides its practical applications, the procedure presented here marks the first step towards the automatic extraction of effective equations of motion of many-body soft flowing systems.

Efficient supersonic flow simulations using lattice Boltzmann methods based on numerical equilibria

A double-distribution-function based lattice Boltzmann method (DDF-LBM) is proposed for the simulation of polyatomic gases in the supersonic regime. The model relies on a numerical equilibrium that has been extensively used by discrete velocity methods since the late 1990s. Here, it is extended to reproduce an arbitrary number of moments of the Maxwell-Boltzmann distribution. These extensions to the standard 5-constraint (mass, momentum and energy) approach lead to the correct simulation of thermal, compressible flows with only 39 discrete velocities in 3D. The stability of this BGK-LBM is reinforced by relying on Knudsen-number-dependent relaxation times that are computed analytically. Hence, high Reynolds-number, supersonic flows can be simulated in an efficient and elegant manner. While the 1D Riemann problem shows the ability of the proposed approach to handle discontinuities in the zero-viscosity limit, the simulation of the supersonic flow past a NACA0012 aerofoil confirms the excellent behaviour of this model in a low-viscosity and supersonic regime. The flow past a sphere is further simulated to investigate the 3D behaviour of our model in the low-viscosity supersonic regime. The proposed model is shown to be substantially more efficient than the previous 5-moment D3Q343 DDF-LBM for both CPU and GPU architectures. It then opens up a whole new world of compressible flow applications that can be realistically tackled with a purely LB approach. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.

Lattice Boltzmann simulations capture the multiscale physics of soft flowing crystals

The study of the underlying physics of soft flowing materials depends heavily on numerical simulations, due to the complex structure of the governing equations reflecting the competition of concurrent mechanisms acting at widely disparate scales in space and time. A full-scale computational modelling remains a formidable challenge since it amounts to simultaneously handling six or more spatial decades in space and twice as many in time. Coarse-grained methods often provide a viable strategy to significantly mitigate this issue, through the implementation of mesoscale supramolecular forces designed to capture the essential physics at a fraction of the computational cost of a full-detail description. Here, we review some recent advances in the design of a lattice Boltzmann mesoscale approach for soft flowing materials, inclusive of near-contact interactions (NCIs) between dynamic interfaces, as they occur in high packing-fraction soft flowing crystals. The method proves capable of capturing several aspects of the rheology of soft flowing crystals, namely, (i) a 3/2 power-law dependence of the dispersed phase flow rate on the applied pressure gradient, (ii) the structural transition between an ex-two and ex-one (bamboo) configurations with the associated drop of the flow rate, (iii) the onset of interfacial waves once NCI is sufficiently intense. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.

Particle dynamics at fluid interfaces studied by the color gradient lattice Boltzmann method coupled with the smoothed profile method

We suggest a numerical method to describe particle dynamics at the fluid interface. We adopt a coupling strategy by combining the color gradient lattice Boltzmann method (CGLBM) and smoothed profile method (SPM). The proposed scheme correctly resolves the momentum transfer among the solid particles and fluid phases while effectively controlling the wetting condition. To validate the present algorithm (CGLBM-SPM), we perform several simulation tests like wetting a single solid particle and capillary interactions in two solid particles floating at the fluid interface. Simulation results show a good agreement with the analytical solutions available and look qualitatively reasonable. From these analyses, we conclude that the key features of the particle dynamics at the fluid interface are correctly resolved in our simulation method. In addition, we apply the present method for spinodal decomposition of a ternary mixture, which contains two-immiscible fluids with solid particles. By adding solid particles, fluid segregation is much suppressed than in the binary liquid mixture case. Furthermore, it has different morphology, such as with the jamming structure of the particles at the fluid interface, and captured images are similar to bicontinuous interfacially jammed emulsion gels in literature. From these results, we confirm the feasibility of the present method to describe soft matters; in particular, emulsion systems that contain solid particles at the interface.

Interface tracking characteristics of color-gradient lattice Boltzmann model for immiscible fluids

We study the interface tracking characteristics of a color-gradient-based lattice Boltzmann model for immiscible flows. Investigation of the local density change in one of the fluid phases, via a Taylor series expansion of the recursive lattice Boltzmann equation, leads to the evolution equation of the order parameter that differentiates the fluids. It turns out that this interface evolution follows a conservative Allen-Cahn equation with a mobility which is independent of the fluid viscosities and surface tension. The mobility of the interface, which solely depends upon lattice speed of sound, can have a crucial effect on the physical dynamics of the interface. Further, we find that, when the equivalent lattice weights inside the segregation operator are modified, the resulting differential operators have a discretization error that is anisotropic to the leading order. As a consequence, the discretization errors in the segregation operator, which ensures a finite interface width, can act as a source of the spurious currents. These findings are supported with the help of numerical simulations.

Microvorticity fluctuations affect the structure of thin fluid films

The dynamic interaction of complex fluid interfaces is highly sensitive to near-contact interactions occurring at the scale of ten of nanometers. Such interactions are difficult to analyze because they couple self-consistently to the dynamic morphology of the evolving interface, as well as to the hydrodynamics of the interstitial fluid film. In this work, we show that, above a given magnitude threshold, near-contact interactions trigger nontrivial microvorticity patterns, which in turn affect the effective near-contact interactions, giving rise to persistent fluctuating ripples at the fluid interface. In such a regime, near-contact interactions may significantly affect the macroscopic arrangement of emulsion configurations, such as those arising in soft-flowing microfluidic crystals.

Mechanisms of Microscopic Displacement During Enhanced Oil Recovery in Mixed-Wet Rocks Revealed Using Direct Numerical Simulation

We demonstrate how to use numerical simulation models directly on micro-CT images to understand the impact of several enhanced oil recovery (EOR) methods on microscopic displacement efficiency. To describe the physics with high-fidelity, we calibrate the model to match a water-flooding experiment conducted on the same rock sample (Akai et al. in Transp Porous Media 127(2):393–414, 2019. 10.1007/s11242-018-1198-8). First we show comparisons of water-flooding processes between the experiment and simulation, focusing on the characteristics of remaining oil after water-flooding in a mixed-wet state. In both the experiment and simulation, oil is mainly present as thin oil layers confined to pore walls. Then, taking this calibrated simulation model as a base case, we examine the application of three EOR processes: low salinity water-flooding, surfactant flooding and polymer flooding. In low salinity water-flooding, the increase in oil recovery was caused by displacement of oil from the centers of pores without leaving oil layers behind. Surfactant flooding gave the best improvement in the recovery factor of 16% by reducing the amount of oil trapped by capillary forces. Polymer flooding indicated improvement in microscopic sweep efficiency at a higher capillary number, while it did not show an improvement at a low capillary number. Overall, this work quantifies the impact of different EOR processes on local displacement efficiency and establishes a workflow based on combining experiment and modeling to design optimal recovery processes.

The impact of drainage displacement patterns and Haines jumps on CO2 storage efficiency

Injection of CO₂ deep underground into porous rocks, such as saline aquifers, appears to be a promising tool for reducing CO₂ emissions and the consequent climate change. During this process CO₂ displaces brine from individual pores and the sequence in which this happens determines the efficiency with which the rock is filled with CO₂ at the large scale. At the pore scale, displacements are controlled by the balance of capillary, viscous and inertial forces. We simulate this process by a numerical technique, multi-GPU Lattice Boltzmann, using X-ray images of the rock pores. The simulations show the three types of fluid displacement patterns, at the larger scale, that have been previously observed in both experiments and simulations: viscous fingering, capillary fingering and stable displacement. Here we examine the impact of the patterns on storage efficiency and then focus on slow flows, where displacements at the pore scale typically happen by sudden jumps in the position of the interface between brine and CO₂, Haines jumps. During these jumps, the fluid in surrounding pores can rearrange in a way that prevent later displacements in nearby pores, potentially reducing the efficiency with which the CO₂ fills the total available volume in the rock.

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.

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.

A numerical study of droplet dynamic behaviors on a micro-structured surface using a three dimensional color-gradient lattice Boltzmann model

Inspired by the experimental work of Raj et al. (high-resolution liquid patterns via three-dimensional droplet shape control), in the present study, a three-dimensional multiphase color-gradient lattice Boltzmann model developed previously by some of the authors is used to simulate droplet dynamic behaviors with different surface micro-pillar arrays. To facilitate the present simulation, wetting boundary conditions are used and the accuracy of color gradient prediction at boundary nodes is enhanced. The experimental findings are confirmed and non-circular contact lines are reproduced numerically for the first time. To justify the existing contact angle formula proposed based on the Wenzel model, a systematic parametric study is conducted, based on which the pillar density is redefined to allow for the influence of pillar height, and then it is used to modify the contact angle. In addition, the evolution of the contact line motion for various droplet shapes is investigated systematically, and both circular and non-circular contact characteristics are well-depicted for different surface micro-pillar arrays.

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.

Pore-scale simulations of concentration tails in heterogeneous porous media

The retention of contaminants in the finest and less-conductive regions of natural aquifer is known to strongly affect the decontamination of polluted aquifers. In fact, contaminant transfer from low to high mobility regions at the back end of a contaminant plume (i.e. back diffusion) is responsible for the long-term release of contaminants during remediation operation. In this paper, we perform pore-scale calculations for the transport of contaminant through heterogeneous porous media composed of low and high mobility regions with two objectives: (i) study the effect of permeability contrast and solute transport conditions on the exchange of solutes between mobile and immobile regions and (ii) estimate the mass of contaminants sequestered in low mobility regions based on concentration breakthrough curves.

Lattice Boltzmann modeling and simulation of liquid jet breakup

A three-dimensional color-fluid lattice Boltzmann model for immiscible two-phase flows is developed in the framework of a three-dimensional 27-velocity (D3Q27) lattice. The collision operator comprises the D3Q27 versions of three suboperators: a multiple-relaxation-time (MRT) collision operator, a generalized Liu-Valocchi-Kang perturbation operator, and a Latva-Kokko-Rothman recoloring operator. A D3Q27 version of an enhanced equilibrium distribution function is also incorporated into this model to improve the Galilean invariance. Three types of numerical tests, namely, a static droplet, an oscillating droplet, and the Rayleigh-Taylor instability, show a good agreement with analytical solutions and numerical simulations. Following these numerical tests, this model is applied to liquid-jet-breakup simulations. The simulation conditions are matched to the conditions of the previous experiments. In this case, numerical stability is maintained throughout the simulation, although the kinematic viscosity for the continuous phase is set as low as 1.8×10^{-4}, in which case the corresponding Reynolds number is 3.4×10^{3}; the developed lattice Boltzmann model based on the D3Q27 lattice enables us to perform the simulation with parameters directly matched to the experiments. The jet's liquid column transitions from an asymmetrical to an axisymmetrical shape, and entrainment occurs from the side of the jet. The measured time history of the jet's leading-edge position shows a good agreement with the experiments. Finally, the reproducibility of the regime map for liquid-liquid systems is assessed. The present lattice Boltzmann simulations well reproduce the characteristics of predicted regimes, including varicose breakup, sinuous breakup, and atomization.