Lattice Boltzmann Research Articles

Numerical investigation of saline gravity currents with different water depth and salinity based on the lattice Boltzmann method

In this paper, we used Lattice Boltzmann Method (LBM) to simulate the motion of saline gravity currents, considering different cases of water depth and salinity, aiming to evaluate the reliability of the LBM model and investigate the longitudinal properties of the gravity currents. The study in this paper was divided into two phases. The first phase explained the basic principles and the implementation process of the numerical model. By comparing the simulation results with laboratory experimental data, it was found that the simulation results were in good agreement with the laboratory experiments. The second phase of the study simulated the saline gravity currents with different water depths and salinities. It was observed that, due to the increasing density gradient, the front velocity of dense current increased with rising water depth and saltwater salinity, and the intensity of turbulence at the interface was enhanced.

Study on heat and mass transfer behavior of coupled electrochemical reaction in porous structure of proton exchange membrane fuel cell

Proton exchange membrane fuel cell (PEMFC) is widely used in transportation, aviation and energy storage due to its unique advantages. Improving the performance of fuel cells depends largely on effective hydrothermal management. In this work, a multi-physical field coupling model based on the lattice Boltzmann method (LBM) is established to analyze the oxygen transport, liquid water transport, heat transfer and electrochemical reaction, mainly considering the difference between the overpotential of the cell and the surface wettability of the structure. The results show that the overpotential is closely related to the reaction process. The rate of water production is significantly accelerated by increasing the overpotential, and the breakage and merging of water clusters are observed. The increase of overpotential will lead to more energy loss in the form of heat, thus increasing the heat production. Enhancing the hydrophobicity of the structure has a positive effect on the performance of the fuel cell, and the possibility of local hot spots in the low-hydrophobic structure is greater. It is feasible to improve water management and fuel cell performance through wettability design.

Investigation on microscopic pore structure optimization and Lattice Boltzmann seepage law in coal modified by N-methylpyrrolidone composite solvents

This study evaluated the impact of composite solvents (1-butyl-3-methylimidazolium tetrafluoroborate [Bmim]BF4, sodium dodecyl sulfate (SDS), and N-methyl pyrrolidone (NMP)) on microscale pore-fracture structures and mesoscopic gas seepage in coal samples; by employing fractal theory and the Lattice Boltzmann method (LBM). Under combined application of three composite solvents: (1) there was a substantial 23.66 % increase in the scanning electron microscopy fractal dimension of the samples, which signifies enhanced complexity and nonhomogeneity of the samples; (2) the percentages of mesopores and macropores in the samples experienced a 10.64 % increase, resulting in a 20.45 % increase in overall porosity; (3) the effective pore fractal dimension (Da) and seepage pore fractal dimension (Ds) exhibited respective decreases of 3.05 % and 0.57 %; and (4) the average gas seepage velocity substantially increased by 53.57 %, with the optimal flow channel development position along the x-direction being closer to the exit (x = 170). These phenomena were attributed to the following: (1) introducing SDS reagents enhanced coal hydrophilicity; (2) NMP and [Bmim]BF4 aqueous solvents could more easily infiltrate the minuscule pores; (3) the synergy of the composite solvents disrupted the pore-fracture structures of the coal matrix, leading to a substantial increase in the aperture and area of the open pores; and (4) this process enhanced the connectivity, consequently increasing the average seepage velocity.

Numerical simulation of corium flow through rod bundle and/or debris bed geometries with a model based on Lattice Boltzmann method

A new model is proposed to investigate the relocation and the distribution of hot corium flows in different configurations (rod bundle, porous debris bed) representative of a severe accident in a Light Water Reactor (LWR). Our model relies on the coupling between a modified Lattice Boltzmann Method (LBM), called Free-Surface LBM, that solves hydrodynamics of unsaturated corium and a Finite Volume Method (FVM) that solves heat transfers. Corium solidification and melting are addressed by implementing a correlation between the temperature and the viscosity. Several simulations on representative elementary volumes were performed, varying configurations (debris bed, rod bundle with and without grid). From the results, it is possible to capture important details of the flow at a scale lower than the pore scale and, at the same time, it is possible to take into account the average effects at the scale of several pores. Presented as a proof of concept these preliminary studies show the interest of this kind of CFD approach to identify which parameters at microstructure scale can potentially govern the corium relocation kinetics at macroscopic scale. It will provide useful information that might improve core degradation models in severe accident codes, such as ASTEC.

Cellular Automata Coupled with Two‐Phase Lattice Boltzmann Model for Modeling of Kinetics of Formation and Structure of Silica‐Based Sol–Gel Materials

A numerical model describing the sol–gel process on a mesoscopic scale is presented. The model is implemented as a cellular automaton‐based system, specifically reaction‐limited aggregation merged with two‐phase lattice Boltzmann method, which allows to describe the sol–gel process together with microscopic phase separation occurring during this process. The influence of model parameters on the structural properties of the resulting gel porosity, mesoporosity, and specific surface area, as well as on the kinetics of the gelation process: the shape of the kinetics curve and the structure formation time, is examined. It is proposed to combine the model parameters with the composition of the reaction mixture (the content of individual reagents and catalysts) and the process conditions.

Influence of external magnetic field on nanofluid dynamics using a two-phase Lattice Boltzmann Mixture Model at low Reynolds numbers

This work examines the behavior of an external magnetic field-induced Al2O3-water nanofluid flow between two parallel plates, with a particular emphasis on low Reynolds number scenarios. Understanding the dynamics of magnetohydrodynamic (MHD) flows in applications including energy systems, cooling systems, and medicinal devices depends on solving this problem. For the first time, a new two-phase lattice Boltzmann method was used to simulate the flow in conjunction with the mixture model. This methodology was specifically designed for nanofluid flow in the presence of magnetic field. Three coupled transport equations for flow velocity, concentration of nanoparticles, and magnetic field intensity are solved using this method. Three various cases were examined numerically. By comparing the simulated velocity profiles with analytical solutions in the first case, model validation was accomplished, demonstrating a strong agreement with less than 1 % variance. The impact of different inflow nanoparticle volume fractions (0.05 and 0.01) on the velocity field at various Reynolds numbers (0.5, 1, 10) and Hartmann numbers (0, 10, 20) was investigated in the second case. The findings showed that for Reynolds numbers of 0.5, 1, and 10, respectively, the velocity magnitude dramatically fell by approximately 75 %, 68 %, and 30 % as the Hartmann number grew from 0 to 20. Alongside this decrease, vortices began to form at Hartmann numbers of 10 and 20. Furthermore, the influence of the magnetic field diminished as the Reynolds number increased from 0.5 to 10, resulting in a noticeable reduction in vortex intensity. In the third case, where the nanoparticle volume fractions at the inlet were closer (e.g., 0.03 and 0.02), the intensity of the vortices decreased compared to the second case. The study demonstrates the robustness of the proposed model and its applicability across scientific and engineering domains. The novelty lies in quantifying MHD effects on nanofluid flow and particle distribution using a two-phase lattice Boltzmann approach, offering more precise and efficient simulations than existing methods. The findings provide new insights into the interaction between magnetic fields and nanofluids, especially at low Reynolds numbers, and emphasize the critical role of nanoparticle distribution in flow dynamics.

Cascaded lattice Boltzmann simulation of Newtonian and non-Newtonian mixture nanofluids with variable thermophysical properties in a cavity with vertical heat radiator

The central moments-based cascaded lattice Boltzmann method (CLBM) for then Newtonian and non-Newtonian Buongiorno’s model mixture nanofluids (CuO, ZnO, Al2O3-water) has been implemented and applied in a square chamber with a vertical heat radiator using accelerated graphics processing unit (GPU) computing through compute unified device architecture (CUDA) C/C++ platform. Due to the higher numerical stability, the CLBM is a superior numerical tool to the raw moments-based MRT-LBM (multiple-relaxation-time lattice Boltzmann method). Three different models for the viscosity and thermal conductivity of the nanofluids: (i) the Binkmann model for the constant viscosity and the Maxwell model for the constant thermal conductivity (ii) Binkmann and Maxwell model with temperature dependent Brownian motion and (iii) Corcione model with non-Newtonian fluid where the temperature and strain rate determine the nanofluid effective thermal conductivity and viscosity, have been used. The enclosure’s upper and bottom walls are thermally adiabatic, but the left and right walls are uniformly cold. A vertical heater is immersed in the middle position of the cavity. The benchmark results for non-Newtonian, Newtonian, and nanofluids for the various computational domains are used to validate the current code adequately. The Bingham number (Bn), the Rayleigh number (Ra), and The volume fraction of the nanoparticles (ϕ) are the three key parameters that are varied in this investigation to demonstrate the effects of natural convection on the isotherms, streamlines, isolines of nanoparticle volume fractionation, yielded and unyeilded zone, and average Nusselt number (Nu¯). The Brownian motion effects of the nanoparticles augmented the average rate of heat transfer and the use of the Bingham nanofluids reduced the heat transfer enhancement. For the CuO-water nanofluid, the augmentation of the rate of heat transfer is 15.42% from ϕ=0 to 4% while Ra=106 and the corresponding heat transfer enhancement for the ZnO-water nanofluid is 11.11%. For the Bingham fluid, the rate of heat transfer increases 7% from Ra=105 to Ra=106 while ϕ=2% and Bn=0.3. The findings can be applied to optimize automotive radiator systems, which are crucial for maintaining engine temperature.

Modified lattice Boltzmann model based on the system performance optimization life cycle for decaying isotropic turbulence simulations

A new optimization strategy based on system performance optimization life cycle (SPOLC) is introduced for high-performance lattice Boltzmann simulations of three-dimensional decaying isotropic turbulence. This strategy improves the performance of turbulent flow simulations in periodic boxes at different resolutions using the lattice Boltzmann method (LBM). The strategy improves the performance by modifying the lattice Boltzmann model, mathematical representation, computational algorithm, software implementation, and computing hardware utilization. The modifications include: (1) Establishing the slice concept as a logical grouping layer added to the LBM, applying an aggregation–disaggregation mechanism, enabling two-dimensional (2D) operation on the three-dimensional (3D) model, (2) improving lattice data access pattern by using an alternative one-dimensional (1D) array for numerical representation instead of the 3D cubic representation, (3) major reduction in memory access iterations by switching from function-wise iteration method to lattice-wise iteration method by applying code fusion to the streaming, velocity and collision model functions and iterations, (4) applying process parallelization and data vectorization, (5) achieving a much more efficient utilization of modern compute units by increasing the adaption of stream processing model. Furthermore, a correctness validation process has been applied by conducting lattice-wise value comparisons between the proposed solution output and the original implementation output. Simulations of decaying isotropic turbulence at resolutions ranging from [Formula: see text] to [Formula: see text] using the LBM are carried out for these purposes. Calculations are performed on two systems with distinct specifications, to validate the effectiveness and portability of the SPOLC strategy. The calculation times are significantly reduced after applying the SPOLC strategy on S1 with the lattice Boltzmann relaxation time [Formula: see text] by over [Formula: see text] compared to S2’s original time, increasing to [Formula: see text] at higher resolutions. Different features of the flow fields are depicted and their characteristics are discussed. Thin tubes are visualized, and the energy spectra are studied. All fields are initialized by a forced turbulent field simulated in a previous study using the LBM.

An efficient flux-reconstructed lattice boltzmann flux solver for flow interaction of multi-structure with curved boundary

Recently, the escalating computational capability provided by advanced GPU technology for numerical simulations is well-suited for tackling large-scale engineering challenges. The lattice Boltzmann flux solver (LBFS), as a relatively new fluid-solving method, combines the parallelization characteristics of the lattice Boltzmann method (LBM) with the ability to handle non-uniform grids. Building upon these advantages, this study aligns its flux computational steps with the demands of the GPU parallel computing environment, thus developing an efficient flux-reconstructed lattice Boltzmann flux solver (FRLBFS), the improved algorithm not only ensures precision but also achieves a significant enhancement in efficiency, reaching up to a remarkable 500-fold improvement. Additionally, this work combines the immersed boundary method, significantly improving the efficiency of addressing hydrodynamic problems with multiple structures. Through numerical validation, under identical GPU hardware conditions, the proposed method in this paper outperform LBM in terms of computational efficiency. Lastly, simulations of flow past an array of eight cylinders at different Reynolds numbers are conducted, instantaneous contour plots at various dimensionless time points and time-dependent curves of drag and lift coefficients for different cylinders are provided, to demonstrate the complex vortex shedding surrounding multiple cylinders and its extraordinary computational efficiency.

Virtual body-fitted grid-based immersed boundary method for simulation of thermal flows with Dirichlet and Neumann boundary conditions

In this work, a virtual body-fitted grid-based immersed boundary method (IBM) combined with the thermal lattice Boltzmann flux solver (TLBFS) is proposed to efficiently simulate thermal flows with Dirichlet and Neumann boundary conditions. The method involves generating a virtual body-fitted grid along the immersed boundary and implementing the boundary conditions using a fractional step technique. In the prediction step, the finite-volume TLBFS is used to obtain the predicted flow field on the Eulerian mesh without considering the immersed boundary, while in the correction step, the correction process of the flow field is conducted on the virtual grid. Thus, the effect of the boundary is transferred to the fluid domain through the virtual grid indirectly. For Dirichlet boundary conditions, such as the no-slip condition and the specified temperature condition, the velocity and temperature corrections are considered unknowns and solved through a matrix system formed from enforcing the boundary conditions. As for the Neumann boundary condition, such as the specified heat flux condition, the temperatures at virtual layers inside the immersed body are regarded as unknowns and computed from those at virtual layers outside the wall according to the quadratic distribution. Several benchmark cases including natural, forced, and mixed convection problems are well simulated to validate the method. The numerical results are in good agreement with reference data, demonstrating the capacity of the present method to simulate thermal flows with Dirichlet and Neumann boundary conditions while requiring fewer Lagrangian points and achieving higher computational efficiency.

Improving UASS pesticide application: optimizing and validating drift and deposition simulations.

As unmanned aerial spraying systems (UASS) usage grows rapidly worldwide, a critical research study was conducted to optimize the simulation of UASS applications, aiming to enhance pesticide delivery efficiency and reduce environmental impact. The study examined several key aspects for accurate simulation of UASS application with lattice Boltzmann method (LBM). Based on these discussions, the most suitable grid size and simulation parameters were selected to create a robust model for optimizing UASS performance in various pest management scenarios, potentially leading to more targeted and sustainable pest control practices. The effect of stability parameter, grid size around the rotor and near ground, and parameters at wake flow were carefully analyzed to improve the precision of pesticide drift predictions and deposition patterns. Optimal grid sizes were identified as 0.2 m generally, 0.025 m near rotors, and a 0.1 + 0.2 m scheme for ground proximity, with finer grids improving accuracy but increasing computation time. Wake resolution and threshold significantly influenced simulation results, while wake distance had minimal impact beyond a certain point. The LBM's accuracy was validated by comparing simulated downwash flow and droplet deposition with field test data. This study optimized UASS simulation parameters, balancing computational efficiency with accuracy. The validated model enhances our ability to design more effective UASS for pest management, potentially leading to more precise and targeted pesticide applications. These advancements contribute to the development of sustainable pest control strategies, aiming to reduce pesticide usage and environmental impact while maintaining crop protection efficacy. © 2024 Society of Chemical Industry.

Enhanced permeability prediction in porous media using particle swarm optimization with multi-source integration

Accurately and efficiently predicting the permeability of porous media is essential for addressing a wide range of hydrogeological issues. However, the complexity of porous media often limits the effectiveness of individual prediction methods. This study introduces a novel Particle Swarm Optimization-based Permeability Integrated Prediction model (PSO-PIP), which incorporates a particle swarm optimization algorithm enhanced with dynamic clustering and adaptive parameter tuning (KGPSO). The model integrates multi-source data from the Lattice Boltzmann Method (LBM), Pore Network Modeling (PNM), and Finite Difference Method (FDM). By assigning optimal weight coefficients to the outputs of these methods, the model minimizes deviations from actual values and enhances permeability prediction performance. Initially, the computational performances of the LBM, PNM, and FDM are comparatively analyzed on datasets consisting of sphere packings and real rock samples. It is observed that these methods exhibit computational biases in certain permeability ranges. The PSO-PIP model is proposed to combine the strengths of each computational approach and mitigate their limitations. The PSO-PIP model consistently produces predictions that are highly congruent with actual permeability values across all prediction intervals, significantly enhancing prediction accuracy. The outcomes of this study provide a new tool and perspective for the comprehensive, rapid, and accurate prediction of permeability in porous media.

Numerical simulation of spherulite and shish-kebab growth for semi-crystalline polymer melts via phase-field model

Polymer crystallization is an important research topic in materials sciences. The phase field model is employed to simulate the growth of spherulites and shish-kebabs for the semi-crystalline polymer under melt flows. Firstly, the phase field equation is discretized by the finite difference method(FDM), the energy equation is solved by the finite volume method(FVM), and the governing equation of viscous polymer melts is modeled and solved by the lattice Boltzmann method(LBM). And then the numerical simulations are conducted for the growth process of spherulites and shish-kebabs under the static and flowing conditions, respectively. Morever, the growth of shish-kebabs are simulated in two different mold cavities under melt flows and compared with each other. Finally, the growth of co-existed spherulites and shish-kebabs are simulated in both static and flowing states. Numerical results show that the coupled FD-FV-LB algorithm could successfully capture the growth interfaces of spherulites and shish-kebabs. The complex cavity makes the flow more complex, thereby changing the crystal morphologies. The melt flow makes the polymer crystals grow faster and densely towards the upstream direction, and increase the temperatures of the crystals.

An automatic approach for the stability analysis of multi-relaxation-time lattice Boltzmann models

This paper is concerned with the weighted L2-stability of the lattice Boltzmann method (LBM) for the incompressible Navier-Stokes equations. Such stability is formulated for the linearized LBM and can lead to convergence proof of the nonlinear problem. A key step in this stability analysis is to find an appropriate decomposition for the Jacobian matrix of the collision term. For multi-relaxation-time (MRT) models, it is very difficult to analytically obtain such a decomposition and how to overcome this difficulty for MRT models is still a challenge. In this paper, we propose an automatic approach to prove the weighted L2-stability of the LBM with general collision models. Instead of exploring the decomposition for each specific model, we partially fix the decomposition and turn to show the symmetry and semi-negative definiteness of the other part of the decomposition, which can be automatically examined by a simple computer code. We apply our automatic approach to ten MRT models and stability conditions are generated by the code immediately. In particular, for the popular D2Q9 orthogonal MRT model, the stability condition we obtained has one less constraint than that given in previous work. As verifications, we also provide some analytical proofs for the stability of orthogonal and weighted-orthogonal MRT models. The proofs are much more complicated than the automatic approach, not to mention that those for nonorthogonal models are unavailable. These demonstrate the efficiency and superiority of the proposed automatic approach. With this approach, proving the weighted L2-stability and thereby the convergence of general MRT models becomes straightforward.

3D printing food flow in different extruders based on crazy and adaptive salp swarm algorithm-deep extreme learning machine improved-lattice Boltzmann method

Extrusion is significant in achieving 3D printing emulsion. The piston and screw extruders are the common structures to achieve the extrusion. The chocolate emulsion is taken for example, two extruders are numerically investigated and compared based on the fluid dynamic analysis. To conduct the simulations, the crazy and adaptive salp swarm algorithm-deep extreme learning machine (CASSA-DELM) is proposed to predict the viscosity of the chocolate emulsion, which is used to replace the traditional fitted model. The built model can avoid non-consistency in the whole shearing rate range. Then, an improved lattice Boltzmann method (I-LBM) is introduced to process the non-Newtonian behavior of the emulsion. In the simulation, the CASSA-DELM model provides the viscosities for each iteration in I-LBM based on the obtained shearing rates. Because the attachment(s) may be generated on the walls, the no-attachment and with-attachment(s) cases are explored, and the necessary results are obtained, which indicate that the piston extruder is more suitable for extruding the single component of food fluid. The screw extruder is recommended for the multiple components of food fluid because the vortex in the X-Y cross-section contributes to further mixing action for the emulsion containing different materials, such as the investigated chocolate emulsion. The indirect experiments are conducted to validate the above conclusions. The current work can contribute to improving the extruding theory of material extrusion technologies.

A numerical simulation study on the spontaneous imbibition and hydro-thermal coupling in soil using the lattice Boltzmann method

This study presents a numerical simulation of underground water spontaneous upward imbibition at high density ratios using the improved lattice Boltzmann method coupled with the P-R equation of state. Porous media was created using the Quartet Structure Generation Set (QSGS) method. The research delved into the impact of factors such as porosity, soil particle size, capillary force, gravity and temperature on spontaneous imbibition. The results indicated that the permeability coefficient of water spontaneous imbibition rises with higher porosity or larger particles. The influence of gravity on spontaneous imbibition became more significant with increased porosity. Three levels of porosity, namely 0.80, 0.65, and 0.50, were simulated to determine the prevailing force between the thermal-driven force and the gravitational hindrance. The variation of groundwater spontaneous imbibition permeability coefficient under the influence of gravity at different temperature gradients was simulated, as was the change in the permeability coefficient without the influence of gravity. The results revealed that for temperature differences above 4 K, gravity had minimal impact with temperature being the main influential factor. For example, for simulation with temperature difference of 10 K, the permeability coefficient differences were 0.006, 0.015, and 0.014 for the three different porosity levels, respectively. When the temperature difference was below 4 K, the disparity in the permeability coefficient increased significantly compared to zero-gravity conditions. Under these conditions, the influence of gravity was greater. For example, for simulation with temperature difference of 2 K or greater, the permeability coefficient differences were 0.306, 0.300, and 0.108 for the corresponding porosity values respectively.

A quantum algorithm for the lattice-Boltzmann method advection-diffusion equation

We present a versatile and efficient quantum algorithm based on the Lattice Boltzmann method (LBM) approximate solution of the linear advection-diffusion equation (ADE). We emphasize that the LBM approximation modifies the diffusion term of the underlying exact ADE and leads to a modified equation (mADE). Due to its versatility in terms of operator splitting, the proposed quantum LBM algorithm for the mADE provides a building block for future quantum algorithms to solve the linearized Navier-Stokes equation on quantum computers. We split the algorithm into four operations: initialization, collision, streaming, and calculation of the macroscopic quantities. We propose general quantum building blocks for each operator, which adapt intrinsically from the general three-dimensional case to smaller dimensions and apply to arbitrary lattice-velocity sets. Based on (sub-linear) amplitude data encoding, we propose improved initialization and collision operations with reduced complexity and efficient sampling-based simulation. Quantum streaming algorithms are based on previous developments. The proposed quantum algorithm allows for the computation of successive time steps, requiring full state measurement and reinitialization after every time step. It is validated by comparison with a digital implementation and based on analytical solutions in one and two dimensions. Furthermore, we demonstrate the versatility of the quantum algorithm for two cases with non-uniform advection velocities in two and three dimensions. Various velocity sets are considered to further highlight the flexibility of the algorithm. We benchmark our optimized quantum algorithm against previous methods employed in sampling-based quantum simulators. We demonstrate sampling efficiency, with sampling accelerated convergence requiring fewer shots.

Three-dimensional mesoscopic investigation of directional coalescence of two droplets impacting on a wall with wettability difference

In this work, a three-dimensional (3D) nonorthogonal pseudopotential lattice Boltzmann method (LBM) was proposed to investigate the coalescence dynamics of two droplets impacting on a wall with wettability difference. The influences of the wettability difference, Weber number, offset distance on the low-wettability side on the coalescence dynamics and the contact-line evolution processes were systematically examined. Both symmetric and asymmetric distributions of the droplet-coalescence behaviors were considered. Our findings reveal that the wettability difference has a significant influence on the asymmetric-retracting and wetting-equilibrium stages, identifying three modes: pin-slip, slip and no-rebound, and slip and rebound. The rebound time is dominated by the high-wettability wall. At a larger Weber number, droplets exhibit a large retracting velocity, which results in increased pumping velocity and earlier rebound time. In addition, a dramatic retraction of the three-phase contact line (TPCL) on the low-wettability wall is observed, leading to the detachment of the liquid bridge from the low-wettability wall, and the formation of a cavity. With increasing offset distance on the low-wettability wall, three different evolution modes are found: coalescence-rebound, coalescence-separation, and non-coalescence. A power function relationship is reported between the Weber number We and the offset distance L* both on the high-wettability wall and low-wettability wall for three modes of coalescence behavior with We∼L*α. The value of the exponent α ranges from 4.6 to 7.4. This study showcases the effectiveness of the 3D nonorthogonal pseudopotential LBM in predicting the complex interface phenomena and characteristics of the multiphase flow structures under investigation.

Effects of Varying Oil/Water Saturations on Miscible and Immiscible CO2 Flooding in Heterogeneous Porous Media: A Lattice Boltzmann Method Simulation Study

Effects of Varying Oil/Water Saturations on Miscible and Immiscible CO₂ Flooding in Heterogeneous Porous Media: A Lattice Boltzmann Method Simulation Study

Hydrodynamic coupling of a cilia–mucus system in Herschel–Bulkley flows

The yield stress and shear thinning properties of mucus are identified as critical for ciliary coordination and mucus transport in human airways. We use here numerical simulations to explore the hydrodynamic coupling of cilia and mucus with these two properties using the Herschel–Bulkley model, in a lattice Boltzmann solver for the fluid flow. Three mucus flow regimes, i.e. a poorly organized regime, a swirly regime, and a fully unidirectional regime, are observed and analysed by parametric studies. We systematically investigate the effects of ciliary density, interaction length, Bingham number and flow index on the mucus flow regime formation. The underlying mechanism of the regime formation is analysed in detail by examining the variation of two physical quantities (polarization and integral length) and the evolution of the flow velocity, viscosity and shear-rate fields. Mucus viscosity is found to be the dominant parameter influencing the regime formation when enhancing the yield stress and shear thinning properties. The present model is able to reproduce the solid body rotation observed in experiments (Loiseau et al., Nat. Phys., vol. 16, 2020, pp. 1158–1164). A more precise prediction can be achieved by incorporating non-Newtonian properties into the modelling of mucus as proposed by Gsell et al. (Sci. Rep., vol. 10, 2020, 8405).