Flow Model Research Articles

Lubrication optimization of high-speed train drive gearbox

The gears in the high-speed heavy-duty gearbox of the high-speed train are typical high-speed heavy-duty gears. Combined with the transmission principle and structural characteristics of the high-speed train drive gearbox, to ensure adequate lubrication of meshing gears and bearings, an optimization of the lubricating oil flow inside the gearbox was conducted. The oil and gas two-phase flow model inside the gearbox adopts the VOF model, and the turbulence model adopts the standard κ-ε model. Fluent is used for simulation calculation. The results show that the exhaust port position of the gearbox has little effect on the flow of lubricating oil inside the gearbox; the overall pressure distribution inside the gearbox is relatively uniform, with higher pressure only at the meshing gears; the distribution of lubricating oil inside the gearbox is related to the rotation of the gears, and the flow velocity of lubricating oil is mainly affected by the rotation of the gears, with the maximum flow velocity appearing around the gears; the flow of lubricating oil inside the gearbox meets the lubrication requirements of the gearbox. These results provide support for the lubrication design, flow channel structure improvement, and effectiveness evaluation of high-speed train transmission gearboxes.

Modelling pressure dynamics of oil–gas two-phase flow in double-porosity media formation with permeability-stress sensitivity

Pressure dynamics can reflect the basic characteristics of fluid flow through underground porous formation. In this research, the oil–gas two-phase flow model for a double-porosity media formation with permeability-stress sensitivity was first established for three kinds of outer boundaries. The unified governing equation was deduced by utilizing the H function. The nonlinear mathematical model in consideration of permeability-stress sensitivity was linearized by implementing the canonical perturbation transformation and then solved by using the Laplace transformation. After that, a sequence of typical log–log curves of pressure dynamics influenced by various model parameters were plotted and analyzed. These curves reflect the typical characteristic of a V shape caused by the inter-porosity fluid flow from matrix toward natural fractures. Oil saturation and permeability-stress sensitivity coefficient have much influence on the pressure dynamics. Ultimately, the established model of oil–gas two-phase flow was validated through a well-test fitting interpretation for a real condensate gas well in a sandstone formation. This research can offer insights into the pressure dynamics dominated by the oil–gas two-phase flow in naturally fractured formations and the permeability-stress sensitivity effect.

Research on Quantifying and Evaluating Tennis Match Momentum Based on Comprehensive Analytical Methods

Momentum is crucial in tennis matches, influencing player performance and match outcomes. However, quantifying and evaluating momentum has long been a challenge in sports science research. This study aims to quantify momentum in tennis matches by establishing a hierarchical analysis-based model for momentum flow. The model analyzes factors affecting momentum through five criteria: Service Level, Catch Level, Competition Result, Finishing Ability, and Winning Streak, with respective weights of approximately (0.1, 0.1, 0.2, 0.4, 0.2). Subsequently, the study assigns scores to these criteria based on different actions within a match. By multiplying the weights and scores, the momentum of each player is quantified, and the ratio of the two players' momentum provides a measure of momentum flow during the match. To assess the impact of momentum on match outcomes, the study employs k-means++ clustering analysis, violin plot analysis, and point-biserial correlation analysis. The point-biserial correlation analysis reveals a positive correlation coefficient of 0.66 between a player's momentum and their victory. Similar results are derived from the violin plot and clustering analysis. Therefore, it can be concluded that there is a significant association between the direction of momentum flow and a player's success in a match.

Simulating PFAS transport in effluent-irrigated farmland using PRZM5, LEACHM, and HYDRUS-1D models.

Application of wastewater effluent to agricultural lands can serve as a sustainable approach to meet irrigation and nutrient needs for crop production. While nitrogen and phosphorous loadings can be effectively managed, concerns have been raised regarding the fate of emerging contaminants, including per- and polyfluoroalkyl substances (PFAS), which are widely detected in wastewater effluent. The objective of this paper was to evaluate the ability of three unsaturated flow and transport models, Pesticide Root Zone Model 5 (PRZM5), LEACHM, and HYDRUS-1D, to predict the distribution of PFAS in the soil profile at the Pennsylvania State University Living Filter site, which has received daily wastewater effluent applications for several decades. The models were modified to include adsorption at the air-water interface (AWI), which has been shown to be an important factor governing PFAS transport and phase distribution in the vadose zone. Simulations showed that PRZM5 did not accurately reproduce the observed perfluorooctanesulfonic acid (PFOS) behavior, which was attributed to the "tipping bucket" approach used for water flow that results in the disappearance of AWI during water flow. In contrast, both LEACHM and HYDRUS-1D captured the observed retention of PFOS and perfluorooctanoic acid (PFOA) over a 50-year simulation period. Due to differences in the approach used to calculate the AWI area, LEACHM predicted greater accumulation of PFOS and PFOA at the AWI compared to HYDRUS-1D. These findings indicate that mathematical models that directly account for unsaturated water flow and adsorption at the AWI are able to provide reasonable predictions of long-term PFAS leaching resulting from land application of wastewater effluent.

The Calibrated Safety Constraints Optimal Power Flow for the Operation of Wind-Integrated Power Systems

As the penetration of renewable energy sources (RESs), particularly wind power, continues to rise, the uncertainty in power systems increases. This challenges traditional optimal power flow (OPF) methods. This paper proposes a Calibrated Safety Constraints Optimal Power Flow (CSCOPF) model that uses the Improved Acceleration Coefficient-Based Bee Swarm algorithm (IACBS) in combination with the equivalent current injection (ECI) model. The proposed method addresses key challenges in wind-integrated power systems by ensuring preventive safety scheduling and enabling effective power incident safety analysis (PISA). This improves system reliability and stability. This method incorporates mixed-integer programming, with continuous and discrete variables representing power outputs and control mechanisms. Detailed numerical simulations were conducted on the IEEE 30-bus test system, and the feasibility of the proposed method was further validated on the IEEE 118-bus test system. The results show that the IACBS algorithm outperforms the existing methods in both computational efficiency and robustness. It achieves lower generation costs and faster convergence times. Additionally, the CSCOPF model effectively prevents power grid disruptions during critical incidents, ensuring that wind farms remain operational within predefined safety limits, even in fault scenarios. These findings suggest that the CSCOPF model provides a reliable solution for optimizing power flow in renewable energy-integrated systems, significantly contributing to grid stability and operational safety.

Flow characteristics and performance optimization of temperature and pressure reducing valve with droplets evaporation

The influence of water spray arrangement on temperature reduction performance is significant in temperature and pressure reducing valves (TPRV). A verified vapor-liquid two-phase flow in TPRV was established by Euler-Lagrange flow and droplets evaporation model. The heat and mass transfer processes in droplet evaporation are presented. The influence of nozzles number, spray position, injection direction on internal flow characteristics and temperature reduction performance of TPRV was analyzed. An optimized spray water arrangement was determined via nonlinear fitting model, the great temperature reduction performance was obtained. The results show that the mass flow rate of TPRV inlet and outlet has a non-linear variation with the valve opening. The significant pressure gradient occurs in the valve core and chamber. The upward oblique jet at throat makes the temperature near the spray area low and the temperature at throat downstream high. The range of high Mach numbers increases with the increasing of valve opening. The temperature variation of parallel injection and reverse injection is different with the increasing of the nozzles number. The vortex intensity and range have a stronger influence on temperature reduction performance ability. The temperature reduction performance of optimized TPRV is improved by 0.6 %- 3.98 %. The optimization of water spray arrangement on temperature reduction performance is applicable to various loads.

Air Leakages at Microvalves: Pressure Decay Measurements and Extended Continuum Modelling of Knudsen Flows

To improve the performance of valves in relation to the leakage rate, a comprehensive evaluation of the valve characteristics and behavior during pressure exposure is important. Often, these low gas flow rates below 0.1 cm3/min cannot be accurately measured with conventional flow sensors. This paper presents a small and low-cost test rig for measuring gas leakage rates accurately, even far below 0.1 cm3/min, with the pressure decay method. These leakage flows are substantiated with a flow model, where we demonstrate the feasibility of modeling those gas flows with an extended Navier–Stokes framework to obtain more accurate theoretical predictions. As expected, the comparison to the experimental results proves that the classical Navier–Stokes system is unsuitable for modeling Knudsen flows. Hence, self-diffusion of gas, a wall-slip boundary condition, and an effective mean free path model were introduced in a physically evident manner. In terms of the calculated mass flow, while self-diffusion and slip boundary conditions explain deviations from the classical Navier–Stokes equation for Knudsen numbers already smaller than 1, the effective mean free path model has an effect, especially when Kn > 1. For simplified conditions, an analytical solution was presented and compared to the results of an OpenFOAM CFD-solver for flow rates through more complex gap-flow geometries of the flap valve. Hereby, acceptable deviations between 10% and 20% were observed. A comparison with measurement results was carried out. The reproducibility of the measurement method was verified by comparing multiple measurements of one silicon microvalve sample to a state-of-the-art flow sensor. Three geometrically similar passive silicon microvalves were measured with air overpressure decreasing from 15 kPa relative to atmospheric pressure. Maximum gas volume flowing in a blocking direction of 1–26 µL/min with high reproducibility and marginal noise were observed.

Impact of Hypertension and Physical Exercise on Hemolysis Risk in the Left Coronary Artery: A Computational Fluid Dynamics Analysis.

Background and Objectives: Hypertension increases the risk of developing atherosclerosis and arterial stiffness, with secondarily enhanced wall stress pressure that damages the artery wall. The coexistence of atherosclerosis and hypertension leads to artery stenosis and microvascular angiopathies, during which the intravascular mechanical hemolysis of red blood cells (RBCs) occurs, leading to increased platelet activation, dysfunction of the endothelium and smooth muscle cells due to a decrease in nitric oxide, and the direct harmful effects of hemoglobin and iron released from the red blood cells. This study analyzed the impact of hypertension and physical exercise on the risk of hemolysis in the left coronary artery. Methods: To analyze many different cases and consider the decrease in flow through narrowed arteries, a flow model was adopted that considered hydraulic resistance in the distal section, which depended on the conditions of hypertension and exercise. The commercial ANSYS Fluent 2023R2 software supplemented with user-defined functions was used for the simulation. CFD simulations were performed and compared with the FSI simulation results. Results: The differences obtained between the FSI and CFD simulations were negligible, which allowed the continuation of analyses based only on CFD simulations. The drops in pressure and the risk of hemolysis increased dramatically with increased flow associated with increased exercise. A relationship was observed between the increase in blood pressure and hypertension, but in this case, the increase in blood pressure dropped, and the risk of hemolysis was not so substantial. However, by far, the case of increased physical activity with hypertension had the highest risk of hemolysis, which is associated with an increased risk of clot formation that can block distal arteries and lead to myocardial hypoxia. Conclusions: The influence of hypertension and increased physical exercise on the increased risk of hemolysis has been demonstrated.

Coupled CFD-DEM modeling of surface erosion in granular soils: Simulation of erosion function apparatus experiments

This study introduces a numerical modeling approach that couples the computational fluid dynamics (CFD) with the discrete element method (DEM) to simulate grain-scale soil erosion processes induced by water flows. In this modeling framework, CFD simulates fluid flows by solving the volume-averaged Navier-Stokes equations, and uses the k-ω turbulent model for turbulent flows. Simultaneously, DEM computes the displacement of solid particles by incorporating the fluid-particle interactions driven by fluid flows while adhering to Newton's laws of motion. These interactions encompass drag force, buoyancy force, pressure-gradient force, and viscous force exerted by fluid flows and acting on the particles. The coupled CFD-DEM modeling adeptly replicates soil erosion processes, demonstrating good alignment with results obtained from laboratory erosion function apparatus (EFA) tests. In particular, the DEM facilitates the estimation of shear stress acting on the soil surface based on fluid-particle interaction forces, which has been roughly approximated by empirical or semi-empirical models. This study underscores the capability of coupled CFD-DEM in providing valuable insights into the grain-scale behavior of soil particles subjected to fluid flows, with the potential for extension to address soil erosion and fines migration.

“Tweet of the town”: Synthesizing Local and Social Media Discourse on Book Bans

This project explores the intersection of local and online discourse around book bannings. I use the McMinn County School Board’s decision in 2022 to remove Art Spiegelman’s graphic memoir, Maus, as a case study for this discourse. Through a combination of interviews with McMinn County residents and data collected from Twitter, I argue that social media has altered local community discourse and responses to book bannings. Interviews with local residents asked them to discuss their experiences when Maus was removed by the school board and to reflect on how the local community responded amidst worldwide scrutiny once the event reached digital spaces via social media. Online discourse on Twitter involved collecting tweets mentioning the McMinn County Schools Twitter account along with tweets discussing Maus to understand the broader online response to the board’s decision. I use Danielle Allen’s discourse flow model as the theoretical framework for this project and in my initial findings, discourse around the Maus ban has traveled as described by Allen. In the age of social media, discourse frequently begins at the local level before traveling online and then back into local spaces. Ongoing data analysis has shown that locally, residents were concerned with not only the board’s decision, but also the perception of their community once news of the banning spread. This is supported by online discourse on Twitter, where initial analysis shows frequent characterization of the McMinn County community in a negative light based on the school board’s actions.

Two-group drift-flux model in tight lattice subchannel

Tight lattice rod bundles can increase equipment compactness and improve heat exchange efficiency, and they are widely adopted in heat exchange engineering. Understanding the flow characteristics of gas-liquid two-phase flow in tight lattice subchannels is essential for developing heat exchangers and fuel assemblies with these tight bundles. The drift-flux model (DFM) is a crucial two-phase flow model extensively used in subchannel analysis codes. Investigating the DFM in tight lattice subchannels benefits the advancement of these codes. For two-phase flow interfacial structures, significant two-group characteristics exist, with bubbles divided into small (group-one) and large (group-two) bubbles. The substantial differences in flow characteristics between these two groups provide a solid foundation for developing a two-group DFM. This study examined the two-group characteristics of two-phase flow in a tight lattice interior subchannel and developed a corresponding two-group DFM. The two-group correlations for the distribution parameters and drift velocities at the tight lattice interior subchannel level were proposed and verified using experimental data. The accuracy of the developed two-group DFM in predicting group-wise void fraction and gas velocity was also verified. The standard relative deviation between the model predictions and experimental data was 8.11 % and 13.1 % for group-one and group-two void fractions and 8.33 % and 11.7 % for group-one and group-two gas velocities, respectively. This indicates satisfactory accuracy for the newly developed two-group DFM in a tight lattice interior subchannel.

Enhancing groundwater management with GRACE-based groundwater estimates from GLDAS-2.2: a case study of the Almonte-Marismas aquifer, Spain

AbstractThe Almonte-Marismas aquifer, southwestern Spain, is a critical ecohydrogeological system that features extensive groundwater monitoring. This study investigates the utility of gravity recovery and climate experiment (GRACE) satellite data, specifically obtained from the global land data assimilation system (GLDAS) version 2.2, for assessing groundwater storage variations in the Almonte-Marismas aquifer. The presented research emphasizes the practical application of readily available GLDAS products that do not require data preprocessing. The study validates the GLDAS-2.2-based ready-to-use groundwater storage (GWS) time series by correlating it with precipitation and piezometric information, highlighting its effectiveness in medium-scale aquifers. The results reveal a strong agreement between GLDAS-2.2-derived GWS anomalies and in-situ measurements, confirming GLDAS-2.2’s potential for assessing aquifer depletion. The study discusses the consistency of seasonal variations in groundwater levels and GLDAS-2.2 data, emphasizing their close alignment with precipitation and pumping activities. Importantly, the study introduces GLDAS-2.2-derived volumetric groundwater storage (VGWS) as a valuable calibration parameter for numerical groundwater flow models, enhancing their accuracy over time. Moreover, the analysis reveals disparities in annual recharge values between GLDAS-2.2-derived data and the soil-water mass balance. These variations suggest the importance of additional inputs to precipitation, possibly related to subsurface or lateral connections. Overall, this study contributes to the ongoing discourse on the practical applications of GLDAS-2.2-derived GWS data in groundwater management, offering insights into its effectiveness in diverse hydrogeological settings, particularly in areas that lack monitoring infrastructure.

Mathematical model of molten iron and slag flow in the hearth

The stable hearth discharge is crucial for the operation of a blast furnace (BF). This study established a mathematical model for hearth discharge based on Bernoulli's principle, which considers the blast pressure, kinetic energy of molten iron and slag, gravitational potential energy, the pressure loss of molten iron and slag flowing through the deadman and taphole. It is found that the sharp increase of molten iron and slag flow is probably due to the fracture of the mud, while the sharp decrease of molten iron and slag flow is probably due to the blockage of the taphole by coke. This paper also studies the effect of operating parameters on the hearth discharge. With the increase of taphole plug time, the production rate and slag viscosity, the tap-end time will increase. With the increase of deadman voidage, the tap-end time will be shortened. The correctness of the mathematical model was verified by the actual flow rate of slag and molten iron.

Analysis of heat generation and viscous dissipation with thermal radiation on unsteady hybrid nanofluid flow over a sphere with double-stratification: Case of modified Buongiorno's model

PurposeThis work uses entropy generation analysis to numerically analyze magnetohydrodynamics (MHD) unsteady flow, heat and mass transfer. The study considers changing viscosity, thermal radiation, viscous dissipation, mass suction, heat generation, and stratification processes in a hybrid nanofluid around a spinning sphere. A two-phase nanofluid flow model (Buongiorno model) is used to tackle the current challenge. Both the free stream velocity and the sphere's angular velocity changed over time. Design/methodology/approachThe case study's complicated partial differential equations are transformed into simpler ordinary differential equations utilizing similarity transformation. Implementing the fourth-order Runge-Kutta Fehlberg method with a shooting scheme in MATHEMATICA has allowed us to get numerical solutions for ordinary differential structures. FindingsThe many aspects of these regulated physical characteristics have been elucidated and thoroughly examined via the use of charts and tables. For increasing values of unsteadiness parameter, the velocity profiles in the x-direction grow while they decrease in the z-direction. On the other hand, the temperature profile exhibits a dual pattern, and the concentration profile decreases. As the chemical reaction parameter climbs from 0.25 to 1.0, the Sherwood number for the nanofluid rises by 6721.39% and for the hybrid nanofluid, 3818.9%. When Nr increases from 0.2 to 0.8, nanofluid Nusselt number climbs 22.5% and hybrid nanofluid's Nusselt number rises 21.9%. The Brinkmann number and nanoparticle volume percentage are strongly associated with entropy production. Entropy generation is dual for the temperature difference, magnetic, radiation, and changeable viscosity parameters. The findings are also compared to those from the existing literature and are in excellent agreement with them.

Nonlinear deterministic dynamic analysis of a GPL micropipe conveying pulsating laminar flow

In several industries, the handling of fluid-filled micropipes is common. New-brand structures are increasingly being manufactured using advanced materials. This article tackles one of the crucial dynamic analyses that an advanced fluid-filled micropipe encounters. The dynamics of a graphene nanoplatelets-reinforced micropipe (GPL micropipe) under pulsating laminar flow for the first time is examined. The Euler-Bernoulli beam model follows the modified couple stress theory (MCST) and von-Karman’s nonlinear strain to formulate the problem. The impression of the flow profile exerted by a real flow as a consequence of fluid viscosity, is taken into account. The plug flow model results are compared to those regarding real flow consideration. Using the method of multiple scales (MMS), we determine the instability area and the steady state response of the GPL micropipe subjected to the principal parametric resonance of one of its modes due to pulsating laminar flow by applying this method to the discretized couple nonlinear gyroscopic governing equations. The Floquet theory treats the linear equations and fourth-order Runge–Kutta (RK4) method attacks nonlinear ones to validate MMS findings. It is confirmed that the 0.3 % addition of the GPL to matrix phase significantly enhances its advanced attributes, making it a highly effective material. The GPL reinforcement phase in the FGO pattern increases the critical flow velocity that exhibits the micropipe to static instability by 37.98 % , and critical flow stimulation amplitude fraction by 152.19 % , while declines instability area bandwidth by 36.95 % , and steady state response by 67.17 % relative to a non-reinforced micropipe. A denser flow degrades the corresponding values by 18.40 % , 42.59 % , 41.67 % , and 227.28 % in comparison to a lighter fluid. The declared findings provide crucial insights into the key design elements affecting significantly the functioning of fluid-filled GPL micropipes system, and regulate future research and expand openings for industry applications.

Engine Mass Flow Estimation through Neural Network Modeling in Semi-Transient Conditions: A New Calibration Approach

Nowadays, engine experimental research represents a very expensive field within the automotive industry, but it remains fundamental for engine and vehicle development. The present work aims to investigate a novel approach for engine control system calibration, by adopting machine learning techniques to model physical parameters of the engine starting from experimental data measured at the test bench. The main goal is to create a methodology which accelerates the calibration process without losing accuracy. A model that estimates air mass flow is created by adopting either a tree ensemble model or an artificial neural network trained on a small dataset, which was previously acquired at the test bench using a random calibration of the volumetric efficiency map. The model’s performance is first validated on a larger, random dataset. Then, the volumetric efficiency calculated from the air mass flow model estimation is used to calibrate the transfer function of the Engine Control Unit. Finally, the sensitivity of the model error correlated with the number of data points acquired is used in order to determine the best practice for a Design Of Experiment, which minimizes data acquisition. The methodology proposed can lead to reduced time and costs of the whole calibration process of the engine, without losing accuracy. The analysis was conducted on the entire vehicle, which is crucial for drivability, especially in motorcycles since they are highly sensitive to air-to-fuel ratio adjustments. This work demonstrates that machine learning models can be adopted for the fine-tuning of the calibration process, which is normally performed manually.

Repercussion of quadratic density variation on nonlinear mixed convective Darcy–Forchhimer Al2O3, Cu\\EG flow over an inclined plate with exponential heat source and Arrhenius equation

Generating and controlling energy at high temperatures is extremely challenging in solar energy applications with hybrid nanofluids (HNFs). This challenge is tackled with nonlinear changes in density with temperature and concentration. Hence, a nonlinear Boussinesq approximation is taken on Darcy – Forchhimer hybrid flow containing aluminium oxide ( A l 2 O 3 ) and copper ( Cu ) nanoparticles with base fluid Ethylene Glycol (EG) over an inclined plate at an angle of ξ = π 6 . The physical model is supported by a space-based exponential heat source (EHS) along with a temperature-based heat source (THS) in the energy equation and Arrhenius equation in diffusion relation with suction and blowing on the wall. The regulating equations are transformed into standard differential equations using the similarity conversions, and these equations are subsequently solved in MAPLE 2022. The thermal field is affected positively by EHS and THS parameters, which fulfil the purpose of including these parameters in the flow model. The rate of heat transport increment for Q E parameter by 1.04% for HNF whereas 1.06% for NF when Su > 0 . Also, Su < 0 heat transfer rate increases by 3.68% for HNF whereas 3.75% for NF. As A l 2 O 3 , Cu ∖EG HNF move from suction to injection, the Nusselt number reduces by more than 50%.

Two‐stage low‐carbon scheduling of integrated energy system based on carbon emission flow model

AbstractUnder the influence of environmental pollution and energy scarcity, integrated energy systems (IES) have received extensive attention in the field of energy supply due to their ability to consume renewable energy and enhance energy utilization. In the context of low‐carbon scheduling for IES, numerous studies calculate the system's carbon emissions based on the carbon emission coefficients of energy devices. However, IES is a multi‐energy coupling system in which a device's energy input can originate from multiple sources with varying degrees of carbon emissions, making it difficult to accurately calculate the resulting carbon emissions using fixed coefficients. Consequently, a carbon emission flow (CEF) model is constructed for the system to calculate carbon emissions. In addition to the basic input–output CEF model, the CEF model for energy storage devices is considered, and carbon emission constraints during system operation are formulated based on the CEF model. Furthermore, many studies on low‐carbon scheduling of IES overlook the uncertainties associated with load and renewable energy. Therefore, a two‐stage scheduling model consisting of day‐ahead stage and intra‐day stage is developed to achieve reliable energy supply. Finally, through experiments, the low‐carbon performance and reliability of the model are validated.

Development and validation of a 1D gas–liquid model for dissolved Mn(II) removal by oxidation process in a square bubble column

Modeling multiphase reactors requires an in-depth multidisciplinary analysis of various phenomena including the chemical kinetics, oxygen mass transfer, as well as the simulation of flows within these contactors. In this study, a 1D model of two-phase flow for Mn(II) removal from drinking water by aeration process is developed and validated. This model is based on the Eulerian description of two-phase gas–liquid flow with the comparison between a one-medium bubble size and a two-bubble class description to represent the bubble population in the heterogeneous flow regime. All the relevant chemical species are simulated by coupling hydrodynamics, gas–liquid mass transfer, and reaction kinetic. A pseudo-first-order model accounting for homogeneous and heterogeneous kinetics is considered for Mn(II) oxidation. The performance of the developed 1D model is compared and validated with experimental data. The 1D model was able to predict quantitatively Mn oxidation as a function of pH, initial Mn(II) and initial Mn(IV) concentrations.

An Allen-Cahn-based lattice Boltzmann model for two-phase flows with surfactants

An Allen-Cahn-based lattice Boltzmann model for two-phase flows with surfactants