Reactive Transport Research Articles

Solution Process–Based Facile Flame–Boosted Low‐Valence Transition Metal Doping on Pristine Oxide for Highly Enhanced Photoelectrochemical Solar Water Oxidation Reaction

ABSTRACTAs for the high sustainable solar hydrogen production via water splitting, transition metal doping on an oxide photoanode in photoelectrochemical (PEC) cells has been recognized as an effective approach. However, conventional thermal‐diffusion‐mediated doping strategies face the challenge of resolving sluggish catalytic kinetics for oxygen evolution reaction (OER) and its practical utilization for the synthesis of photoanode films. Herein, we introduce facile ultrafast flame‐boosted doping of Mo into a BiVO4 (FL MoBVO) film for 20 s to achieve an efficient PEC OER. Mo elements in a low‐valence state (i.e., Mo6−δ) and Mo6+ are successfully doped into the photoanode, which manipulate the energy band structure, facilitating the downward shift of band edges and promoting the surface catalytic kinetics. Consequently, the flame‐boosted Mo‐doping results in superior PEC performance in a mild environment with neutral electrolyte without introducing any other additives or co‐catalysts, where the photocurrent density at 1.23 VRHE under 1 sun illumination in pH 7 is outstandingly enhanced, over 9‐fold higher than that of a pristine BiVO4. The flame‐boosted doping induces significantly enhanced photoexcited charge transport and catalytic reaction kinetics performances simultaneously. Our report provides the effective strategy boosting both the thermodynamic and kinetic charge migration properties for sustainable materials.

Inertia-induced mixing and reaction maximization in laminar porous media flows

Solute transport and biogeochemical reactions in porous and fractured media flows are controlled by mixing, as are subsurface engineering operations such as contaminant remediation, geothermal energy production, and carbon sequestration. Porous media flows are generally regarded as slow, so the effects of fluid inertia on mixing and reaction are typically ignored. Here, we demonstrate through microfluidic experiments and numerical simulations of mixing-induced reaction that inertial recirculating flows readily emerge in laminar porous media flows and dramatically alter mixing and reaction dynamics. An optimal Reynolds number that maximizes the reaction rate is observed for individual pore throats of different sizes. This reaction maximization is attributed to the effects of recirculation flows on reactant availability, mixing, and reaction completion, which depend on the topology of recirculation relative to the boundary of the reactants or mixing interface. Recirculation enhances mixing and reactant availability, but a further increase in flow velocity reduces the residence time in recirculation, leading to a decrease in reaction rate. The reaction maximization is also confirmed in a flow channel with grain inclusions and randomized porous media. Interestingly, the domain-wide reaction rate shows a dramatic increase with increasing Re in the randomized porous media case. This is because fluid inertia induces complex three-dimensional flows in randomized porous media, which significantly increases transverse spreading and mixing. This study shows how inertial flows control reaction dynamics at the pore scale and beyond, thus having major implications for a wide range of environmental systems.

Direct observation of ultrafast cluster dynamics in supercritical carbon dioxide using X-ray Photon Correlation Spectroscopy

Supercritical fluids exhibit distinct thermodynamic and transport properties, making them of particular interest for a wide range of scientific and engineering applications. These anomalous properties emerge from structural heterogeneities due to the formation of molecular clusters at conditions above the critical point. While the static behavior of these clusters and their effects on the thermodynamic response functions have been recognized, the relation between the ultrafast cluster dynamics and transport properties remains elusive. By measuring the intermediate scattering function in carbon dioxide at conditions near the critical point with X-ray photon correlation spectroscopy, we directly capture the cross-over dynamics between 4 and 13 picoseconds, revealing the transition between ballistic and diffusive motion. Complementary analysis using large-scale molecular dynamics simulations reveals that this behavior arises from collisions between unbound molecules and clusters. This study provides direct evidence of the ultrafast momentum exchange between clusters, which has significant impact on transport properties, solvation processes, and reaction kinetics in supercritical fluids.

Utilization of Electric Fields to Modulate Molecular Activities on the Nanoscale: From Physical Properties to Chemical Reactions.

As a primary energy source, electricity drives broad fields from everyday electronic circuits to industrial chemical catalysis. From a chemistry viewpoint, studying electric field effects on chemical reactivity is highly important for revealing the intrinsic mechanisms of molecular behaviors and mastering chemical reactions. Recently, manipulating the molecular activity using electric fields has emerged as a new research field. In addition, because integration of molecules into electronic devices has the natural complementary metal-oxide-semiconductor compatibility, electric field-driven molecular devices meet the requirements for both electronic device miniaturization and precise regulation of chemical reactions. This Review provides a timely and comprehensive overview of recent state-of-the-art advances, including theoretical models and prototype devices for electric field-based manipulation of molecular activities. First, we summarize the main approaches to providing electric fields for molecules. Then, we introduce several methods to measure their strengths in different systems quantitatively. Subsequently, we provide detailed discussions of electric field-regulated photophysics, electron transport, molecular movements, and chemical reactions. This review intends to provide a technical manual for precise molecular control in devices via electric fields. This could lead to development of new optoelectronic functions, more efficient logic processing units, more precise bond-selective control, new catalytic paradigms, and new chemical reactions.

BioRT-HBV 1.0: A Biogeochemical Reactive Transport Model at the Watershed Scale.

Reactive Transport Models (RTMs) are essential tools for understanding and predicting intertwined ecohydrological and biogeochemical processes on land and in rivers. While traditional RTMs have focused primarily on subsurface processes, recent watershed-scale RTMs have integrated ecohydrological and biogeochemical interactions between surface and subsurface. These emergent, watershed-scale RTMs are often spatially explicit and require extensive data, computational power, and computational expertise. There is however a pressing need to create parsimonious models that require minimal data and are accessible to scientists with limited computational background. To that end, we have developed BioRT-HBV 1.0, a watershed-scale, hydro-biogeochemical RTM that builds upon the widely used, bucket-type HBV model known for its simplicity and minimal data requirements. BioRT-HBV uses the conceptual structure and hydrology output of HBV to simulate processes including advective solute transport and biogeochemical reactions that depend on reaction thermodynamics and kinetics. These reactions include, for example, chemical weathering, soil respiration, and nutrient transformation. The model uses time series of weather (air temperature, precipitation, and potential evapotranspiration) and initial biogeochemical conditions of subsurface water, soils, and rocks as input, and output times series of reaction rates and solute concentrations in subsurface waters and rivers. This paper presents the model structure and governing equations and demonstrates its utility with examples simulating carbon and nitrogen processes in a headwater catchment. As shown in the examples, BioRT-HBV can be used to illuminate the dynamics of biogeochemical reactions in the invisible, arduous-to-measure subsurface, and their influence on the observed stream or river chemistry and solute export. With its parsimonious structure and easy-to-use graphical user interface, BioRT-HBV can be a useful research tool for users without in-depth computational training. It can additionally serve as an educational tool that promotes pollination of ideas across disciplines and foster a diverse, equal, and inclusive user community.

Patterns of nitrate load variability under surface water-groundwater interactions in agriculturally intensive valley watersheds

Nitrate pollution is a significant environmental issue closely related to human activities, complicated hydrological interactions and nitrate fate in the valley watershed strongly affects nitrate load in hydrological systems. In this study, a nitrate reactive transport model by coupling SWAT-MODFLOW-RT3D between surface water and groundwater interactions at the watershed scale was developed, which was used to reproduce the interaction between surface water and groundwater in the basin from 2016 to 2019 and to reveal the nitrogen transformation process and the evolving trend of nitrate load within the hydrological system of the valley watershed. The results showed that the basin exhibited groundwater recharge to surface water in 2016-2019, particularly in the northwestern and northeastern mountainous regions of the valley watershed and the southern Beishan Reservoir vicinity. Groundwater recharge to surface water declined by 20.17% from 2016 to 2019 due to precipitation. Nitrate loads in the hydrologic system of the watershed are primarily derived from human activities (including fertilizer application from agricultural activities and residential wastewater discharges) and the nitrogen cycle. Nitrate loads in surface water declined 16.05% from 2016 to 2019. Nitrate levels are higher in agricultural farming and residential areas on the eastern and northern sides of the watershed. Additionally, hydrological interactions are usually accompanied by material accumulation and environmental changes. Nitrate levels tend to rise with converging water flows, a process that becomes more pronounced during precipitation events and cropping seasons in agriculturally intensive valley watersheds. However, environmental changes alter nitrogen transformation processes. Nitrogen fixation, nitrification, and ammonification intensify nitrogen inputs during river pooling, enhancing nitrogen cycling fluxes and elevating nitrate loads. These processes are further enhanced during groundwater recharge to surface water, leading to evaluated nitrate load. Enhanced denitrification, dissimilatory nitrate reduction to ammonium (DNRA), anaerobic ammonia oxidation, and assimilation promote the nitrogen export from the system and reduce the nitrate load during surface water recharge to groundwater.

Simulation of rapid sand filters to understand and design sequential iron and manganese removal using reactive transport modelling

Iron (Fe2+), manganese (Mn2+), and ammonium (NH4+) oxidation processes were studied in three single media and three dual media full-scale rapid sand filters (RSFs) using reactive transport modelling (RTM) in PHREEQC and parameter estimation using PEST. Here, we present the insights gained into the spatial distribution of Fe and Mn mineral coatings in RSFs and its influence on the oxidation sequence and rates. Fe2+ and Mn2+ oxidation predominantly occurred simultaneously in the RSFs, contrary to the expected sequential oxidation based on Gibbs free energy calculations. During backwashing, RSF grains become fully mixed, which initiates heterogeneous Mn2+ oxidation on Mn-coated grains that end up in the top layer. The resulting grains have a mixed Fe/Mn mineral coating, which is limiting heterogeneous Mn2+ oxidation due to the limited Mn mineral surface available. Mixed coatings did not seem to affect Fe2+ oxidation rates, instead oxidation rates were increasing at lower pH. We found that RSFs can be designed to spatially separate Fe2+ and Mn2+ oxidation, which results in optimal conditions for Mn2+ oxidation. The RSF needs to consist of two layers with varying density to inhibit mixing and complete Fe2+ oxidation should occur in the top layer. The developed RTM can be used to estimate the depth at which Fe2+ oxidation is complete, and thus the ideal intersection depth of the two layers. A novel perspective is provided on how mineral coating distribution in single and dual media filters influence removal rates and the sequence of oxidation, which contributes to the design of more efficient groundwater filters.

Controls on microbially-induced carbonate precipitation in geologic porous media

Microbially-induced carbonate precipitation (MICP) provides a natural biomineralization approach to secure the geologic storage of gases (e.g., carbon dioxide, hydrogen and methane). Cracks in embrittled wellbore cement, for example, provide a pathway for atmospheric gas leakage, while permeability heterogeneities in the storage reservoir leads to fingering effects that diminish the storage capacity. The design of MICP processes, however, remains a challenge due to limited understanding of the coupled nonlinear reaction kinetics and multiphase transport involved. Specifically, previous attempts at MICP through porous media have been encumbered by carbonate precipitation localized to the first ∼ cm of the bulk injection surface. In this study, we investigate the reactive transport controls on MICP necessary to enable deep MICP penetration into the formation. We use a micromodel with pore geometry and geochemistry representative of real geologic media to image direct pore- and pore-ensemble-level mineral, fluid, and microbial distributions. An approach to adsorb microbes uniformly across the micromodel, rather than local accumulation near the inlet, is developed that enables deep MICP penetration into the porous medium. A sensitivity analysis was performed to investigate the impact of injection conditions (e.g., rates, concentrations) required to maximize CaCO3 precipitation away from the injection site. With multiple cycles of MICP, a ∼ 78 % reduction in permeability was achieved with ∼8 % carbonate pore volume occupation. Overall, this study establishes the possibility of MICP as an effective and controllable method to enhance the security of gas storage in geologic media.

Inverse method to determine hydraulic conductivity from a velocity field using graph theory

A numerical inverse method called FlowPaths is presented to solve for the hydraulic conductivity field of an isotropic heterogeneous porous medium from a known specific discharge field (and constant-head boundary conditions). This method makes possible a new approach to reactive transport experiments, aimed at understanding the dynamic spatial and temporal evolution of hydraulic conductivity, which simultaneously record the evolving reaction and the evolving flow geometry. This inverse method assumes steady, two-dimensional flow through a square matrix of grid blocks. A graph-theoretical approach is used to find a set of flow paths through the porous medium using the known components of the specific discharge, where every vertex is traversed by at least one path from the upstream high-head boundary to the downstream low-head boundary. Darcy’s law is used to create an equation for the unknown head drop across each edge. Summation of these edge equations along each path through the network generates a set of linearly independent head-drop equations that is solved directly for the hydraulic conductivity field. FlowPaths is verified by generating 12,740 hydraulic conductivity fields of varying size and heterogeneity, calculating the corresponding specific discharge field for each, and then using that specific discharge field to estimate the underlying hydraulic conductivity field. When estimates from FlowPaths are compared to the simulated hydraulic conductivity fields, the inverse method is demonstrated to be accurate and numerically stable. Accordingly, within certain limitations, FlowPaths can be used in field or laboratory applications to find hydraulic conductivity from a known velocity field.

Effect of reaction rate and pore structure heterogeneity on reactive solute transport in porous media

CO2 geological storage is the most direct and reliable method to reduce CO2 emission, and deep saline aquifers have the greatest storage potential of CO2. In the process of CO2 storage in saline aquifers, mineral precipitation and dissolution caused by reactive solute transport have a significant impact on reservoir storage potential. In order to predict the transport characteristics and storage potential of CO2 in saline aquifers, it is critical to understand the relationship between chemical reactions and transport properties. The governing equations of porosity evolution of porous media considering chemical reaction processes are proposed, and the relationship between effective reaction area and porosity is considered, and finally a kinetic model is established. Considering different reaction rates and different pore structure heterogeneity, the evolution characteristics of porosity, species concentration and fluid pressure were obtained by combining advection-diffusion equation and Darcy's law. The simulation results show that the dimensionless porosity of porous media transforms from uniform variation to extreme non-uniform variation under low Da number, typical Da number and high Da number condition. The dimensionless concentration can not reach the saturation concentration under low Da number condition. The dimensionless concentration decreases significantly in the inlet region and reaches the saturation concentration under typical Da number condition. The dimensionless concentration reaches the saturation concentration rapidly in the inlet region under high Da number condition. The variation of dimensionless pressure gradient in porous media is significantly correlated with the porosity distribution. The dimensionless advection mass flux of porous media is negatively correlated with the pore structure heterogeneity, while the dimensionless diffusion mass flux is positively correlated with the pore structure heterogeneity. The specie peak concentration decreased with increasing heterogeneity, and the time to reach the peak concentration increased with increasing heterogeneity. The research results can provide a theoretical foundation for the assessment of the transport pathways of CO2 storage in saline aquifers.

Performance evaluation and field synergy analysis of PEMFC with novel snake coil flow field

In the development process of proton exchange membrane fuel cells (PEMFC), the design of the flow field structure plays an important role in improving its mass transfer and performance. In this survey, a novel serpentine channel flow field (SCFF) construction is initially proposed, a 3D multiphase mathematical model is developed, and the accuracy of the mathematical model is confirmed by means of experimental data. Secondly, based on the fluid simulation software, the performance difference between SCFF with different numbers of turns and conventional flow fields (single serpentine and parallel flow fields) in terms of electrochemical reaction and reactant transportation is comparatively analyzed. Finally, the effect on PEMFC performance of the mass transport capability with the novel flow field is evaluated by the theory of mass-transfer loss rate and field synergy. The studies indicate that as the number of turns grows, the output performance of the proposed flow field progressively enhances. The net power density of the flow channel structure with five turns (SC-5) is increased by 35.3% compared with that of the flow channel structure with two turns (SC-2), and the SC-5 flow field also has higher output performance compared with the two conventional flow fields, with an increase of 7.2% and 27.9% in net power, respectively. Meanwhile, the synergistic efficacy between velocity vector field and concentration field is gradually enhanced with the increase in the number of turns, and the results show that SC-5 has the most optimal mass-transfer capability.

Reactive transport modelling of autogenous self-healing in cracked concrete

Autogenous self-healing can close cracks in water-retaining concrete structures. However, its inconsistent efficiency in building practice indicates that the underlying processes are not fully understood. Therefore, this study characterizes reactive transport through cracked concrete and models it using PHREEQC to develop a comprehensive understanding of chemical processes promoting autogenous self-healing. Driven by the dissolution of portlandite, the main cause of healing is the precipitation of CaCO3, which contributes to a crack closure of up to 113 μm. This process is supported by the formation of M-S-H and C-S-H. As self-healing progresses, the rates of dissolution and precipitation processes that promote healing decrease exponentially. At initial flow rates >2 L h−1, CaCO3 precipitation is favored towards the crack outlet. At lower initial flow rates, the formation of CaCO3 shifts towards the crack inlet. These findings underscore the need to reconsider the reliance on effective healing in practical applications.

Anatomy of a deep Piedmont critical zone: Evaluating hypotheses on regolith depth controls through comparison of ridge and valley boreholes

AbstractControls on the physical and chemical architecture of the subsurface critical zone are somewhat controversial, with multiple hypotheses proposed to account for variations in the depth of weathering between sites, and with landscape position at a site. In the Piedmont region of the Mid‐Atlantic US weathering of crystalline bedrock has been observed to extend tens of meters below the surface and groundwater in a'bow‐tie’ shape – i.e. weathering extends to lower elevations below ridges than below channels. The chemical and physical structure of a hillslope transect in the Maryland Piedmont was explored with a 45 m borehole in the ridge, as well as shallow bedrock boreholes at the toe of the slope and valley. Chemical weathering fronts were characterized using elemental abundances and mineralogical analysis. The ridge borehole did not extend deeper than the chemically and physically weathered rock. Surface and borehole geophysics and density measurements were used to characterize the weathered rock and saprolite. Na and Ca results suggest that plagioclase feldspar weathering is similar between samples collected from 45 m under the ridge and 2.2 m under the valley bottom. A narrow Fe oxidation garnet weathering front co‐insides with the transition from weathered bedrock to saprolite, suggesting that this reaction may generate initial saprolite porosity. Muscovite weathering co‐occurs with complete depletion of plagioclase a few meters above the Fe oxidation front. These nested weathering fronts in the saprolite appear to follow a subdued version of the surface topography. The location and shape of the nested saprolite weathering fronts may be controlled by the feedback between the transport of reactants and solutes and reaction‐generated porosity, consistent with the conceptual “valve” hypothesis. Differing dominant control mechanisms on deep bedrock weathering and saprolite initiating reactions may explain the thickness and structure of the critical zone at our site.

Balancing the Charge Separation and Surface Reaction Dynamics in Twin-Interface Photocatalysts for Solar-to-Hydrogen Production.

Solar-driven photocatalytic green hydrogen (H2) evolution reaction presents a promising route toward solar-to-chemical fuel conversion. However, its efficiency has been hindered by the desynchronization of fast photogenerated charge carriers and slow surface reaction kinetics. This work introduces a paradigm shift in photocatalyst design by focusing on the synchronization of charge transport and surface reactions through the use of twin structures as a unique platform. With CdS twin structure (CdS-T) as a model, the role of twin boundaries in modulating surface reactions and facilitating charge migration is systematically investigated. Utilizing transient absorption (TA) and time-resolved infrared (TRIR) spectroscopies, it is revealed that CdS-T achieves charge separation on a picosecond timescale and, importantly, the surface reaction at the twin boundary with the involvement of holes also occurs within 100ps to 3ns. This synchronization of charge donation and surface regeneration significantly enhances the hydrogen evolution process. Accordingly, CdS-T exhibits superior activity for visible light photocatalytic H2 production, withthe H2 production rate of 55.61mmol h-1 g-1 and remarkable stability (>30h), outperforming pristine CdS significantly. This study underscores the transformative potential of twin structures in photocatalysis, offering a new avenue to synchronize charge transport and surface reactions.

Effects of CO2-brine-rock Fracture Interaction on Reactive Solute Transport Properties During CO2 Sequestration in Deep Saline Aquifers

Effects of CO2-brine-rock Fracture Interaction on Reactive Solute Transport Properties During CO2 Sequestration in Deep Saline Aquifers

DecTree: a physics-based geochemical surrogate for surface complexation of uranium on clay

Abstract. Geochemistry is usually the computational bottleneck in coupled reactive transport simulations, which hampers the complexity of the systems and of the processes they can investigate. In recent years, promising speedups have been obtained by substituting the numerical solution of geochemical models with approximated surrogates borrowed from artificial intelligence and machine learning (AI/ML). In the framework of the DONUT/EURAD project a set of benchmarks were defined to assess the performance and the accuracy of different surrogate approaches in settings relevant to the safety assessment of nuclear waste repositories, such as the surface complexation and exchange of U(VI) on clay. In this context, this work introduces am original surrogate modelling approach based on recursive partitioning of parameter space, which exploits prior domain knowledge for the training. The surrogate, which can be represented as a decision tree, hence the DecTree name, performs dimensionality reduction by identifying functional relationships between outputs and input variables using a straightforward non-monotonic extension of the Spearman's rank correlation coefficient. New predictions are then interpolated from the partitioned training data. Applied to a low-dimensional geochemical model, DecTree shows virtually no training time and excellent accuracy, ensuring a throughput of around 500 000 predictions per second on a single CPU core.

Localized corrosion behavior on a heterogeneous surface involving multicomponent reactive transport and morphology evolution

AbstractLocalized corrosion sometimes brings about unanticipated and catastrophic damages in petrochemical pipelines and pressure vessels. For localized corrosion modeling, multicomponent reactive transport and corrosion morphology evolution are two arduous problems that involve multi–physical‐(electro) chemical processes along with multi–temporal and spatial scales. In this study, the lattice Boltzmann method (LBM) is employed to shed some light on the evolution of localized corrosion on a heterogeneous surface focusing on the effects of electrolyte ohmic resistance and diffusion. The corrosion pit is always initiated at the junction of anode and cathode sites; however, quite different morphologies are prompted under ohmic control or ohmic‐diffusion control. Under ohmic control, the pit propagates along the interface of the anode and cathode. Under ohmic‐diffusion control, the pathway of reactive species is broadened, and the corrosion morphology is developed into a more regular shape, like a flattened semicircle in 2‐D modeling. This work presents the huge potential of LBM in long‐term corrosion modeling.

A One-Dimensional Reactive Transport Model for Microbially Induced Calcium Carbonate Precipitation (MICP) in Phreeqc

Microbially induced calcium carbonate precipitation (MICP) is a geotechnical solution with a low ecological footprint. Conducting MICP inside a porous medium can be used for biocementation. Despite many models and tools being published for simulating MICP, a computationally light, easy-to-use, and freely-available simulation tool is lacking. In this work, we present a reactive transport model using the native capabilities of the Phreeqc software (a free and open-source geochemical solver). We model MICP inside a column packed with sands and inoculated with bacteria. Our model is a one-dimensional representation of the column that accounts for the kinetics of precipitation and ureolysis as well as porosity change. We verify our model by simulating previously published MICP experiments to show our model gives reasonably well predictions. Sensitivity analysis of our model’s input parameters and discussions around their range are presented. Additionally, we calculate the supersaturation of calcite as a function of space and time—a feature that could be important for precipitation, but it is commonly ignored in MCIP modeling. Our scripts developed for running simulations are accessible publicly. Due to the low computational effort required for the simulations, our Phreeqc scripts can be used to design and test different treatment recipes for conducting MICP.

Parametric influences on flow, heat transfer, and nutrient transport in the knee joint cavity, a numerical approach

A novel aspect of this study is the investigation of the impact of temperature-dependent Arrhenius reactions and metabolic heat generation on the overall heat transfer within a knee joint cavity. This is a unique contribution where the interaction between thermal effects and metabolic activity is shown to influence the transport of nutrients and the removal of waste products. For the first time, the study also aims to examine the influence of key non-dimensional numbers on the characteristics of mixed convection flow, providing new insights into the dominant physical mechanisms at play. An innovative feature of the model is the incorporation of a non-linear reaction term to address the balance between protein synthesis and degradation. By integrating both thermal and biochemical dynamics, this approach offers a comprehensive analysis of protein aggregation in the knee joint, with potential implications for understanding and treating joint diseases, particularly those related to the health of synovial fluid and cartilage, such as osteoarthritis. The findings have the potential to inform the development of improved therapeutic strategies for managing these conditions. In the context of knee joint cavity dynamics, a low Cauchy number Ca plays a crucial role in ensuring steady and laminar flow, which reduces inertia and ensures that the continuity equation is satisfied. This laminar nature of the flow is essential for maintaining stable synovial fluid movement within the cavity, which aids in the smooth transport of nutrients and waste products. Additionally, higher Peclet number Pe values indicate an increased dominance of convective transport over diffusion, thereby enhancing the supply of essential nutrients to cartilage and bone, while also facilitating the removal of waste products and inflammatory mediators. This efficient convective transport mechanism is vital for the overall health of the joint and for mitigating inflammation. Furthermore, the Zeldovich number β significantly influences the temperature sensitivity of the Arrhenius reaction term within the cavity, where higher values reflect increased reactivity to temperature changes. This temperature dependence impacts metabolic heat generation and protein dynamics, further influencing the biochemical processes that occur within the joint. Collectively, these non-dimensional parameters highlight key aspects of synovial fluid dynamics, nutrient transport, and biochemical reactions that are essential to the functioning and health of the knee joint.

Integrating Enzyme-Based Kinetics in Reactive Transport Models to Simulate Spatiotemporal Dynamics of Biomarkers during Chlorinated Ethene Degradation.

Biomarkers such as functional gene mRNA (transcripts) and proteins (enzymes) provide direct proof of metabolic regulation during the reductive dechlorination (RD) of chlorinated ethenes (CEs). Yet, current models to simulate their spatiotemporal variability are not flexible enough to mimic the homologous behavior of RDase functional genes. To this end, we developed new enzyme-based kinetics to model the concentrations of CEs together with the transcript and enzyme levels during RD. First, the model was calibrated to existing microcosm data on RD of cis-DCE. The model mirrored the tceA and vcrA gene expression and the production of their enzymes in Dehalococcoides spp. Considering tceA and vcrA as homologous instead of nonhomologous improved fitting of the mRNA time series. Second, CEs and biomarker patterns were explored as a proof of concept under groundwater flow conditions, considering degraders occurring in immobile and mobile states. Under both microcosm and flow conditions, biomarker-rate relationships were nonlinear hysteretic because tceA and vcrA acted as homologous genes. The mobile biomarkers additionally undergo advective-dispersive transport, which increases the nonlinearity and makes the observed patterns even more challenging to interpret. The model offers a thorough mechanistic description of RD while also allowing simulation of spatiotemporal dynamic patterns of various key biomarkers in aquifers.