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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS2014

Analytical Model for Steady Flow through a Finite Channel with One Porous Wall with Arbitrary Variable Suction or Injection

This paper presents an exact solution of two-dimensional laminar flow through a finite length channel with one porous wall. It improves upon previous solutions by (1) satisfying the no-slip boundary condition at the channel dead end, (2) adding a turbulent term to the porous wall boundary condition, (3) allowing for arbitrary variable suction or injection across the porous wall, and (4) model validation against new cryogenic liquid hydrogen and oxygen experimental data. Of particular interest in the current work is the modeling of cryogenic propellant flow through a porous liquid acquisition device (LAD) screen and channel inside a propellant tank. First, a detailed review of the literature is presented for previously attempted solutions to channel flow with one porous wall. Next, the governing equations, boundary conditions, and model assumptions are used to derive the analytical flow solution and present general model results for pressure and velocity fields within the channel. Then, the model solution is compared with horizontal LAD channel flow data in liquid oxygen as well as vertical LAD channel flow data in an inverted outflow configuration in liquid hydrogen. Model results are used to update the static cryogenic bubble point pressure model with a dynamic bubble point term which factors in enhanced convection and cooling at the screen during propellant outflow. Convective heat transfer at the LAD screen during outflow is also quantified by comparing model and data. The new analytical flow solution with the dynamic bubble point model is shown to compare well with available cryogenic experimental data

Navier Stokes Equations↗

DOE OSTI2026

Field-tailoring quantum materials via magneto-synthesis: metastable metallic and magnetically suppressed phases in a trimer iridate

We demonstrate that applying modest magnetic fields (< 0.1 T) during high-temperature crystal growth can profoundly alter the structure and ground state of a spin-orbit-coupled, antiferromagnetic trimer lattice. Using BaIrO₃ as a model system, whose ground state is intricately dictated by the trimer lattice, we show that magneto-synthesis , a field-assisted synthesis approach, stabilizes a structurally compressed, metastable metallic and magnetically suppressed phases inaccessible via conventional methods. These effects include a 0.85% reduction in unit cell, 4-order-of-magnitude decrease in resistivity, a 10-fold enhancement of the Sommerfeld coefficient, and the collapse of long-range magnetic order -- all intrinsic and bulk in origin. First-principles calculations confirm that the field-stabilized structure lies substantially above the ground state in energy, highlighting its metastable character. These large, coherent and correlated changes across multiple bulk properties, unlike those caused by dilute impurities, defects or off-stoichiometry, point to an intrinsic field-induced mechanism. The findings establish magneto-synthesis as a powerful new pathway for accessing non-equilibrium quantum phases in strongly correlated materials.

magneto-synthesis↗

NASA NTRS2026

Predicting Operational Performance of xEMU Boot at Lunar South Pole Temperatures using Thermal Desktop ®

The spacesuit boots that will be used on Artemis lunar south pole surface missions will be exposed to extremely cold temperatures (down to ~50 K). To assess the performance of the government’s Exploration Extravehicular Mobility Unit (xEMU) lunar boot in these permanently shadowed regions, testing was performed at the Jet Propulsion Lab (JPL) in the Cryogenic Ice Transfer, Acquisition Development, and Excavation Laboratory (CITADEL) thermal vacuum (TVAC) chamber. This paper documents the data analysis, thermal boot model correlation, and operational predictions conducted using data from the xEMU CITADEL TVAC test. Expected thermal conductances within the boot and between the boot and environment were calculated from test data, which was then used as an initial guess for conductances within a Thermal Desktop (TD) model. Correlation of the TD model using the internal SOLVER feature was performed across 10 different test points which varied external temperature, internal boot ventilation flowrate, and contact pressure. Operational performance at the lunar south pole was then predicted using results from the correlated model. While the predictions provide evidence for acceptable performance of the boots at the 100K environment test point, there is still substantial uncertainty in performance, especially at the 48K test point. This uncertainty is due in part to testing limitations such as contacting the foot to a hard metal plate rather than granular regolith, and model limitations such as the lack of a realistic foot model. These limitations and their impacts are addressed in detail in this paper. The results of this test series and model correlation underscore the importance of additional improved testing and modeling for characterizing the expected thermal resistance between the outside of the boot and the lunar surface.

Spacesuit↗

DOE OSTI2026

Optimal binning of correlated measurements

Experimental measurements are commonly represented on a discrete grid, requiring a balance between granularity and statistical noise. Two strategies have traditionally been used to improve such representations: selecting an appropriate bin width to control discretization error and applying kernel-based smoothing to suppress fluctuations. Despite their shared goal, these approaches have largely developed independently, without a unified statistical description of how discretization and correlation jointly determine measurement precision. Here, we extend the discussion of optimal interval averaging to a correlation-aware setting by Gaussian process regression, which explicitly accounts for correlations among neighboring bins. Starting from first principles, we derive the mean-squared error of discretized measurements and obtain closed-form asymptotic expressions for the optimal bin width and correlation length. When recast in reduced variables, the theory reveals distinct universal scaling laws governing the error in the correlation-free and correlation-controlled regimes. Characterized by intrinsically smooth intensity profiles and counting-based statistics, neutron scattering measurements are well suited for demonstrating the enhanced error contraction enabled by inter-bin correlations. We show that such improvement is achievable over the experimentally accessible Q-range and across multiple instruments and material systems. These results show that explicitly accounting for correlations systematically reshapes the limits of precision in discretized, noise-limited measurements. More broadly, the framework provides a transferable statistical foundation for optimizing data representation, inference, and experimental design across the physical and data sciences.

Tung, Chi-Huan [ORNL] (ORCID:0000000221972074)↗

NASA NTRS1994

Protein Crystal Growth Results From the United States Microgravity Laboratory-1 Mission

Protein crystal growth experiments have been performed by this laboratory on 18 Space Shuttle missions since April, 1985. In addition, a number of microgravity experiments also have been performed and reported by other investigators. These Space Shuttle missions have been used to grow crystals of a variety of proteins using vapor diffusion, liquid diffusion, and temperature-induced crystallization techniques. The United States Microgravity Laboratory - 1 mission (USML-1, June 25 - July 9, 1992) was a Spacelab mission dedicated to experiments involved in materials processing. New protein crystal growth hardware was developed to allow in orbit examination of initial crystal growth results, the knowledge from which was used on subsequent days to prepare new crystal growth experiments. In addition, new seeding hardware and techniques were tested as well as techniques that would prepare crystals for analysis by x-ray diffraction, a capability projected for the planned Space Station. Hardware that was specifically developed for the USML-1 mission will be discussed along with the experimental results from this mission.

L J Delucas↗

DOE OSTI2026

Concerted Electron-Ion Transport by Polyacrylonitrile Elucidated with Reactive Deep Learning Potentials

Charge transport in polymers, such as polyacrylonitrile (PAN), is crucial for electronics and energy storage. For instance, PAN can transport cations e.g., Li + , by facilitating dynamic cation-nitrile coordination in batteries. However, little is known regarding the underlying role of complex reactive polymer configurations. Herein, we develop a deep-learning potential, trained on ab initio energies and forces of nonequilibrium reactive PAN configurations, to unravel the kinetics of PAN cyclization initiated by a nucleophile (OH – dissociated from LiOH) attacking the terminal nitrile carbon. We find, based on the reaction free-energetics, rates, and charge analysis, that the nucleophile attack producing the first ring is the rate-limiting step, which subsequently triggers Li + -coupled electron transfer along the PAN backbone, causing ∼10 4 times faster sequential ring-formation of the remaining nitriles. PAN’s extended configurations, where dipolar and H-bonding interactions are minimal, enable such rapid kinetics. By validating our computational findings with IR and NMR experiments, we establish a pathway for designing reactive polymers with enhanced charge transport for energy applications.

Chahal-Crockett, Rajni [Oak Ridge National Laborat↗

NASA NTRSDate not supplied

Swamp Works Regolith Compaction Technologies

While the level of compaction below the lunar surface increases quickly after only a few cm of depth, in many cases during a construction mission there will be a need to excavate and transport regolith to a new location for cut-and-fill or horizontal construction of structures such as berms. In these cases to achieve high levels of bulk density, compaction must be per-formed. Additionally, in some cases surface technologies such as systems that sinter/melt the surface may desire the maximum possible compaction at the sur-face to improve melting/heating performance and the final material strength properties. Kennedy Space Center’s (KSC) Swamp Works has developed two means of compaction, lunar and mar-tian compaction. Planetary Autonomous Compaction Technology (PACT) which is part of the Multifunction End Effector for Regolith Compaction Acquisition and Transfer (MEERCAT) robotic arm end effector system’s capabilities and the Site Preparation Tooling for Operations on Mobility Platforms (STOMP) vibratory roller compactor. PACT on MEERCAT has been demonstrated to a TRL 5 and STOMP to a TRL 4 in ambient testing. The results of PACT on MEERCAT and STOMP testing will be shared with results for various simulants including BP-1, ICN-LHT-1G (aka CSM-LHT-1G), RDW-LHT-1GH (a simulant developed for the Mason Tipping Point to match characteristics of ICN-LHT-1G), and Exolith LHS-1E. This will also include discussions on methods used to verify relative density before and after compaction and means to verify density effects below depth. To calculate relative density, maximum and minimum densities for simulants were taken from literature and additional lab testing (publication in work).

redwire↗

DOE OSTI2026

Overview of IMPACT Data Acquisition System and Data Reduction Process

This report documents the development of the data acquisition system (DAS) and data reduction methodologies for the Irradiated Material Property Accelerated Characterization Test (IMPACT) experiment at the Advanced Test Reactor (ATR). The IMPACT experiment is designed to enable in-pile measurement of thermal conductivity in metallic nuclear fuels, specifically U-10Zr, using an instrumented thermal conductivity probe. The DAS supports both passive temperature monitoring and active thermal interrogation of the probe through controlled AC and DC excitation. Significant modifications to laboratory-scale systems were required to accommodate the higher resistance paths associated with the in-pile application. Custom electronics and relay-controlled measurement sequencing were developed to enable the measurement and sufficient power delivery to the sensing region. A reduced-order, axisymmetric thermal model based on the thermal quadrupoles method is presented to support data interpretation. This model enables efficient evaluation of transient heat transfer behavior and facilitates solution of the inverse problem required to extract thermal properties from measured signals. Multiple boundary condition formulations are discussed to address varying experimental time scales and geometries. Additionally, machine learning techniques are introduced to support data reduction and improve confidence in inverse solutions. Convolutional neural networks are applied to identify the presence of gas gaps and other evolving geometric features that significantly impact thermal response during irradiation. These efforts contribute to the broader integration of digital twin frameworks and real-time modeling capabilities within the Advanced Fuels Campaign.

46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN↗

DOE OSTI2026

Direct Measurement of Cl − Activity in Metal Chloride Molten Salts using a Cl 2 /Cl − Electrode

Molten metal chloride salts are promising candidates for advanced heat transfer fluids in generation IV nuclear reactors and beyond. The activity of the chloride ion in the salt has a large influence on the redox characteristics of the corresponding molten salt. There exists a knowledge gap for the direct measurement of chlorobasicity (Lewis basicity) in molten-salt mixtures. Here, the focus of this work was to develop a Cl 2 /Cl − electrode for the direct measurement of chloride activity in molten metal-chloride salt mixtures. The LiCl–KCl eutectic system was utilized as the reference melt to determine the change in chloride ion activity as increasing concentrations of MgCl 2 are added to the LiCl–KCl eutectic working electrode. The results of the measurements indicated a reduction in chloride ion activity as the concentration of magnesium chloride increased, consistent with the complexation of free chlorides by Lewis acidic magnesium cationic species. The Temkin model was used to estimate the thermodynamic properties of MgCl 4 2− complex.

Chloride↗

DOE OSTI2024

N-Doped Graphene (N-G)/MOF(ZIF-8)-Based/Derived Materials for Electrochemical Energy Applications: Synthesis, Characteristics, and Functionality

In recent years, graphene-type materials originating from metal–organic frameworks (MOFs) or integrated with MOFs have exhibited notable performances across various applications. However, a comprehensive understanding of these complex materials and their functionalities remains obscure. While some studies have reviewed graphene/MOF composites from different perspectives, due to their structural–functional intricacies, it is crucial to conduct more in-depth reviews focusing on specific sets of graphene/MOF composites designed for particular applications. In this review, we thoroughly investigate the syntheses, characteristics, and performances of N-G/MOF(ZIF-8)-based/derived materials employed in electrochemical energy conversion and storage systems. Special attention is given to realizing their fundamental functionalities. The discussions are divided into three segments based on the application of N-G/ZIF-8-based/derived materials as electrode materials for batteries, electrodes for electrochemical capacitors, and electrocatalysts. As electrodes for batteries, N-G/MOF(ZIF-8) materials can mitigate issues like an electrode volume expansion for Li-ion batteries and the ‘shuttle effect’ for Li-S batteries. As electrodes for electrochemical capacitors, these materials can considerably improve the ion transfer rate and electronic conductivity, thereby enhancing the specific capacitance while maintaining the structural stability. Also, it was observed that these materials could occasionally outperform standard platinum-based catalysts for the electrochemical oxygen reduction reaction (ORR). The reported electrochemical performances and structural parameters of these materials were carefully tabulated in uniform units and scales. Through a critical analysis of the present synthesis trends, characteristics, and functionalities of these materials, specific aspects were identified that required further exploration to fully utilize their inherent capabilities.

Electrochemistry↗

NASA NTRSDate not supplied

Following the αCen Ab Candidate Using the Roman Coronagraph Instrument

The Roman Space Telescope Coronagraph offers a unique opportunity to observe our nearest solar twin, Alpha Centauri A, and characterize the habitable-zone gas giant candidate, Alpha Cen Ab. The candidate uniquely stands out among all imaged exoplanets to date as the one most similar in temperature, age and location to the planets in our own Solar System. Roman CGI offers the tantalizing opportunity to observe the candidate—determining its radius, temperature, and albedo—and to constrain its orbit. Observing Alpha Cen Ab with Roman would make it the first exoplanet to be imaged in both thermal emission and reflected light and would motivate an exciting search for habitable exomoons with the upcoming ELTs and HWO. In addition, this candidate will inform the planet formation history and current dynamics of the Alpha Centauri AB system, including potentially habitable planets around both stars. In this talk, we describe our plan to observe this target using the Roman CGI, including the timing strategy to minimize contrast and avoid background objects. We also describe the key technical insights about coronagraph performance that we aim to gain, such as measuring companion leakage intensity, evaluating the impact of the large stellar diameter, and assessing CGI performance on very bright targets. In subsequent observations, we aim to demonstrate Multi-Star Wavefront Control (MSWC) on-sky, observing Alpha Cen A using the Wide FoV Shaped Pupil MSWC contributed mode in the Roman CGI. The insights from these technology demonstrations are crucial preparation for the planned HWO mission.

Coronagraph↗

NASA NTRSDate not supplied

Mass Economy Evaluation for Integrated ECLSS and Propulsion Architecture

As missions in Low Earth Orbit (LEO) lengthen and extend to deep space, minimizing resupply needs becomes vital for sustaining crewed operations. Traditional life support systems depend on consumables resupplied from Earth, a method that is increasingly impractical for missions beyond LEO, such as lunar outposts or Mars transit. Long-duration missions require more efficient, autonomous systems that can recycle essential resources, particularly water and oxygen, to minimize the frequency and mass of resupply missions. The Environmental Control and Life Support System (ECLSS) is essential to such missions, with the International Space Station (ISS) serving as a testbed for advanced water recovery and partial oxygen recycling via physico-chemical methods. Yet, ECLSS and propulsion subsystems generally operate independently, despite overlapping requirements and potential areas for synergy. For instance, ECLSS byproducts, water, CO₂, and hydrogen, could be repurposed for propulsion, potentially reducing dedicated propellant mass and increasing overall system efficiency. One promising approach is to develop shared-resource architectures that integrate ECLSS with propulsion systems. This study examines the potential of such integration through the Sabatier CO₂ reduction process, focusing on water management as a key factor in system mass trade-offs. The Sabatier reaction produces water and methane from metabolic CO₂ and electrolytic hydrogen, partially closing the life support loop and providing methane, which could serve as a propellant. This integration could minimize waste, reduce resupply requirements, and enhance mission mass efficiency. A dynamic modeling framework will be used to simulate resource flows over long missions, capturing interactions between life support and propulsion. By comparing integrated versus separate system configurations, the study aims to quantify mass benefits and penalties, informing future habitat designs and trade studies for missions prioritizing autonomy and mass efficiency.

ECLSS↗

DOE OSTI2025

Detection of visible-wavelength aurora on Mars

Mars hosts various auroral processes despite the planet’s tenuous atmosphere and lack of a global magnetic field. To date, all aurora observations have been at ultraviolet wavelengths from orbit. We describe the discovery of green visible-wavelength aurora, originating from the atomic oxygen line at 557.7 nanometers, detected with the SuperCam and Mastcam-Z instruments on the Mars 2020 Perseverance rover. Near–real-time simulations of a Mars-directed coronal mass ejection (CME) provided sufficient lead-time to schedule an observation with the rover. The emission was observed 3 days after the CME eruption, suggesting that the aurora was induced by particles accelerated by the moving shock front. To our knowledge, detection of aurora from a planetary surface other than Earth has never been reported, nor has visible aurora been observed at Mars. This detection demonstrates that auroral forecasting at Mars is possible, and that during events with higher particle precipitation, or under less dusty atmospheric conditions, aurorae will be visible to future astronauts.

Science & Technology - Other Topics↗

NASA NTRS2026

Mass Economy Evaluation for Integrated ECLSS and Propulsion Architecture

As missions in low Earth orbit (LEO) lengthen and extend to deep space, minimizing resupply needs becomes vital for sustaining crewed operations. Traditional life support systems depend on consumables resupplied from Earth, a method that is increasingly impractical for missions beyond LEO, such as lunar outposts or Mars transit. Long-duration missions require more efficient, autonomous systems that can recycle essential resources, particularly water and oxygen, to minimize the frequency and mass of resupply missions. The Environmental Control and Life Support System (ECLSS) is essential to such missions, with the International Space Station (ISS) serving as a testbed for advanced water recovery and partial oxygen recycling via physico-chemical methods. Yet, ECLSS and propulsion subsystems generally operate independently, despite overlapping requirements and potential areas for synergy. For instance, ECLSS byproducts, water, CO 2 , and hydrogen, could be repurposed for propulsion, potentially reducing dedicated propellant mass and increasing overall system efficiency. One promising approach is to develop shared-resource architectures that integrate ECLSS with propulsion systems. This study examines the potential of such integration through the Sabatier CO₂ reduction process, focusing on water management as a key factor in system mass trade-offs. The Sabatier reaction produces water and methane from metabolic CO 2 and electrolytic hydrogen, partially closing the life support loop and providing methane, which could serve as a propellant. This integration could minimize waste, reduce resupply requirements, and enhance mission mass efficiency. A dynamic modeling framework will be used to simulate resource flows over long missions, capturing interactions between life support and propulsion. By comparing integrated versus separate system configurations, the study aims to quantify mass benefits and penalties, informing future habitat designs and trade studies for missions prioritizing autonomy and mass efficiency.

ECLSS↗

NASA NTRS2026

Swamp Works Regolith Compaction Technologies

While the level of compaction below the lunar surface increases quickly after only a few cm of depth, in many cases during a construction mission there will be a need to excavate and transport regolith to a new location for cut-and-fill or horizontal construction of structures such as berms. In these cases to achieve high levels of bulk density, compaction must be per-formed. Additionally, in some cases surface technolo-gies such as systems that sinter/melt the surface may desire the maximum possible compaction at the sur-face to improve melting/heating performance and the final material strength properties. Kennedy Space Center’s (KSC) Swamp Works has developed two means of compaction, lunar and mar-tian compaction. Planetary Autonomous Compaction Technology (PACT) which is part of the Multifunction End Effector for Regolith Compaction Acquisition and Transfer (MEERCAT [1]) robotic arm end effector system’s capabilities and the Site Preparation Tooling for Operations on Mobility Platforms (STOMP [2]) vibratory roller compactor. PACT on MEERCAT has been demonstrated to a TRL 5 and STOMP to a TRL 4 in ambient testing. The results of PACT on MEERCAT and STOMP testing will be shared with results for various simulants including BP-1, ICN-LHT-1G (aka CSM-LHT-1G), RDW-LHT-1GH (a simulant developed for the Mason Tipping Point to match characteristics of ICN-LHT-1G), and Exolith LHS-1E. This will also include discus-sions on methods used to verify relative density before and after compaction and means to verify density effects below depth. To calculate relative density, maximum and minimum densities for simulants were taken from literature [3] [4] [5] and additional lab test-ing (publication in work).

vibration↗

DOE OSTI2023

CFD Simulation of the Dosing Behavior within the Atomic Layer Deposition Feeding System

The effective operation of atomic layer deposition (ALD) feeding system is the premise of realizing specific ALD processes. In the present work, a detailed computational fluid dynamics (CFD) model of the feeding system has been developed and validated, which accounts for the roles of ALD valves and manifolds. A numerical simulation of the compressible fluid flow and heat/mass transfer within the feeding system was conducted. The dosing amounts and the spatiotemporal distributions of the precursors can be accurately predicted using the CFD model, as validated by experimental results. Different precursors, operating conditions, and structures of the feeding system were simulated and analyzed to examine the operating flexibility of the feeding system. The simulation results can be adopted as the upstream boundary conditions for simulations of the ALD process in the reaction chamber. The substrate-scale simulation indicates that the effect of the feeding system on the film deposition is highly related to the surface kinetics of ALD. The present work can serve as a guide for the development and optimization of different ALD-based processes via proper operation and even the design of the feeding system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Mechanisms of Alkali Ionic Transport in Amorphous Oxyhalides Solid State Conductors

Amorphous oxyhalides have attracted significant attention due to their relatively high ionic conductivity (1 mS cm –1 ), excellent chemical stability, mechanical softness, and facile synthesis routes via standard solid‐state reactions. These materials exhibit an ionic conductivity that is almost independent of the underlying chemistry, in stark contrast to what occurs in crystalline conductors. In this work, we employ machine learning interatomic potentials to construct large‐scale molecular dynamics trajectories encompassing hundreds of nanoseconds to obtain statistically converged transport properties. We find that the amorphous state consists of chain fragments of metal‐anion tetrahedra of various lengths. By analyzing the residence time of alkali cations migrating around tetrahedrally‐coordinated metals, we find that oxygen anions limit alkali diffusion. By computing the full Einstein expression of the ionic conductivity, we demonstrate that the alkali transference number of these materials is strongly influenced by distinct‐particles correlations, while alkali transport is dictated by uncorrelated self‐diffusion. By extending this analysis to chemical compositions AMX 2.5 O 0.75 , spanning different alkaline (A = Li, Na, K), metallic (M = Al, Ga, In), and halogen (X = Cl, Br, I) species, we clarify why the diffusion properties of these materials remain largely insensitive to variations in atomic isovalent chemistry.

amorphous materials↗

NASA NTRS1995

Analysis of Gas Absorption to A Thin Liquid Film in the Presence of A Zero-Order Chemical Reaction

The paper presents a detailed theoretical analysis of the process of gas absorption to a thin liquid film adjacent to a horizontal rotating disk. The film is formed by the impingement of a controlled liquid jet at the center of the disk and subsequent radial spreading of liquid along the disk. The chemical reaction between the gas and the liquid film can be expressed as a zero-order homogeneous reaction. The process was modeled by establishing equations for the conservation of mass, momentum, and species concentration and solving them analytically. A scaling analysis was used to determine dominant transport processes. Appropriate boundary conditions were used to solve these equations to develop expressions for the local concentration of gas across the thickness of the film and distributions of film height, bulk concentration, and Sherwood number along the radius of the disk. The partial differential equation for species concentration was solved using the separation of variables technique along with the Duhamel's theorem and the final analytical solution was expressed using confluent hypergeometric functions. Tables for eigenvalues and eigenfunctions are presented for a number of reaction rate constants. A parametric study was performed using Reynolds number, Ekman number, and dimensionless reaction rate as parameters. At all radial locations, Sherwood number increased with Reynolds number (flow rate) as well as Ekman number (rate of rotation). The enhancement of mass transfer due to chemical reaction was found to be small when compared to the case of no reaction (pure absorption), but the enhancement factor was very significant when compared to pure absorption in a stagnant liquid film. The zero-order reaction processes considered in the present investigation included the absorption of oxygen in aqueous alkaline solutions of sodiumdithionite and rhodium complex catalyzed carbonylation of methanol. Present analytical results were compared to previous theoretical results for limiting conditions, and were found to have very good agreement.

S Rajagopalan↗