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At least 235 records · Page 13

Dissolution Flowsheet for U-10Mo Scrap Generated from the Fabrication of High Performance Research Reactor Fuel

The Savannah River National Laboratory was requested to develop dissolution flowsheets for low enriched uranium scrap streams generated during the fabrication of high performance research reactor (HPRR)fuel. The scrap streams include U-10Mo-Zr foil and rejected Al-clad plates. Co-rolled U-10Mo-Zr foils and Alclad U-10Mo-Zr mini-plates which have been through the hot isostatic pressing process were obtained from BWX Technologies, Inc. for use in this work. Small-scale dissolution experiments were performed to identify the flowsheet conditions required to safely and efficiently dissolve the fuel fabrication scrap for subsequent U recovery. Experiments were performed to demonstrate the dissolution of the U-10Mo-Zr foil, removal of the Al cladding from the mini-plates, and the dissolution of the mini-plates following cladding removal.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Effects of increasing the initial nitric acid concentration from a maximum of 7.5 to 8.5 M during the dissolution of aluminum spent nuclear fuel

H-Canyon is blending solutions from the dissolution of High Flux Isotope Reactor (HFIR) and Material Test Reactor (MTR) fuels with Target Residue Material (TRM) to prepare feed solution for the 1st Cycle of solvent extraction. The initial acid concentration for HFIR fuel dissolution is limited to 7.5 M by the flowsheet; however, an increase in the initial concentration is desirable to more easily achieve the target acidity for solvent extraction using the current blending strategy. To provide flexibility in batching the highly enriched uranium (HEU) solutions, the Savannah River National Laboratory (SRNL) was requested to evaluate the potential for increasing the maximum HNO3 concentration for HFIR fuel dissolution from 7.5 to 8.5 M. In response to this request, a literature review was performed to evaluate the impact of a higher starting HNO3 concentration on the dissolution of aluminum spent nuclear fuels (ASNF) including both HFIR and MTR fuels.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Dissolution of a Can Carrier Pin in Concentrated Nitric Acid

H=Canyon will be dissolving Fast Critical Assembly (FCA) fuel from the Japan Atomic Energy Agency (JAEA). The FCA fuel will be dissolved in the electrolytic dissolver in a solution that is a 50 wt.% nitric acid (HNO 3 ), 0.5 g/l gadolinium (Gd), and 0.05 M potassium fluoride (KF). The nitric acid concentration is expected to decrease during the batch process from 10.3 to 7 M. The temperature of the nitric acid solution may be as low as 15 °C. The fuel can will be placed in the dissolver basket insert utilizing a reusable charging device. The charging device is a coated stainless-steel rod with a clevis design. The charging device employs a linchpin to secure the FCA fuel can as it is being charged into the H-canyon dissolver. Prior to beginning the electrolytic dissolution process, the pin will be dissolved, the fuel can will remain in the dissolver basket insert and the charging device will be removed. Currently the time necessary for complete dissolution of the pin is unknown and thus the timing of the removal of the charging device cannot be planned. This process is to be performed remotely and therefore complete dissolution of the pin will not be able to be visually determined. The pin will be made of a material that dissolves in the concentrated nitric acid solution in the dissolver. The facility desired to know the time that the pin would be dissolved so that the charging device for the FCA can could be removed from the dissolver. In particular, the pin dissolution time as a function of the nitric acid concentration and the temperature was desired. The facility would like to ensure that the solution environment was such that the charging device could be removed within an operational shift (8-12 hours).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Dissolution Flowsheet for Non-Aluminum Spent Nuclear Fuel Campaign 1

As part of the Accelerated Basin De-inventory (ABD) program, H Canyon plans to dissolve non-aluminum spent nuclear fuel (NASNF) in the 6.3D electrolytic dissolver. NASNF Campaign 1 plans to electrolytically dissolve 68 bundles of fuel assemblies from the Carolinas-Virginia Tube Reactor (CVTR), Heavy Water Components Test Reactor (HWCTR), and Experimental Boiling Water Reactor (EBWR). The fuel assemblies are intact Zircaloy or stainless steel (SS) clad UO 2 rods, tubes, and plates. The H Canyon electrolytic dissolver previously dissolved a variety of UO 2 core fuel types in SS, Zircaloy, Nichrome, or Incoloy cladding from 1969 to 1980. The objective of this study was to identify flowsheet conditions through literature review and laboratory experimentation to safely dissolve NASNF Campaign 1 bundles in the H Canyon electrolytic dissolver. Bench-scale electrolytic dissolution tests were performed to demonstrate a flowsheet for NASNF Campaign 1 bundles. The outer bundles are composed of SS or Al alloy, Al 6061-T6, and contain intact Zircaloy or SS clad UO 2 fuel assemblies. The key objectives of these tests were to determine bounding dissolver chemistries and the sparge requirement to ensure H 2 concentration remain less than 60 vol % of the lower flammability limit (LFL) during dissolution. The impact of HNO 3 concentration and the addition of fluoride on the dissolution efficiency of Zircaloy, 304L SS, Al 6061-T6, and Inconel 625 were examined. While SS, Al, and Inconel 625 readily dissolve utilizing electrolytic dissolution, Zircaloy disintegrated anodically; the surface of Zircaloy oxidized and the oxide layer spalled off and settled at the bottom of the dissolver as an insoluble material. The black flakes were identified as ZrO 2 and 85% of the Zr processed was converted to black ZrO 2 flakes when Zr was anodically disintegrated in 9.5 M HNO 3 .

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Influence of metal ion complexation on the radiolytic longevity of butyramide extractants under direct dissolution conditions

The direct dissolution of volox-treated used nuclear fuel (UNF) into an organic solution—comprised of diluent and specialized extractants—poses a promising alternative to the traditional liquid-liquid solvent extraction approach to reprocessing UNF. However, moving to direct dissolution removes the presence of a concentrated nitric acid aqueous phase, which has been shown to significantly influence the radiolytic longevity of extractants in liquid-liquid solvent extraction flowsheets. With this in mind, and given the limited knowledge of radiation effects under direct dissolution conditions, we present a time-resolved and dose accumulation study on the impact of direct dissolution conditions on the radiolytic longevity of two candidate butyramide extractants—N,N-di-(2-ethylhexyl) butyramide (DEHBA) and N,N-di-(2-ethylhexyl)isobutyramide (DEHiBA)—in pre-equilibrated n-dodecane solvent in the presence and absence of process relevant metal ions, uranium and rhenium. Rhenium, and by extension technetium, extraction had little impact (=10%) on the overall radiolytic stability of these ligands, despite observed increases in chemical kinetic reactivity (>2×) of the corresponding complexes with the n-dodecane radical cation. Uranium-loading on the other hand, significantly improved the lifetime of both ligands (>30%) under gamma irradiation, with a greater stabilization observed for DEHBA over DEHiBA. This draft manuscript has been prepared in fulfillment of NTRD-MRWFD-2024 M3FT-24IN030101115.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Rapid dissolution without elemental fractionation by laser driven hydrothermal processing

Traditional dissolution of geologic samples often requires a significant time investment. Here, we present an alternative method for the dissolution of geologic materials using laser-driven hydrothermal processing (LDHP). LDHP uses laser energy directed onto a submerged sample, which increases the temperature and pressure at the liquid–sample interface and drives the hydrothermal dissolution coupled with photomechanical spallation, an ablative process. This uses focused 527 nm laser energy at 40 W average power, 1 kHz pulse repetition rate, and 115 ns pulse duration. Importantly, when LDHP is performed on basalt geostandards (BCR-2 and BHVO-2) using the conditions outlined, we show that LDHP does not produce significant elemental fractionation and, thus, can be considered an alternative processing method to traditional mechanical crushing and acid digestion. Additionally, it is possible using LDHP to utilize the spatially confined beam to target and selectively isolate individual phases in a rock, potentially alleviating the need for mechanical separation of inclusions that are difficult to physically isolate. Furthermore, using this outlined method of LDHP, we demonstrate full dissolution of 120 mg of obsidian in 85 minu, meaning that LDHP is a potentially very useful method when sample processing is time sensitive.

58 GEOSCIENCES↗

Learning the factors controlling mineral dissolution in three-dimensional fracture networks: applications in geologic carbon sequestration

We perform a set of high-fidelity simulations of geochemical reactions within three-dimensional discrete fracture networks (DFN) and use various machine learning techniques to determine the primary factors controlling mineral dissolution. The DFN are partially filled with quartz that gradually dissolves until quasi-steady state conditions are reached. At this point, we measure the quartz remaining in each fracture within the domain as our primary quantity of interest. We observe that a primary sub-network of fractures exists, where the quartz has been fully dissolved out. This reduction in resistance to flow leads to increased flow channelization and reduced solute travel times. However, depending on the DFN topology and the rate of dissolution, we observe substantial variability in the volume of quartz remaining within fractures outside of the primary subnetwork. This variability indicates an interplay between the fracture network structure and geochemical reactions. We characterize the features controlling these processes by developing a machine learning framework to extract their relevant impact. Specifically, we use a combination of high-fidelity simulations with a graph-based approach to study geochemical reactive transport in a complex fracture network to determine the key features that control dissolution. We consider topological, geometric and hydrological features of the fracture network to predict the remaining quartz in quasi-steady state. We found that the dissolution reaction rate constant of quartz and the distance to the primary sub-network in the fracture network are the two most important features controlling the amount of quartz remaining. This study is a first step towards characterizing the parameters that control carbon mineralization using an approach with integrates computational physics and machine learning.

54 ENVIRONMENTAL SCIENCES↗

The Effect of Heavy Ion Irradiation on the Forward Dissolution Rate of Borosilicate Glasses Studied In Situ and Real Time by Fluid-Cell Raman Spectroscopy

Borosilicate glasses are the favored material for immobilization of high-level nuclear waste (HLW) from the reprocessing of spent fuel used in nuclear power plants. To assess the long-term stability of nuclear waste glasses, it is crucial to understand how self-irradiation affects the structural state of the glass and influences its dissolution behavior. In this study, we focus on the effect of heavy ion irradiation on the forward dissolution rate of a non-radioactive ternary borosilicate glass. To create extended radiation defects, the glass was subjected to heavy ion irradiation using 197 Au ions that penetrated ~50 µm deep into the glass. The structural damage was characterized by Raman spectroscopy, revealing a significant depolymerization of the silicate and borate network in the irradiated glass and a reduction of the average boron coordination number. Real time, in situ fluid-cell Raman spectroscopic corrosion experiments were performed with the irradiated glass in a silica-undersaturated, 0.5 M NaHCO 3 solution at temperatures between 80 and 85 °C (initial pH = 7.1). The time- and space-resolved in situ Raman data revealed a 3.7 ± 0.5 times increased forward dissolution rate for the irradiated glass compared to the non-irradiated glass, demonstrating a significant impact of irradiation-induced structural damage on the dissolution kinetics.

36 MATERIALS SCIENCE↗

Solubility Product of Vanadinite Pb 5 (VO 4 ) 3 Cl at 25 °C—A Comprehensive Approach to Incongruent Dissolution Modeling

Although vanadinite (Pb 5 (VO 4 ) 3 Cl occurs in abundance in various terrestrial geochemical systems of natural and anthropogenic origin and is seriously considered as a potential nuclear waste sequestering agent, its actual application is severely limited by a lack of understanding of its basic thermodynamic parameters. In this regard, the greatest challenge is posed by its incongruent dissolution, which is a pivotal hurdle for effective geochemical modeling. Our paper presents an universal approach for geochemical computing of systems undergoing incongruent dissolution which, along with unique, long-term experiments on vanadinites’ stability, allowed us to determine the mineral solubility constant. The dissolution experiments were carried out at pH = 3.5 for 12 years. Vanadinite has dissolved incongruently, continuously re-precipitating into chervetite (Pb 2 V 2 O 7 ) with the two minerals remaining in mutual equilibrium until termination of the experiments. The empirically derived solubility constant K sp,V,298 = 10 –91.89 ± 0.05 of vanadinite was determined for the first time. The proposed modeling method is versatile and can be adopted to other mineral systems undergoing incongruent dissolution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Investigating the Impacts of Direct Dissolution Conditions on the Radiolytic Longevity of Butyramide Extractants

Removing the nitric acid (HNO3) dissolution step in used nuclear fuel (UNF) reprocessing would reduce the volume of radioactive waste streams generated, thereby, improving process efficiency. A promising strategy for this is the direct dissolution of UNF that has been pretreated by voloxidation into an organic solvent composed of specialized extractants and diluent. However, removal of the aqueous HNO3 phase from the envisioned reprocessing system has the potential to drastically change the suite of radiation-induced processes occurring, and thus, alter the longevity of proposed reagents. Furthermore, the impacts of fission product and transuranic metal ion complexation on the aforementioned radiation-induced processes is poorly understood, and yet can cause significant changes in radiolytic longevity. To bridge these knowledge gaps and support the continued development of direct dissolution strategies, we present an investigation into the impacts of direct dissolution conditions on the gamma radiation-induced degradation of N,N-di-(2-ethylhexyl) butyramide (DEHBA) and N,N-di-(2-ethylhexyl)isobutyramide (DEHiBA) ligands—candidate replacements for tributyl phosphate—in pre-equilibrated n-dodecane solvent in the presence and absence of envisioned loading amounts of uranium.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Investigating the impacts of used nuclear fuel direct dissolution on the radiolytic longevity of solvent and butyramide extractants

Removing the nitric acid (HNO3) dissolution step in used nuclear fuel (UNF) reprocessing would reduce the volume of radioactive waste streams generated, thereby, improving process efficiency. A promising strategy for this is the direct dissolution of UNF that has been pretreated by voloxidation into an organic solvent composed of specialized extractants and diluent. However, removal of the aqueous HNO3 phase from the envisioned reprocessing system has the potential to drastically change the suite of radiation-induced processes occurring, and thus, alter the longevity of proposed reagents. Furthermore, the impacts of fission product and transuranic metal ion complexation on the aforementioned radiation-induced processes is poorly understood, and yet can cause significant changes in radiolytic longevity. To bridge these knowledge gaps and support the continued development of direct dissolution strategies, we present an investigation into the impacts of direct dissolution conditions on the gamma radiation-induced degradation of N,N-di-(2-ethylhexyl) butyramide (DEHBA) and N,N-di-(2-ethylhexyl)isobutyramide (DEHiBA) ligands—candidate replacements for tributyl phosphate—in pre-equilibrated n-dodecane solvent in the presence and absence of envisioned loading amounts of uranium.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Reaction rates and prediction of thermal instability during aluminum alloy 6061 dissolution

Here, chemical kinetics of dissolution of aluminum alloy 6061 was investigated for the processing of Pu-238 for deep space missions. The rate of dissolution was measured by the heat release and appeared to be controlled by the rate of release of Al(OH) 4 – from the metal surface. Rates of reaction were measured from 273 to 365 K, giving an activation energy of 72 ± 13 kJ•(mol Al) –1 and a pre-exponential factor of 5 ± 3 × 10 9 dm 3 mol –1 min –1 . Minor alloying elements did not appear to affect the reaction kinetics. The average heat of dissolution was –360 ± 70 kJ•(mol NaAlO 2 ) –1 . When extrapolated to an infinitely dilute solution of aluminum, kJ•(mol NaAlO 2 ) –1 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

GLAMOR – OR HOW WE ACHIEVED A COMMON UNDERSTANDING ON THE DECREASE OF GLASS DISSOLUTION KINETICS THROUGH INTERNATIONAL COOPERATION

The objective of the EC funded GLAMOR project was to achieve a common understanding of the processes that control the decrease of the dissolution rate of high-level waste glass in water when silica becomes saturated. Is affinity control or a protective layer dominating? The following steps were taken: (1) review of the literature, (2) selection ofselect an experimental dataset, and selection of the models r(t) and GM2003, and (3) application apply by the GLAMOR partners of the models to the datasets. The main focus has beenwas on dissolution tests in pure water at different values of surface-to-volume and pH. Some of the main conclusions were: (1) both affinity and protective layer concepts must be considered in the interpretation of the rate decreasing stage, (2) the residual dissolution rate observed beyond the silica saturation stage is far more important in view of the long-term performance of the glass, and deserves more attention in future R&D. In the GLAMOR final report, we also discussed in detail the modeling parameters, such as the silica saturation concentration, the silica diffusion coefficient, the silica retention factor in the reaction layer, and the water diffusion coefficient.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Suppressing Manganese Dissolution from Lithium Manganese Oxide Spinel Cathodes with Single-Layer Graphene

Spinel-structured LiMn 2 O 4 (LMO) is a desirable cathode material for Li-ion batteries due to its low cost, abundance, and high power capability. However, LMO suffers from limited cycle life that is triggered by manganese dissolution into the electrolyte during electrochemical cycling. Here, it is shown that single-layer graphene coatings suppress manganese dissolution, thus enhancing the performance and lifetime of LMO cathodes. Relative to lithium cells with uncoated LMO cathodes, cells with graphene-coated LMO cathodes provide improved capacity retention with enhanced cycling stability. X-ray photoelectron spectroscopy reveals that graphene coatings inhibit manganese depletion from the LMO surface. Additionally, transmission electron microscopy demonstrates that a stable solid electrolyte interphase is formed on graphene, which screens the LMO from direct contact with the electrolyte. Density functional theory calculations provide two mechanisms for the role of graphene in the suppression of manganese dissolution. First, common defects in single-layer graphene are found to allow the transport of lithium while concurrently acting as barriers for manganese diffusion. Second, graphene can chemically interact with Mn 3+ at the LMO electrode surface, promoting an oxidation state change to Mn 4+ , which suppresses dissolution.

Environmental Molecular Sciences Laboratory↗

How exudates production along a phosphorus gradient influences mineral dissolution across contrasting soil development stages

Harnessing rhizosphere processes offers a valuable opportunity to optimize nutrient use efficiency in agroecosystems. In nutrient-limited soils, plants discharge part of photosynthate surplus via root exudation, including carboxylates, which may enhance mineral dissolution and nutrient mobilization. We aimed to assess how plant responses to nutrient limitation translated into changes in exudate profiles, and how these exudates, in turn, drive bioweathering processes across soils of contrasting mineralogy and weathering degree. We conducted a hydroponic experiment with Lupinus albus grown under five phosphorus (P) concentrations (5, 10, 20, 30, and 50 µM) over seven weeks. We measured plant biomass and root traits, performed a metabolomics analysis and quantified seven carboxylates in root exudates using gas chromatography-mass spectrometry. To assess bioweathering processes across contrasted soil domains, we conducted batch dissolution tests with exudates using three soil horizons—35 each with distinct physicochemical properties: enriched in organic matter, iron oxides, or primary silicates. At the intermediate level of P supply, shoot biomass was comparable to that under high P, but plants produced more root biomass and a higher total carboxylate exudation rate. Despite low carboxylate concentrations (<100 ppb), exudates promoted the dissolution of Ca, Mg, Si, Fe, P and K in all horizons. Yet, the degree of element released varied among horizons. These findings highlight the importance of root exudates in enhancing mineral dissolution, with effects dependent on soil physicochemical properties. The results suggest that managing agroecosystems under moderate nutrient limitation could be a sustainable strategy to increase root-to-shoot ratios, enhance bioweathering processes and nutrient release in soil solution.

Pollet, Sasha L.↗

Electrochemistry of soluble UO 2 2+ from the direct dissolution of UO 2 CO 3 in acidic ionic liquid containing water

The direct dissolution of UO 2 CO 3 in neat and “wet” ionic liquid (IL) trimethyl-n-butylammonium bis(trifluoromethansulfonyl)imide [Me 3 N n Bu][TFSI] is examined. The ionic liquid serves as both the solvent for the direct dissolution of UO 2 CO 3 (s) and the electrolyte solution for the electrochemical analysis of the soluble uranyl species. The solubility data indicate that displacement of the CO 3 2- occurs slowly due to the low concentration of protons available from residual water in the pristine IL. Enhanced dissolution of UO 2 CO 3 through the formation of carbonic acid H 2 CO 3 is achieved after the addition of acid, bis(trifluoromethanesulfonyl)amide (HTFSI) and water. The soluble uranyl cation can then coordinate with the TFSI anion in place of the displaced CO 3 2- anion following the decomposition of carbonic acid and purging of CO 2 (g) and water from the IL. The solubility of UO 2 CO 3 was examined using liquid scintillation counting of 233 U for the pristine ionic liquid. The “wet” ionic liquid containing HTFSI and soluble UO 2 CO 3 was evaluated using UV/vis spectroscopy before and after dissolution. The electrochemical deposition of uranium species from ionic liquid was evaluated using cyclic voltammetry. The potential mediated deposition of uranium species was achieved and verified using scanning electron microscopy (SEM) and the solid uranium deposits were evaluated using energy dispersive X-ray emission spectroscopy (EDX).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Cobalt Dissolution from Metal Oxides and Battery Cathode Materials with Acetic Acid-Based Deep Eutectic Solvents

Recovery of critical metals with alternative solvents beyond those in traditional pyrometallurgy and hydrometallurgy is needed in consideration of environmental challenges and the growing demand for metals in energy technologies. Deep eutectic solvents (DESs) have emerged as sustainable alternatives for solvometallurgy in metal separation and recovery. In this study, DESs based on hydrogen bond acceptors (HBAs) including choline chloride (ChCl), acetylcholine chloride (AChCl), and betaine (Bet) were investigated for their effectiveness when paired with acetic acid (AA) as the hydrogen bond donor (HBD) for the dissolution of cobalt from cobalt oxide (CoO), lithium cobalt oxide (LiCoO 2 ), and lithium nickel manganese cobalt oxide (LNMC). Based on the spectroscopic analysis of the metal dissolution and coordination, Bet:AA was found to provide the highest solubility for CoO (0.33 M) in the form of an octahedral complex. On the other hand, ChCl:AA solvent was more effective at dissolving LiCoO 2 with 0.04 M Co 2+ corresponding to 17% dissolution efficiency and LNMC with 0.06 M Co 2+ corresponding to 72% dissolution efficiency at 50 °C, compared to Bet:AA (9% for LiCoO 2 and 31% for LNMC). Although the solubilities of LiCoO 2 and LNMC have not significantly improved in ChCl:AA, this difference in effectiveness between the solvents clearly reveals the role of the HBA in solubilization. The coordination synergy between the chloride and the –OH moiety facilitates the breakdown of the LiCoO 2 driven by the alteration of the solvent polarity. Cobalt in these solutions was found dominantly as a tetrahedral [CoCl 4 ] 2– complex. A chemical separation of cobalt oxalate from a mixed-metal oxide system based on Co, Fe, and Ni was also demonstrated, confirming the potential of these solvents for practical metal recovery.

Cobalt separation↗

Convective carbon dioxide dissolution in a closed porous medium at low pressure

Motivated by the persistence of natural carbon dioxide ( $\text{CO}_{2}$ ) fields, we investigate the convective dissolution of $\text{CO}_{2}$ at low pressure (below 1 MPa) in a closed system, where the pressure in the gas declines as convection proceeds. This introduces a negative feedback that reduces the convective dissolution rate even before the brine becomes saturated. We analyse the case of an ideal gas with a solubility given by Henry’s law, in the limits of very low and very high Rayleigh numbers. The equilibrium state in this system is determined by the dimensionless dissolution capacity, $\unicode[STIX]{x1D6F1}$ , which gives the fraction of the gas that can be dissolved into the underlying brine. Analytic approximations of the pure diffusion problem with $\unicode[STIX]{x1D6F1}>0$ show that the diffusive base state is no longer self-similar and that diffusive mass transfer declines rapidly with time. Direct numerical simulations at high Rayleigh numbers show that no constant flux regime exists for $\unicode[STIX]{x1D6F1}>0$ ; nevertheless, the quantity $F/C_{s}^{2}$ remains constant, where $F$ is the dissolution flux and $C_{s}$ is the dissolved concentration at the top of the domain. Simple mathematical models are developed to predict the evolution of $C_{s}$ and $F$ for high-Rayleigh-number convection in a closed system. The negative feedback that limits convection in closed systems may explain the persistence of natural $\text{CO}_{2}$ accumulations over millennial time scales.

Mechanics↗