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At least 19 records

Results of Oklo Diffusion Couple Experiments

Through the Gateway for Accelerated Innovation in Nuclear (GAIN) initiative, the U.S. Department of Energy funded a GAIN Nuclear Energy Voucher to perform out-of-pile experiments related to the fuel design for Oklo Inc., headquartered in Santa Clara, CA. GAIN’s goal is to accelerate the innovation and application of advanced nuclear technologies, and voucher recipients do not receive direct financial awards but are provided access to national laboratory capabilities at no cost. This report documents the results of diffusion couple experiments performed as part of the GAIN-funded project for Oklo. This work addresses the specific problem of filling the gap in understanding of the fuel-cladding chemical interaction (FCCI) that result from the past focus on a particular fuel design. These knowledge and mechanistic modeling gaps make it difficult to extrapolate from prior fuel performance data to advance an economically competitive fuel design. Specifically, the current state-of-the-art fuel performance modeling cannot separate the entangled effects of temperature ranges, burnups, materials, and geometries.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Nd, SbNd and Sb 3 Nd 4 and their interactions with the cladding alloy HT9

Lanthanide fission products, such as neodymium, formed during the irradiation of metallic fuels are known to cause deleterious effects from chemical interactions occurring at the fuel-cladding interface; a phenomenon known as fuel-cladding chemical interaction (FCCI). The use of fuel-based additives that bind with the lanthanide elements within the fuel meat, alleviating their interactions at the fuel-cladding interface, is one potential method proposed to mitigate the FCCI phenomenon and extend the burnup potential of such metallic fuel systems. In this study, antimony (Sb) is evaluated as one such additive, and neodymium (Nd) is used to represent the lanthanides. A Sb-Nd alloy is fabricated, which consists of two intermetallic phases, SbNd and Sb 3 Nd 4 . Isothermal diffusion couple experiments are carried out at 675 °C for 24 h between Nd and the Fe-12Cr based HT9 cladding alloy. The results are compared against similar diffusion couple experiments carried out between the Sb-Nd alloy and also HT9. Inter-diffusion between Nd/HT9 diffusion couple is characterized and the phases Fe 17 Nd 5 and Fe 17 Nd 2 were found to form whereas no interactions were observed in the Sb-Nd/HT9 diffusion couple. The lack of compound forming tendencies between Fe, the primary alloying constituent of HT9, and SbNd is elucidated through density functional theory (DFT) calculations on enthalpy of mixing, aligning well with the experimental observations. Lastly, the strong binding of Nd with Sb appears to be favorable, alleviating Nd interactions with HT9 constituent elements.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Understanding the interface interaction between U3Si2 fuel and SiC cladding

Abstract Triuranium disilicide (U 3 Si 2 ) fuel with silicon carbide (SiC) composite cladding is being considered as an advanced concept/accident tolerant fuel for light water reactors thus, understanding their chemical compatibility under operational and accident conditions is paramount. Here we provide a comprehensive view of the interaction between U 3 Si 2 and SiC by utilizing density functional theory calculations supported by diffusion couple experiments. From the calculated reaction energies, we demonstrate that triuranium pentasilicide (U 3 Si 5 ), uranium carbide (UC), U 20 Si 16 C 3 , and uranium silicide (USi) phases can form at the interface. A detailed study of U 3 Si 2 and SiC defect formation energies of the equilibrated materials yielding the interfacial phases U 20 Si 16 C 3 , U 3 Si 5 and UC reveal a thermodynamic driving force for generating defects in both fuel and cladding. The absence of either the U 3 Si 2 or SiC phase, however, causes the defect formation energies in the other phase to be positive, removing the driving force for additional interfacial reactions. The diffusion couple experiments confirm the conclusion with demonstrated restricted formation of U 3 Si 5 , UC, and U 20 Si 16 C 3 /USi phases at the interface. The resulting lack of continuous interaction between the U 3 Si 2 and SiC, reflects the diminishing driving force for defect formation, demonstrating the substantial stability of this fuel-cladding system.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Diffusion and phase formation in the γ-uranium-technetium system

Phase formation in the U-Tc binary system at 800 °C was investigated using a diffusion couple experiment. Scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS) identified four novel potential intermetallic phases - U 7 Tc 3 , U 13 Tc 12 , U 3 Tc 5 , and UTc 4 . Diffusion coefficients were calculated for the intermetallic phases using the Boltzmann-Matano method and were respectively found to be – 120, 38.2, 15.6, and 1.51 × 10 −18 m 2 /s. Tc also exhibits a solid-solution phase with high penetration into the U with a diffusion coefficient of ∼ 10 −14 m 2 /s. Furthermore, these findings expand the number of known U-Tc phases and provide the first diffusion coefficients for the U-Tc system, and contribute valuable data to the broader field of actinide metallurgy.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Chemical interaction and compatibility of uranium mononitride and alumina forming austenitic stainless steel

Uranium mononitride (UN) and alumina forming austenitic (AFA) stainless steel are a potential fuel-cladding combination for the lead-cooled fast reactor (LFR). Chemical compatibility between UN and AFA steel needs to be verified before implementation in a nuclear reactor. Diffusion couple experiments at 823 K and 1023 K were conducted for nonirradiated UN samples in contact with as-cast (no thermally grown Al 2 O 3 ) and preoxidized (with thermally grown Al 2 O 3 ) AFA for 500 and 1000 h in an inert environment. Preoxidized AFA exhibited little to no interaction with all UN samples tested at both 823 K and 1023 K, displaying the stability and capability of the Al 2 O 3 layer to prevent chemical interaction and inter-diffusion with UN. Chemical interaction occurs between UN and as-cast AFA. At 1023 K, an aluminum and nitrogen rich phase (likely AlN) formed along the interface of as-cast AFA and UN samples. At 823 K the AlN phase was not prominently observed due to the reduced diffusivity of aluminum through AFA. The aluminum and nitrogen-enriched phase was also observed in a high temperature pressure-assisted test sample of UN and as-cast AFA thermally treated at 1373 K. Finally, in UN samples doped with a low weight percent of UO 2 (< 3 wt%), AlN was not detected along the interface at either temperatures, and an Al 2 O 3 layer likely formed along the interface and prevented further chemical interaction between UN and as-cast AFA.

36 MATERIALS SCIENCE↗

Evaluation of Sb-Nd and Te-Nd phases within the U-Zr fuel matrix and their interactions with HT9 alloy

Antimony (Sb) and tellurium (Te) were investigated as potential additives for U-10Zr (wt.%) metallic fuel to limit the fuel-cladding chemical interaction (FCCI) with HT-9 alloy. Neodymium (Nd) was utilized to simulate the formation of lanthanide-based solid fission products which are known to play a detrimental role in FCCI. Fuel alloys of U-Zr-Sb-Nd and U-Zr-Te-Nd were evaluated in their annealed condition and compared against their as-cast conditions. Isothermal diffusion couple experiments were performed between U-Zr-Nd, U-Zr-Sb-Nd, and U-Zr-Te-Nd against the cladding alloy HT9 to evaluate the effectiveness of the additives to stabilize Nd within the fuel alloys, as well as investigate the interaction regions that form between the different fuel alloys and HT9. Further, SbNd and Sb 3 Nd 4 , and TeNd are found to be the primary neodymium-based phases formed in the U-Zr-Sb-Nd and U-Zr-Te-Nd alloys, respectively. The zirconium-based phase, Zr 2 Sb, is also found to form within the former alloy. All phases were found to remain stable through the diffusion experiments and exhibited no interaction with HT9 constituent elements. Preferential interaction between Nd with additivities Te and Sb compared to constituting elements in HT9 was further verified based on density functional theory (DFT) calculated enthalpy of mixing.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Precipitation Model Validation in 3rd Generation Aeroturbine Disc Alloys

In support of application of the DARPA-AIM methodology to the accelerated hybrid thermal process optimization of 3rd generation aeroturbine disc alloys with quantified uncertainty, equilibrium and diffusion couple experiments have identified available fundamental thermodynamic and mobility databases of sufficient accuracy. Using coherent interfacial energies quantified by Single-Sensor DTA nucleation undercooling measurements, PrecipiCalc(TM) simulations of nonisothermal precipitation in both supersolvus and subsolvus treated samples show good agreement with measured gamma particle sizes and compositions. Observed longterm isothermal coarsening behavior defines requirements for further refinement of elastic misfit energy and treatment of the parallel evolution of incoherent precipitation at grain boundaries.

Olson, G. B.↗

Diffusion in liquid state and solidification of binary system (M-7)

Diffusion is one of the most fundamental physical phenomena. It relates to the manufacturing of almost all materials. Therefore, the precise knowledge of diffusivities of relevant materials is necessary for the optimization of these processes. On the other hand, such knowledge is indispensable to understanding the diffusion mechanism and structure of liquid metal in the field of physical metallurgy. Many diffusion experiments on solid metal were undertaken and a lot of data were accumulated. But on liquid metals there are few measurements because of experimental difficulties, such as thermal convection, induced by very slight temperature gradients in the specimen. Under microgravity conditions, the movement of liquid metal due to density differences and thermal convection must be suppressed markedly. Therefore, the transportation process will be controlled only by the diffusion of constituent atoms. These conditions offer the optimum environments for the diffusion experiment. The experiments are briefly described. Diffusion couples are prepared by attaching end to end two rods of different pure metals using hot press equipment. These couples are inserted into a graphite crucible and then doubly enclosed by two silica ampoules, respectively. The specimen is inserted into a tantalum cartridge, which is welded in a vacuum using an electron-beam apparatus. These cartridges are charged in the continuous heating furnace in space and held at a given temperature for a predetermined time and then solidified. The concentration distribution of elements in these specimens will be measured along the rod axis by means of an electron probe microanalyzer. The counterdiffusivity of the liquid metal binary system is determined on the basis of the compensated concentration distribution profile for thermal contraction.

Dan, T.↗

A reaction–diffusion model for grayscale digital light processing 3D printing

We report that digital light processing (DLP) 3D printing is an additive manufacturing process that utilizes light patterns to photopolymerize a liquid resin into a solid. Due to the accuracy of modern digital micromirror devices (DMD) and recent advances in resin chemistry, it is now possible to create functionally graded structures using different light intensity values, also known as grayscale DLP (g-DLP). Different intensities of light lead to differences in the polymer crosslinking density after curing, which ultimately produces a part with gradients of material properties. However, g-DLP is a complicated process. First, the DLP printing is a highly coupled chemical and physical process that involves light propagation, chemical reactions, species diffusion, heat transfer, volume shrinkage, and changes in mechanical behaviors of the curing resin. Second, in g-DLP, light gradients create strong in plane gradients of chemical species concentrations in the curing liquid resin due to the strong dependence of light intensity on the rate of monomer crosslinking. Furthermore, light gradients through the depth create concentration gradients due to the degree of cure dependent light absorption and the use of photoabsorbers. These complex physical features of the printing process must be understood in order to properly control printing parameters such as light exposure time, printing speed, and grayscale variations to achieve accurate mechanical properties. In this paper, a photopolymerization reaction–diffusion model is developed and used in conjunction with experiments to investigate the coupled effects of light propagation, chemical reaction rates, and species diffusion during g-DLP 3D printing. The model is implemented numerically utilizing the finite difference method and simulation results are compared to experimental findings of simple printed structures. The agreement between experimental and model predictions of simple quantities of interest, such as geometric feature sizes, shows that the model can capture the overcure due to free-radical and other species diffusion during printing when grayscale patterns are employed. This model lays the groundwork for future extensions that can incorporate more complex coupled physics such as heat transfer, volume shrinkage, and material property evolution, which are critically important in utilizing g-DLP 3D printing for the fabrication of high-performance parts which excellent geometric and material property tolerances.

36 MATERIALS SCIENCE↗

A physics-based model of cladding wastage layer formation rate

In this report, lower length scale simulations to inform an engineering-scale model of fuel-cladding chemical interaction (FCCI) conducted under the auspices of the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program in FY22 are described. An overall strategy for the implementation of the BISON model is described, and the past and current lower length scale work on FCCI formation is put into the context of this overall strategy. Density functional theory and kinetic Monte Carlo simulations are used to determine the diffusion coefficient of neodymium in iron. Density functional theory calculations are also used to parameterize a parabolic approximation for the dependence of free energy on composition for the intermetallic compound Fe 17 Nd 2 . A phase-field model of the Fe-Nd system was developed that includes the random solid solution body-centered cubic phase and the intermetallic Fe 17 Nd 2 . The model was used to simulate growth of the intermetallic layer in a diffusion couple and the results were compared to experiment. The model’s prediction of the parabolic growth constant is within 40 % of the experimental value. The model is also used to simulate the formation of a grain boundary attack layer that is observed in experiment. The simulations show enhanced Nd concentration along the grain boundaries, but do not clearly show formation of a Fe 17 Nd 2 layer

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Coupled Lattice Boltzmann Modeling Framework for Pore-Scale Fluid Flow and Reactive Transport

In this paper, we propose a modeling framework for pore-scale fluid flow and reactive transport based on a coupled lattice Boltzmann model (LBM). We develop a modeling interface to integrate the LBM modeling code parallel lattice Boltzmann solver and the PHREEQC reaction solver using multiple flow and reaction cell mapping schemes. The major advantage of the proposed workflow is the high modeling flexibility obtained by coupling the geochemical model with the LBM fluid flow model. Consequently, the model is capable of executing one or more complex reactions within desired cells while preserving the high data communication efficiency between the two codes. Meanwhile, the developed mapping mechanism enables the flow, diffusion, and reactions in complex pore-scale geometries. We validate the coupled code in a series of benchmark numerical experiments, including 2D single-phase Poiseuille flow and diffusion, 2D reactive transport with calcite dissolution, as well as surface complexation reactions. The simulation results show good agreement with analytical solutions, experimental data, and multiple other simulation codes. In addition, we design an AI-based optimization workflow and implement it on the surface complexation model to enable increased capacity of the coupled modeling framework. Compared to the manual tuning results proposed in the literature, our workflow demonstrates fast and reliable model optimization results without incorporating pre-existing domain knowledge.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Oscillatory Extinction Of Spherical Diffusion Flames

Since extinction has been observed in an oscillatory manner in Le greater than 1 premixed flames, it is not unreasonable to expect that extinction could occur in an unsteady manner for diffusion flames. Indeed, near-limit oscillations have been observed experimentally under microgravity conditions for both candle flames and droplet flames. Furthermore, the analysis of Cheatham and Matalon on the unsteady behavior of diffusion flames with heat loss, identified an oscillatory regime which could be triggered by either a sufficiently large Lewis number (even without heat loss) or an appreciable heat loss (even for Le=1). In light of these recent understanding, the present investigation aims to provide a well-controlled experiment that can unambiguously demonstrate the oscillation of diffusion flames near both the transport- and radiation-induced limits. That is, since candle and jet flames are stabilized through flame segments that are fundamentally premixed in nature, and since premixed flames are prone to oscillate, there is the possibility that the observed oscillation of these bulk diffusion flames could be triggered and sustained by the oscillation of the premixed flame segments. Concerning the observed oscillatory droplet extinction, it is well-known that gas-phase oscillation in heterogeneous burning can be induced by and is thereby coupled with condensed-phase unsteadiness. Consequently, a convincing experiment on diffusion flame oscillation must exclude any ingredients of premixed flames and other sources that may either oscillate themselves or promote the oscillation of the diffusion flame. The present experiment on burner-generated spherical flames with a constant reactant supply endeavored to accomplish this goal. The results are further compared with those from computational simulation for further understanding and quantification of the flame dynamics and extinction.

Law, C. K.↗

High-throughput approach for investigating interdiffusion in medium- and high-entropy alloys

Interdiffusion experiments are usually time-consuming and tedious since diffusion couples must be annealed at several temperatures for a long time. The efforts required to study interdiffusion in multicomponent alloys increase dramatically as multiple diffusion couples are required to cover broad composition ranges and determine the diffusivities of individual elements in different chemical environments. To circumvent this challenge, we present a high-throughput approach applicable to single-phase and compositionally complex alloys, which are assumed to approximate ideal solid solutions. Here, a simple diffusion-multiple experiment combined with a physically based kinetic model is proposed to efficiently determine the diffusion coefficients of the constituent elements in quaternary CrFeCoNi alloys. Compared with tracer diffusivities reported in the literature, the results, thus, obtained do not differ by more than a factor of 2 and were obtained from a single interdiffusion experiment. In contrast, the diffusivities simulated with commercial mobility and thermodynamic databases are strongly overestimated by a factor ranging from 1 to 16. Therefore, our approach enables high-throughput determination of diffusivities and can help in the design of alloys for high-temperature applications where diffusion plays a key role.

36 MATERIALS SCIENCE↗

Summary Report on Ion Irradiation Study of Ceramic Coating on Suppressing FCCI

Advanced cladding is critical for advanced nuclear reactors with an enhanced performance in radiation tolerance and neutron transparency. Using advanced cladding will ensure the adequate thermal conductivity and mechanical stability of the cladding base material, corrosion resistance, high-temperature coolant compatibility of the cladding surface, and chemical stability in the cladding inner wall against fuel cladding chemical interaction (FCCI). An innovative cladding with a three-layer structure (i.e., a modified surface, a clad base material, and a modified inner wall) promises to meet all these requirements. Initial research and development (R&D) regarding this innovative cladding seek to demonstrate the effectiveness of a thin ceramic coating in suppressing FCCI under ion irradiation to high dose. This United States (U.S.) Department of Energy (DOE)–Office of Nuclear Energy (NE) project report summarizes the results of recent ion irradiation studies of diffusion-couple samples with details of an ion irradiation experiment, the characterization of the interface microstructure of cerium (Ce)/titanium nitride (TiN)/oxide-dispersion strengthened (ODS), Ce/TiN/iron (Fe), Ce/ODS, and Ce/Fe samples irradiated with 80 million electron-volts (MeV) of xenon (Xe) ions to 100 displacements per atom (dpa) at 500?C using the Argonne Tandem Linac Accelerator System (ATLAS) facility at Argonne National Laboratory (ANL). The results of the ODS-substrate sample are encouraging and demonstrate the effectiveness of a thin ceramic coating on FCCI mitigation under irradiation. The results from an Fe-substrate sample revealed a complex microstructure, and the root cause is discussed.

36 MATERIALS SCIENCE↗

Reaction–Diffusion Coupling Facilitates the Sequential Precipitation of Metal Ions from Battery Feedstock Solutions

Here, the development of new technologies for chemical separations is urgently needed to meet the surging demand for critical materials that has strained resources and caused environmental challenges. Inspired by the classic Liesegang experiment, we demonstrated the separation of critical metal ions based on the coupling of ion diffusion and precipitation kinetics. For this purpose, a model feedstock solution simulating dissolved battery electrodes was placed on top of a hydrogel loaded with a precipitating agent, namely sodium hydroxide. As the lithium, manganese, cobalt, and nickel ions diffused into the gel, a gradient of precipitates formed along the length of the reactor. Elemental analysis of the spatially distributed precipitates showed the enrichment of nickel near the gel-solution interface, followed by the formation of an almost pure (>96%) manganese product further along the reactor. Optimization experiments revealed that a sodium hydroxide concentration of 10 mM and a gel/solution volume ratio of 2:1 favored efficient separations. The robustness of the method was demonstrated in four out of five feedstock compositions of typically used battery cathodes. Our proof-of-concept experiments present a paradigm for critical materials separations that does not require specialty chemicals, binding agents, membranes, or toxic solvents.

25 ENERGY STORAGE↗

Status Report on Ion Irradiation Study of Ceramic Coating in Suppressing Fuel/Cladding Chemical Interaction

Advanced cladding is critical for the development of advanced nuclear reactors with enhanced performance in radiation tolerance and neutron transparency. It will ensure adequate thermal conductivity and mechanical stability of cladding base material, corrosion resistance and high temperature coolant compatibility of cladding surface. Finally, it provides chemical stability in the cladding inner wall against fuel/cladding chemical interaction (FCCI). An innovative cladding with a three-layer structure (i.e., a treated surface, a base material, and a treated inner-wall) promises to meet all the listed requirements. The initial work on innovative researching and developing these cladding materials seeks to demonstrate the effectiveness of a thin ceramic coating in suppressing FCCI through ion-irradiation. It consists of a study of Ce/TiN/Fe diffusion couples. This report provides an update on the status of ceramic-coating preparation and the testing of diffusion couple samples, the design of an ion-irradiation experiment, and characterization of the microstructure of a legacy-coupon sample coated with 1 µm of TiN and irradiated with 5 MeV Fe ions to 200 dpa at 500°C.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Microgravity Transport Phenomena Experiment (MTPE) Overview

The Microgravity Transport Phenomena Experiment (MTPE) is a fluids experiment supported by the Fundamentals in Biotechnology program in association with the Human Exploration and Development of Space (BEDS) initiative. The MTP Experiment will investigate fluid transport phenomena both in ground based experiments and in the microgravity environment. Many fluid transport processes are affected by gravity. Osmotic flux kinetics in planar membrane systems have been shown to be influenced by gravimetric orientation, either through convective mixing caused by unstably stratified fluid layers, or through a stable fluid boundary layer structure that forms in association with the membrane. Coupled transport phenomena also show gravity related effects. Coefficients associated with coupled transport processes are defined in terms of a steady state condition. Buoyancy (gravity) driven convection interferes with the attainment of steady state, and the measurement of coupled processes. The MTP Experiment measures the kinetics of molecular migration that occurs in fluids, in response to the application of various driving potentials. Three separate driving potentials may be applied to the MTP Experiment fluids, either singly or in combination. The driving potentials include chemical potential, thermal potential, and electrical potential. Two separate fluid arrangements are used to study membrane mediated and bulk fluid transport phenomena. Transport processes of interest in membrane mediated systems include diffusion, osmosis, and streaming potential. Bulk fluid processes of interest include coupled phenomena such as the Soret Effect, Dufour Effect, Donnan Effect, and thermal diffusion potential. MTP Experiments are performed in the Microgravity Transport Apparatus (MTA), an instrument that has been developed specifically for precision measurement of transport processes. Experiment fluids are contained within the MTA fluid cells, designed to create a one dimensional flow geometry of constant cross sectional area, and to facilitate fluid filling and draining operations in microgravity. The fluid cells may be used singly for bulk solutions, or in a Stokes diaphragm configuration to investigate membrane mediated phenomena. Thermal and electrical driving potentials are applied to the experiment fluids through boundary plates located at the ends of the fluid cells. In the ground based instrument, two constant temperature baths circulate through reservoirs adjacent to the boundary plates, and establish the thermal environment within the fluid cells. The boundary plates also serve as electrodes for measurement and application of electrical potentials. The Fluid Manipulation System associated with the MTA is a computer controlled system that enables storage and transfer of experiment fluids during on orbit operations. The system is used to automatically initiate experiments and manipulate fluids by orchestrating pump and valve operations through scripted sequences. Unique technologies are incorporated in the MTA for measurement of fluid properties. Volumetric Flow Sensors have been developed for precision measurement of total fluid volume contained within the fluid cells over time. This data is most useful for measuring the kinetics of osmosis, where fluid is transported from one fluid cell to another through a semipermeable membrane. The MicroSensor Array has been designed to perform in situ measurement of several important fluid parameters, providing simultaneous measurement of solution composition at multiple locations within the experiment fluids. Micromachined sensors and interface electronics have been developed to measure temperature, electrical conductivity, pH, cation activity, and anion activity. The Profile Refractometer uses a laser optical system to directly image the fluid Index of Refraction profile that exists along the MTA fluid cell axis. A video system acquires images of the RI profile over time, and records the transport kinetics that occur upon application of chemical, thermal, or electrical driving potentials. Image processing algorithms have been developed to analyze the refractometer images on a pixel by pixel basis, calibrating and scaling the measured Index of Refraction profile to correlated solution properties of interest such as density, concentration, and temperature. Additional software has been developed to compile the processed images into a three dimensional matrix that contains fluid composition data as a function of experiment time and position in the fluid cell. These data are combined with data from the other sensor systems, and analyzed in the context of transport coefficients associated with the various transport phenomena. Analysis protocols have been developed to measure the transient kinetics, and steady state distribution of fluid components that occur in response to the applied driving potentials. The results are expressed in terms of effective transport coefficients. Experiments have been performed using a variety of solutes, and results generated are that are in agreement with published transport coefficient values.

Mason, Larry W.↗