Large Density Changes Research Articles

Preliminary Core Design Study of Small Supercritical Fast Reactor with Single-Pass Cooling

A supercritical water-cooled reactor (SCWR) adopts a once-through direct cycle, which is compatible with a small modular reactor class (SMR) plant system. The core is cooled by supercritical light water, which does not exhibit phase change, but undergoes large temperature and density changes. A super fast reactor (Super FR) is a fast reactor type concept of SCWR. Unlike other SCWR core concepts, it adopts the single coolant pass flow scheme, in which the coolant passes the core only once from the bottom to the top without any reverse flows or preheating stages. In the meantime, reducing the core size tends to increase the core power peaking and reduce criticality. Therefore, the key issues with the small Super FR core design is reducing the core power peaking and achieving high average core outlet temperature with the single coolant pass scheme. This study aims to highlight the design issues through conceptual core designs of SMR class Super FR. To evaluate the core characteristics, three-dimensional coupled core calculations are carried out. The proposed design with small fuel assemblies, which are equivalent to those of boiling water reactors, attains a high core average outlet temperature of about 500 °C, which is compatible to that of typical large SCWR core design.

Research progress of mesoporous silica-based composite phase change materials

Increasing concerns surrounding the rising global energy demand has forced humans to look for alternative energy sources such as the development and utilization of natural gas and nuclear energy, or to increase the efficiency of energy use, thereby optimizing the use of energy. Improving energy efficiency is an effective method that can quickly and efficiently reduce the energy demand and supply gap. Furthermore, developing new technologies for energy storage and energy saving is an effective way to solve the energy crisis, which is of great significance for the sustainable development of energy. Latent heat storage has become a popular research topic owing to its large energy storage density and small temperature changes during energy storage and its excellent thermal stability and high safety. Currently, phase-change materials have been widely used in solar heating systems, air conditioning systems, thermally regulated textiles, energy-efficient building construction, temperature-controlled greenhouses and other fields. The development of phase-change energy storage technology is significant for promoting the development of alternative energy sources and improving energy efficiency. However, phase change materials are prone to liquid leakage during the solid-liquid phase transition, which limits their application. To solve this problem, researchers have started introducing porous support materials to phase-change materials. Porous support materials have attracted extensive research attention in recent years owing to their outstanding properties such as high specific surface area, large pore volume, and low density. Porous support materials can absorb phase-change materials in their pores through the physical adsorption phenomena such as capillary action and interfacial tension, and thereby gradually develop into important substrates for phase-change material encapsulation. Inorganic materials are used as carriers for phase change energy storage materials. Compared with organic carrier materials, inorganic carrier materials have higher mechanical strength, flame retardancy and thermal conductivity, which can reduce the production cost of phase-change energy storage materials, and have a high research value. Mesoporous silica materials have good physical and chemical stability, biocompatibility, flame retardancy, low toxicity, corrosion resistance, controllable size, adjustable surface morphology and high specific surface area. They can comprehensively improve the performance of various aspects of phase change composites and broaden the application space of phase change energy storage materials. In this review, the effects of pore size, pore structure, and pore surface properties on the crystallization behavior of phase change materials in mesoporous silica carriers developed in recent years were comprehensively analyzed, and prospects of research methods for heat storage efficiency were explored.

Mammographic density change in a cohort of premenopausal women receiving tamoxifen for breast cancer prevention over 5 years

BackgroundA decrease in breast density due to tamoxifen preventive therapy might indicate greater benefit from the drug. It is not known whether mammographic density continues to decline after 1 year of therapy, or whether measures of breast density change are sufficiently stable for personalised recommendations.MethodsMammographic density was measured annually over up to 5 years in premenopausal women with no previous diagnosis of breast cancer but at increased risk of breast cancer attending a family-history clinic in Manchester, UK (baseline 2010-2013). Tamoxifen (20 mg/day) for prevention was prescribed for up to 5 years in one group; the other group did not receive tamoxifen and were matched by age. Fully automatic methods were used on mammograms over the 5-year follow-up: three area-based measures (NN-VAS, Stratus, Densitas) and one volumetric (Volpara). Additionally, percentage breast density at baseline and first follow-up mammograms was measured visually. The size of density declines at the first follow-up mammogram and thereafter was estimated using a linear mixed model adjusted for age and body mass index. The stability of density change at 1 year was assessed by evaluating mean squared error loss from predictions based on individual or mean density change at 1 year.ResultsAnalysis used mammograms from 126 healthy premenopausal women before and as they received tamoxifen for prevention (median age 42 years) and 172 matched controls (median age 41 years), with median 3 years follow-up. There was a strong correlation between percentage density measures used on the same mammogram in both the tamoxifen and no tamoxifen groups (all correlation coeficients > 0.8). Tamoxifen reduced mean breast density in year 1 by approximately 17–25% of the inter-quartile range of four automated percentage density measures at baseline, and from year 2, it decreased further by approximately 2–7% per year. Predicting change at 2 years using individual change at 1 year was approximately 60–300% worse than using mean change at 1year.ConclusionsAll measures showed a consistent and large average tamoxifen-induced change in density over the first year, and a continued decline thereafter. However, these measures of density change at 1 year were not stable on an individual basis.

60Fe deposition during the late Pleistocene and the Holocene echoes past supernova activity

Nuclides synthesized in massive stars are ejected into space via stellar winds and supernova explosions. The solar system (SS) moves through the interstellar medium and collects these nucleosynthesis products. One such product is 60Fe, a radionuclide with a half-life of 2.6 My that is predominantly produced in massive stars and ejected in supernova explosions. Extraterrestrial 60Fe has been found on Earth, suggesting close-by supernova explosions ∼2 to 3 and ∼6 Ma. Here, we report on the detection of a continuous interstellar 60Fe influx on Earth over the past ∼33,000 y. This time period coincides with passage of our SS through such interstellar clouds, which have a significantly larger particle density compared to the local average interstellar medium embedding our SS for the past few million years. The interstellar 60Fe was extracted from five deep-sea sediment samples and accelerator mass spectrometry was used for single-atom counting. The low number of 19 detected atoms indicates a continued but low influx of interstellar 60Fe. The measured 60Fe time profile over the 33 ky, obtained with a time resolution of about ±9 ky, does not seem to reflect any large changes in the interstellar particle density during Earth's passage through local interstellar clouds, which could be expected if the local cloud represented an isolated remnant of the most recent supernova ejecta that traversed the Earth ∼2 to 3 Ma. The identified 60Fe influx may signal a late echo of some million-year-old supernovae with the 60Fe-bearing dust particles still permeating the interstellar medium.

Macroscopic Traffic Flow Characterization at Bottlenecks

Traffic congestion is a significant issue in urban areas. Realistic traffic flow models are crucial for understanding and mitigating congestion. Congestion occurs at bottlenecks where large changes in density occur. In this paper, a traffic flow model is proposed which characterizes traffic at the egress and ingress to bottlenecks. This model is based on driver response which includes driver reaction and traffic stimuli. Driver reaction is based on time headway and driver behavior which can be classified as sluggish, typical or aggressive. Traffic stimuli are affected by the transition width and changes in the equilibrium velocity distribution. The explicit upwind difference scheme is used to evaluate the Lighthill, Whitham, and Richards (LWR) and proposed models with a continuous injection of traffic into the system. A stability analysis of these models is given and both are evaluated over a road of length 10 km which has a bottleneck. The results obtained show that the behavior with the proposed model is more realistic than with the LWR model. This is because the LWR model cannot adequately characterize driver behavior during changes in traffic flow.

Conceptual design of Super FR for MA transmutation with axially heterogeneous core

Supercritical water cooled Fast Reactor (Super FR) is featured with the large coolant density reduction by almost 1/10 from the core inlet to the outlet. Since Minor Actinides (MAs) not only have large neutron capture cross sections for thermal neutrons, but also can fission with fast neutrons, MA transmutation performance of Super FR may greatly depend on MA loading positions in the core axial direction of Super FR.However, such investigations have never been conducted. Hence, this study aims to design a Super FR transmutation core concept with the axial configuration of multiple layers of Mixed Oxide (MOX) and blanket fuels, with a focus on the influence of the large axial coolant density change on MA transmutation and core characteristics.With the design criteria of the negative Void Reactivity Coefficient (VRC), the Maximum Cladding Surface Temperature (MCST) < 650 ℃ and the Maximum Linear Heat Generation Rate (MLHGR) < 39 kW/m, three-dimensional neutronics and thermal-hydraulics coupled core burnup calculations have been carried out. Assembly-wise coolant flow rate distribution is determined to attain high core average outlet temperature and the core characteristics of different designs have been evaluated for the equilibrium core after the cores have reached equilibrium states with given fuel shuffling schemes. It has been shown that the MA transmutation amount is limited by deterioration of VRC due to increase of Pu enrichment for compensating the reactivity penalty by MA loading. Moreover, such influence has been found to be more significant in the lower region of the core, where the coolant density is relatively high. Hence, the core design with MA loading to the upper MOX layer is favorable for improving the MA transmutation performance. However, the trade-off relationship between the MA transmutation amount and thermal-hydraulics performance (increase of MLHGR and decrease of average outlet temperature) has been revealed. To overcome the issue, the core radial zoning has been applied and it has been found effective to suppress the trade-off relationship.

High-pressure freezing followed by freeze substitution of a complex and variable density miniorgan: the wool follicle.

Cryofixation by high-pressure freezing (HPF) followed by freeze substitution (FS) is a preferred method to prepare biological specimens for ultrastructural studies. It has been shown to achieve uniform vitrification and ultrastructure preservation of complex structures in different cell types. One limitation of HPF is the small sample volume of <200 µm thickness and about 2000 µm across. A wool follicle is a rare intact organ in a single sample about 200 µm thick. Within each follicle, specialized cells derived from multiple cell lineages assemble, mature and cornify to make a wool fibre, which contains 95% keratin and associated proteins. In addition to their complex structure, large density changes occur during wool fibre development. Limited water movement and accessibility of fixatives are some issues that negatively affect the preservation of the follicle ultrastructure via conventional chemical processing. Here, we show that HPF-FS of wool follicles can yield high-quality tissue preservation for ultrastructural studies using transmission electron microscopy.

A discontinuous Galerkin method for the simulation of compressible gas-gas and gas-water two-medium flows

In this paper, we develop a new discontinuous Galerkin method for the simulation of shocks and interfaces in compressible gas-gas and gas-water two-medium flows by solving the γ-based model. The spatial discretization is carefully designed to possess the following features: discrete conservation in terms of the total mass, total momentum and total energy; high-order accuracy and consistency for smooth flows; free of oscillations at an isolated material interface. In order to handle potential discontinuities arising in the simulation, a nonlinear limiter based on the weighted essentially non-oscillatory (WENO) strategy is employed to suppress numerical oscillations and to preserve high order of accuracy in regions of smooth flows. The WENO reconstruction is imposed on suitably selected quantities, rather than the conserved ones. In case for discontinuities with large pressure ratio, low density and dramatic change of material property where unphysical variables may be encountered, a posteriori solution correction on the subcell level is locally adopted to enhance the robustness. A series of typical test cases for both one- and two-dimensional problems are provided to demonstrate the performance of the proposed method.

Interactive Polymer Gels as Biomimetic Sensors for Carbohydrate Interactions and Capture–Release Devices for Pathogens

AbstractAdhesive processes mediated by carbohydrate‐decorated interfaces play a crucial role in many biological processes such as cell development or pathogen invasion. The involved carbohydrate scaffolds are soft and present multiple subsites forming complex and dynamic bonds to carbohydrate binding proteins. New tools and data are needed to understand how ligand presentation and mechanical properties drive these binding processes. This article highlights recent developments in the area of adhesion assays with a focus on soft biomimetic carbohydrate scaffolds as probes of adhesion forces. Key findings state that carbohydrate functionalized polymer networks largely show additive multivalency (statistical effects) and that the overall interaction forces are strongly affected by the stiffness of the network. These results indicate that phase transitions of carbohydrate bearing polymer gels may enable tunable affinity toward carbohydrate binding proteins. As an example, polymer networks undergoing large changes in mechanical rigidity, density, and spacing of carbohydrate ligands upon temperature stimulus are shown to bind or release carbohydrate binding bacteria such as Escherichia coli. The presented adhesion assays and the developed responsive systems can provide new insights into the mechanism through which carbohydrates mediate adhesion processes and establish new avenues toward scaffolds for the capture or release of cells or pathogens.

Improving breeding performance of Super FR with fuel shuffling in multi-axial layers

Super FR is the fast reactor version of SuperCritical Light Water Reactor (SCWR), which operates under supercritical condition of light water, so that designing the core with high coolant outlet temperature above the pseudo-critical point is possible. To raise the core outlet temperature of Super FR, axially heterogeneous core concept was proposed by the preceding study. It consisted of alternatively arranged two seed layers and two blanket layers (i.e., four-layers core). Furthermore, the core was axially divided to two sections and fuel shuffling was considered in each of the two axial sections independently to improve breeding performance. However, the study assumed the same fuel depletion history along the axial direction of the core, despite the large coolant density change. The core outlet temperature was only 387 C and the Compound System Doubling Time (CSDT) was about 98 years, which was not as short as desired. Hence, this study aims to reveal more comprehensive understanding of the concept of improving the performance of Super FR with fuel shuffling in multi-axial layers through design analyses. A five-layers core is considered, which consists of the lower blanket, lower seed, inner blanket, upper seed, and the upper blanket layers. Influences of the lower blanket/upper blanket discharge burnup on the core characteristics, such as the CSDT, void reactivity, and core outlet temperature have been studied with different coolant inlet temperatures for the first time. Different fuel depletion histories are considered for each of the axial layers with consideration of the axial coolant density change (which had not been considered in the preceding study). The present results show that it is preferable to keep the lower blanket discharge burnup relatively low, compared with that of the upper blanket to improve breeding performance with respect to achieving short CSDT. However, it leads to slight reduction in the core outlet temperature. Based on the sensitivity analyses, a representative design is proposed, which achieves CSDT of 74 years and average core outlet temperature of 492 C, which show significant improvement from the preceding design.

Hidden scale invariance at high pressures in gold and five other face-centered-cubic metal crystals

Recent density functional theory simulations showed that metals have a hitherto overlooked symmetry termed "hidden scale invariance" [Hummel et al., Phys. Rev. B 92, 174116 (2015)PRBMDO1098-012110.1103/PhysRevB.92.174116]. This scaling property implies the existence of lines in the thermodynamic phase diagram, so-called isomorphs, along which structure and dynamics are invariant to a good approximation when given in properly reduced units. This means that the phase diagram becomes effectively one-dimensional with regard to several physical properties. This paper investigates consequences and implications of the isomorph theory in six metallic crystals: Au, Ni, Cu, Pd, Ag, and Pt. The data are obtained from molecular dynamics simulations employing many-body effective medium theory (EMT) to model the atomic interactions realistically. We test the predictions from isomorph theory for structure and dynamics by means of the radial distribution and the velocity autocorrelation functions, as well as the prediction of instantaneous equilibration after a jump between two isomorphic state points. Many properties of crystals tend to be dominated by defects, and many of the properties associated with these defects are expected to be isomorph invariant as well. This is investigated in this paper for the case of vacancy diffusion. In regard to the perfect crystal properties, we find the predicted invariance of structure and also, though less perfectly, of dynamics. We show results on the variation of the density-scaling exponent γ, which can be related to the Grüneisen parameter, for all six metals. We consider large density changes up to a factor of two, corresponding to very high pressures. Unlike systems modeled using the Lennard-Jones potential where the density-scaling exponent γ is almost constant, this quantity varies substantially when using the EMT potential and is also strongly material dependent.

Vegetation Indices Do Not Capture Forest Cover Variation in Upland Siberian Larch Forests

Boreal forests are changing in response to climate, with potentially important feedbacks to regional and global climate through altered carbon cycle and albedo dynamics. These feedback processes will be affected by vegetation changes, and feedback strengths will largely rely on the spatial extent and timing of vegetation change. Satellite remote sensing is widely used to monitor vegetation dynamics, and vegetation indices (VIs) are frequently used to characterize spatial and temporal trends in vegetation productivity. In this study we combine field observations of larch forest cover across a 25 km2 upland landscape in northeastern Siberia with high-resolution satellite observations to determine how the Normalized Difference Vegetation Index (NDVI) and the Enhanced Vegetation Index (EVI) are related to forest cover. Across 46 forest stands ranging from 0% to 90% larch canopy cover, we find either no change, or declines in NDVI and EVI derived from PlanetScope CubeSat and Landsat data with increasing forest cover. In conjunction with field observations of NDVI, these results indicate that understory vegetation likely exerts a strong influence on vegetation indices in these ecosystems. This suggests that positive decadal trends in NDVI in Siberian larch forests may correspond primarily to increases in understory productivity, or even to declines in forest cover. Consequently, positive NDVI trends may be associated with declines in terrestrial carbon storage and increases in albedo, rather than increases in carbon storage and decreases in albedo that are commonly assumed. Moreover, it is also likely that important ecological changes such as large changes in forest density or variable forest regrowth after fire are not captured by long-term NDVI trends.

Finite element model of load adaptive remodelling induced by orthodontic forces

Many hypotheses have been formulated to explain orthodontic tooth movement. However, none of them can satisfactorily explain how small static orthodontic forces can induce bone remodelling. Our hypothesis assumes that small orthodontic forces do not lead to bone remodelling response directly, but rather indirectly by offsetting the tooth, leading to changes in bone loading during chewing that far exceed the changes caused by the orthodontic force alone. We developed a finite element model of a tooth with the periodontal ligament and the surrounding bone, and calculated the changes in strain energy density caused by the chewing force alone, the orthodontic force alone, and the combined action of the chewing and orthodontic forces. The results (average strain energy density 0.0005–0.01 kPa) demonstrate that the orthodontic loading alone does not produce strain energy density values in a range that is expected to induce remodelling (0.016–1.6 kPa). However, when the chewing and orthodontic forces are applied together, the highest values for the average strain energy density (0.02–0.99 kPa) as well as large changes in the bone tissue strain energy density (31.19–166.65%) are obtained. We conclude that the proposed hypothesis can indeed explain the observed bone remodelling that agrees with Wolff's law.

Eolianite Grain Size Distributions as a Proxy for Large Changes in Planetary Atmospheric Density

AbstractAtmospheres are dynamic over geologic timescales, making large changes in planetary air density possible. For the Earth, geological proxies suggest that air density in the Neoarchean was similar to or lower than today. This air density variation possibly affected eolian dune grain sizes by controlling the trajectories of grains though the air. Balancing the fall velocity and threshold friction velocity, a metric separating saltation and suspension transport, suggests that a lower air density could increase the mean grain size of dunes because decreased air drag extends the size range of grains in modified saltation and incipient suspension regimes. Consequently, the dune‐forming sand left behind in pure saltation, the dominant dune‐forming transport mode, could have coarser grains. We analyzed size distributions of two eolianites from 2.64 and 1.5 Ga (billion years ago) for deviations from modern sand dunes emplaced at sea level, which globally exhibit similar mean grain sizes. Both aeolianites have mean grain sizes within one standard deviation of the modern mean and are not statistically separable at 95% confidence. Overall, this suggests that while air density is important in eolian physics, a factor of 2 to 4 change in density is insufficient to produce an unambiguous grain size signal. This suggests that while eolian dune grain sizes have not significantly changed over the range of Earth's atmospheric conditions, they could be useful when investigating the order of magnitude changes thought to have occurred on Mars.

Numerical construction of the density-potential mapping

We demonstrate how a recently developed method Nielsen et al. [Nielsen et al., EPL 101, 33001 (2013)] allows for a comprehensive investigation of time-dependent density functionals in general, and of the exact time-dependent exchange-correlation potential in particular, by presenting the first exact results for two- and three-dimensional multi-electron systems. This method is an explicit realization of the Runge–Gross correspondence, which maps time-dependent densities to their respective potentials, and allows for the exact construction of desired density functionals. We present in detail the numerical requirements that makes this method efficient, stable and precise even for large and rapid density changes, irrespective of the initial state and two-body interaction. This includes among others the proper treatment of low density regions, a subtle interplay between numerical time-propagation and zero boundary conditions, the choice of time-stepping strategy, and an error damping mechanism based on both the density and current density residuals. These considerations are also relevant for computing time-independent density-functionals and lead to a more precise implementation of quantum mechanics in general, which is mainly relevant for cases in which there is notable contact with a boundary or when the low density regions matter.

The EXP pair-potential system. II. Fluid phase isomorphs.

This paper continues the investigation of the exponentially repulsive EXP pair-potential system of Paper I [A. K. Bacher et al., J. Chem. Phys. 149, 114501 (2018)] with a focus on isomorphs in the low-temperature gas and liquid phases. As expected from the EXP system's strong virial potential-energy correlations, the reduced-unit structure and dynamics are isomorph invariant to a good approximation. Three methods for generating isomorphs are compared: the small-step method that is exact in the limit of small density changes and two versions of the direct-isomorph-check method that allows for much larger density changes. Results from the latter two approximate methods are compared to those of the small-step method for each of the three isomorphs generated by 230 one percent density changes, covering one decade of density variation. Both approximate methods work well.

Magnetic Levitation To Characterize the Kinetics of Free-Radical Polymerization.

This work describes the development of magnetic levitation (MagLev) to characterize the kinetics of free-radical polymerization of water-insoluble, low-molecular-weight monomers that show a large change in density upon polymerization. Maglev measures density, and certain classes of monomers show a large change in density when monomers covalently join in polymer chains. MagLev characterized both the thermal polymerization of methacrylate-based monomers and the photopolymerization of methyl methacrylate and made it possible to determine the orders of reaction and the Arrhenius activation energy of polymerization. MagLev also made it possible to monitor polymerization in the presence of solids (aramid fibers, and carbon fibers, and glass fibers). MagLev offers a new analytical technique to materials and polymer scientists that complements other methods (even those based on density, such as dilatometry), and will be useful in investigating polymerizations, evaluating inhibition of polymerizations, and studying polymerization in the presence of included solid materials (e.g., for composite materials).

Flexible core design of Super FBR with multi-axial fuel shuffling

To utilize the merit of supercritical water cooling, the Super FBR core concept, which is compatible with both the high breeding and the high enthalpy rise needs to be developed. One possible solution to meet such requirements may be to compose an axially heterogeneous core with MOX and blanket layers, with consideration of the large density change and specific heat of supercritical water at vicinity of the pseudocritical point. A new design concept of Super FBR has been proposed with “with multi-axial fuel shuffling”, which has flexibility in designing fuel shuffling schemes in the lower part and upper part of the core independently. Fully coupled neutronics and thermal-hydraulics core calculations were carried out to investigate impact of designing independent number of fuel batches and shuffling patterns in the upper and the lower parts of the core. Promising results were obtained, showing possibility of improving the core breeding performance with respect to the compound system doubling time (CSDT) by reducing the reactor doubling time (RDT) with designing of the independent fuel shuffling. Moreover, reduction in the ex-core factor (EF) was shown to be possible with such independent fuel shuffling. The combined effects of reductions in RDT and EF showed significant reduction in CSDT. It is the first design concept of Super FBR with coolant enthalpy rise, which covers from the liquid like state (below the pseudo-critical point) to the gas-like state (above the pseudo-critical point) of supercritical water. Further design investigations may be necessary to reduce CSDT and increase the average core outlet temperature.

Fuel Cells Operating at 200 to 500 Celsius: Lessons Learned from the ARPA-E REBELS Program

In 2014, the Advanced Research Projects Agency-Energy (ARPA-E) launched the Reliable Electricity Based on ELectrochemical Systems (REBELS) program with the goal of pursuing alternate fuel cell materials and operating conditions that could enable system cost reductions and new electrochemical functionality. This presentation will briefly revisit the original REBELS vision by elaborating the potential benefits of operation in an intermediate temperature range of 200-500 C. Trends in the U.S. electrical grid will be discussed, which reveal the benefits of enhanced fuel cell functionality such as in-situ charge storage and gas-to-liquids (GTL) capabilities. The most significant technical accomplishments from REBELS project teams will be highlighted, including several examples in which the program objective of a current density of 200 mA/cm2 at 0.78 V and 500 C on methane fuel was achieved. Furthermore, teams were able to demonstrate thousands of hours of operation on internally-reformed methane fuel at 500 C with no evidence of coke formation. Fuel cells with charge storage functionality in or near the anode showed a more rapid response to large changes in current density and a lower voltage decrease with high fuel utilization. The needs for further techno-economic assessment to evaluate this concept will be highlighted. Progress towards fuel cells that can also convert methane to liquid fuels will be summarized. Finally, overall lessons learned from the REBELS program will be discussed, such as the ability of ceramic proton conductors to deliver high current density at 500 C on non-hydrogen fuels with minimal degradation. The need for future work in this field will be stressed, especially a continued examination of whether stacks in this temperature range possess the appropriate combination of performance and cost to accelerate the commercialization of high efficiency fuel cells worldwide.

Similarity law for Widom lines and coexistence lines.

The coexistence line of a fluid separates liquid and gaseous states at subcritical pressures, ending at the critical point. Only recently, it became clear that the supercritical state space can likewise be divided into regions with liquidlike and gaslike properties, separated by an extension to the coexistence line. This crossover line is commonly referred to as the Widom line, and is characterized by large changes in density or enthalpy, manifesting as maxima in the thermodynamic response functions. Thus, a reliable representation of the coexistence line and the Widom line is important for sub- and supercritical applications that depend on an accurate prediction of fluid properties. While it is known for subcritical pressures that nondimensionalization with the respective species critical pressures p_{cr} and temperatures T_{cr} only collapses coexistence line data for simple fluids, this approach is used for Widom lines of all fluids. However, we show here that the Widom line does not adhere to the corresponding states principle, but instead to the extended corresponding states principle. We resolve this problem in two steps. First, we propose a Widom line functional based on the Clapeyron equation and derive an analytical, species specific expression for the only parameter from the Soave-Redlich-Kwong equation of state. This parameter is a function of the acentric factor ω and compares well with experimental data. Second, we introduce the scaled reduced pressure p_{r}^{*} to replace the previously used reduced pressure p_{r}=p/p_{cr}. We show that p_{r}^{*} is a function of the acentric factor only and can thus be readily determined from fluid property tables. It collapses both subcritical coexistence line and supercritical Widom line data over a wide range of species with acentric factors ranging from -0.38 (helium) to 0.34 (water), including alkanes up to n-hexane. By using p_{r}^{*}, the extended corresponding states principle can be applied within corresponding states principle formalism. Furthermore, p_{r}^{*} provides a theoretical foundation to compare Widom lines of different fluids.