Seven Questions About Supercritical Fluids
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Lecture Notes: BCS Theory of Superconductivity
Lecture Notes: BCS theory of superconductivity Prof. Rafael M. Fernandes Here we will discuss a new ground state of the interacting electron gas: the superconducting state. In this macroscopic quantum state, the electrons form coherent bound states called Cooper pairs, which dramatically change the macroscopic properties of the system, giving rise to perfect conductivity and perfect diamagnetism. We will mostly focus on conventional superconductors, where the Cooper pairs originate from a small attractive electron-electron interaction mediated by phonons. However, in the so- called unconventional superconductors - a topic of intense research in current solid state physics - the pairing can originate even from purely repulsive interactions. 1 Phenomenology Superconductivity was discovered by Kamerlingh-Onnes in 1911, when he was studying the transport properties of Hg (mercury) at low temperatures. He found that below the liquifying temperature of helium, at around 4:2 K, the resistivity of Hg would suddenly drop to zero. Although at the time there was not a well established model for the low-temperature behavior of transport in metals, the result was quite surprising, as the expectations were that the resistivity would either go to zero or diverge at T = 0, but not vanish at a finite temperature. In a metal the resistivity at low temperatures has a constant contribution from impurity scattering, a T 2 contribution from electron-electron scattering, and a T 5 contribution from phonon scattering. Thus, the vanishing of the resistivity at low temperatures is a clear indication of a new ground state. Another key property of the superconductor was discovered in 1933 by Meissner. -
Supercritical Fluid Extraction of Positron-Emitting Radioisotopes from Solid Target Matrices
XA0101188 11. United States of America Supercritical Fluid Extraction of Positron-Emitting Radioisotopes From Solid Target Matrices D. Schlyer, Brookhaven National Laboratory, Chemistry Department, Upton, Bldg. 901, New York 11973-5000, USA Project Description Supercritical fluids are attractive as media for both chemical reactions, as well as process extraction since their physical properties can be manipulated by small changes in pressure and temperature near the critical point of the fluid. What is a supercritical fluid? Above a certain temperature, a vapor can no longer be liquefied regardless of pressure critical temperature - Tc supercritical fluid r«gi on solid a u & temperature Fig. 1. Phase diagram depicting regions of solid, liquid, gas and supercritical fluid behavior. The critical point is defined by a critical pressure (Pc) and critical temperature (Tc) for a particular substance. Such changes can result in drastic effects on density-dependent properties such as solubility, refractive index, dielectric constant, viscosity and diffusivity of the fluid[l,2,3]. This suggests that pressure tuning of a pure supercritical fluid may be a useful means to manipulate chemical reactions on the basis of a thermodynamic solvent effect. It also means that the solvation properties of the fluid can be precisely controlled to enable selective component extraction from a matrix. In recent years there has been a growing interest in applying supercritical fluid extraction to the selective removal of trace metals from solid samples [4-10]. Much of the work has been done on simple systems comprised of inert matrices such as silica or cellulose. Recently, this process as been expanded to environmental samples as well [11,12]. -
Equation of State for the Lennard-Jones Fluid
Equation of State for the Lennard-Jones Fluid Monika Thol1*, Gabor Rutkai2, Andreas Köster2, Rolf Lustig3, Roland Span1, Jadran Vrabec2 1Lehrstuhl für Thermodynamik, Ruhr-Universität Bochum, Universitätsstraße 150, 44801 Bochum, Germany 2Lehrstuhl für Thermodynamik und Energietechnik, Universität Paderborn, Warburger Straße 100, 33098 Paderborn, Germany 3Department of Chemical and Biomedical Engineering, Cleveland State University, Cleveland, Ohio 44115, USA Abstract An empirical equation of state correlation is proposed for the Lennard-Jones model fluid. The equation in terms of the Helmholtz energy is based on a large molecular simulation data set and thermal virial coefficients. The underlying data set consists of directly simulated residual Helmholtz energy derivatives with respect to temperature and density in the canonical ensemble. Using these data introduces a new methodology for developing equations of state from molecular simulation data. The correlation is valid for temperatures 0.5 < T/Tc < 7 and pressures up to p/pc = 500. Extensive comparisons to simulation data from the literature are made. The accuracy and extrapolation behavior is better than for existing equations of state. Key words: equation of state, Helmholtz energy, Lennard-Jones model fluid, molecular simulation, thermodynamic properties _____________ *E-mail: [email protected] Content Content ....................................................................................................................................... 2 List of Tables ............................................................................................................................. -
Equation of State and Phase Transitions in the Nuclear
National Academy of Sciences of Ukraine Bogolyubov Institute for Theoretical Physics Has the rights of a manuscript Bugaev Kyrill Alekseevich UDC: 532.51; 533.77; 539.125/126; 544.586.6 Equation of State and Phase Transitions in the Nuclear and Hadronic Systems Speciality 01.04.02 - theoretical physics DISSERTATION to receive a scientific degree of the Doctor of Science in physics and mathematics arXiv:1012.3400v1 [nucl-th] 15 Dec 2010 Kiev - 2009 2 Abstract An investigation of strongly interacting matter equation of state remains one of the major tasks of modern high energy nuclear physics for almost a quarter of century. The present work is my doctor of science thesis which contains my contribution (42 works) to this field made between 1993 and 2008. Inhere I mainly discuss the common physical and mathematical features of several exactly solvable statistical models which describe the nuclear liquid-gas phase transition and the deconfinement phase transition. Luckily, in some cases it was possible to rigorously extend the solutions found in thermodynamic limit to finite volumes and to formulate the finite volume analogs of phases directly from the grand canonical partition. It turns out that finite volume (surface) of a system generates also the temporal constraints, i.e. the finite formation/decay time of possible states in this finite system. Among other results I would like to mention the calculation of upper and lower bounds for the surface entropy of physical clusters within the Hills and Dales model; evaluation of the second virial coefficient which accounts for the Lorentz contraction of the hard core repulsing potential between hadrons; inclusion of large width of heavy quark-gluon bags into statistical description. -
1 Fluid Flow Outline Fundamentals of Rheology
Fluid Flow Outline • Fundamentals and applications of rheology • Shear stress and shear rate • Viscosity and types of viscometers • Rheological classification of fluids • Apparent viscosity • Effect of temperature on viscosity • Reynolds number and types of flow • Flow in a pipe • Volumetric and mass flow rate • Friction factor (in straight pipe), friction coefficient (for fittings, expansion, contraction), pressure drop, energy loss • Pumping requirements (overcoming friction, potential energy, kinetic energy, pressure energy differences) 2 Fundamentals of Rheology • Rheology is the science of deformation and flow – The forces involved could be tensile, compressive, shear or bulk (uniform external pressure) • Food rheology is the material science of food – This can involve fluid or semi-solid foods • A rheometer is used to determine rheological properties (how a material flows under different conditions) – Viscometers are a sub-set of rheometers 3 1 Applications of Rheology • Process engineering calculations – Pumping requirements, extrusion, mixing, heat transfer, homogenization, spray coating • Determination of ingredient functionality – Consistency, stickiness etc. • Quality control of ingredients or final product – By measurement of viscosity, compressive strength etc. • Determination of shelf life – By determining changes in texture • Correlations to sensory tests – Mouthfeel 4 Stress and Strain • Stress: Force per unit area (Units: N/m2 or Pa) • Strain: (Change in dimension)/(Original dimension) (Units: None) • Strain rate: Rate -
Ionic Liquid and Supercritical Fluid Hyphenated Techniques for Dissolution and Separation of Lanthanides, Actinides, and Fission Products
Project No. 09-805 Ionic Liquid and Supercritical Fluid Hyphenated Techniques for Dissolution and Separation of Lanthanides, Actinides, and Fission Products ItIntegrat tdUied Universit itPy Programs Dr. Chien Wai University of Idaho In collaboration with: Idaho National Laboratory Jack Law, Technical POC James Bresee, Federal POC 1 Ionic Liquid and Supercritical Fluid Hyphenated Techniques For Dissolution and Separation of Lanthanides and Actinides DOE-NEUP Project (TO 00058) Final Technical Report Principal Investigator: Chien M. Wai Department of Chemistry, University of Idaho, Moscow, Idaho 83844 Date: December 1, 2012 2 Table of Contents Project Summary 3 Publications Derived from the Project 5 Chapter I. Introduction 6 Chapter II. Uranium Dioxide in Ionic Liquid with a TP-HNO3 Complex – Dissolution and Coordination Environment 9 1. Dissolution of UO2 in Ionic Liquid with TBP(HNO3)1.8(H2O)0.6 2. Raman Spectra of Dissolved Uranyl Species in IL 13 3. Transferring Uranium from IL Phase to sc-CO2 15 Chapter III. Kinetic Study on Dissolution of Uranium Dioxide and Neodymium Sesquioxide in Ionic Liquid 19 1. Rate of Dissolution of UO2 and Nd2O3 in RTIL 19 2. Temperature Effect on Dissolution of UO2 and Nd2O3 24 3. Viscosity Effect on Dissolution of UO2 in IL with TBP(HNO3)1.8(H2O)0.6 Chapter IV. Separation of UO2(NO3)2(TBP)2 and Nd(NO3)3(TBP)3 in Ionic Liquid Using Diglycolamide and Supercritical CO2 Extraction 30 1. Complexation of Uranyl with Diglycolamide TBDGA in Ionic Liquid 31 2. Complexation of Neodymium(III) with TBDGA in Ionic Liquid 35 3. Solubility and Distribution Ratio of UO2(NO3)2(TBP)2 and Nd(NO3)3(TBP)3 in Supercritical CO2 Phase 38 4. -
Chapter 3 Equations of State
Chapter 3 Equations of State The simplest way to derive the Helmholtz function of a fluid is to directly integrate the equation of state with respect to volume (Sadus, 1992a, 1994). An equation of state can be applied to either vapour-liquid or supercritical phenomena without any conceptual difficulties. Therefore, in addition to liquid-liquid and vapour -liquid properties, it is also possible to determine transitions between these phenomena from the same inputs. All of the physical properties of the fluid except ideal gas are also simultaneously calculated. Many equations of state have been proposed in the literature with either an empirical, semi- empirical or theoretical basis. Comprehensive reviews can be found in the works of Martin (1979), Gubbins (1983), Anderko (1990), Sandler (1994), Economou and Donohue (1996), Wei and Sadus (2000) and Sengers et al. (2000). The van der Waals equation of state (1873) was the first equation to predict vapour-liquid coexistence. Later, the Redlich-Kwong equation of state (Redlich and Kwong, 1949) improved the accuracy of the van der Waals equation by proposing a temperature dependence for the attractive term. Soave (1972) and Peng and Robinson (1976) proposed additional modifications of the Redlich-Kwong equation to more accurately predict the vapour pressure, liquid density, and equilibria ratios. Guggenheim (1965) and Carnahan and Starling (1969) modified the repulsive term of van der Waals equation of state and obtained more accurate expressions for hard sphere systems. Christoforakos and Franck (1986) modified both the attractive and repulsive terms of van der Waals equation of state. Boublik (1981) extended the Carnahan-Starling hard sphere term to obtain an accurate equation for hard convex geometries. -
Two-Way Fluid–Solid Interaction Analysis for a Horizontal Axis Marine Current Turbine with LES
water Article Two-Way Fluid–Solid Interaction Analysis for a Horizontal Axis Marine Current Turbine with LES Jintong Gu 1,2, Fulin Cai 1,*, Norbert Müller 2, Yuquan Zhang 3 and Huixiang Chen 2,4 1 College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China; [email protected] 2 Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA; [email protected] (N.M.); [email protected] (H.C.) 3 College of Energy and Electrical Engineering, Hohai University, Nanjing 210098, China; [email protected] 4 College of Agricultural Engineering, Hohai University, Nanjing 210098, China * Correspondence: fl[email protected]; Tel.: +86-139-5195-1792 Received: 2 September 2019; Accepted: 23 December 2019; Published: 27 December 2019 Abstract: Operating in the harsh marine environment, fluctuating loads due to the surrounding turbulence are important for fatigue analysis of marine current turbines (MCTs). The large eddy simulation (LES) method was implemented to analyze the two-way fluid–solid interaction (FSI) for an MCT. The objective was to afford insights into the hydrodynamics near the rotor and in the wake, the deformation of rotor blades, and the interaction between the solid and fluid field. The numerical fluid simulation results showed good agreement with the experimental data and the influence of the support on the power coefficient and blade vibration. The impact of the blade displacement on the MCT performance was quantitatively analyzed. Besides the root, the highest stress was located near the middle of the blade. The findings can inform the design of MCTs for enhancing robustness and survivability. -
Liquid-Liquid Transition in Supercooled Aqueous Solution Involving a Low-Temperature Phase Similar to Low-Density Amorphous Water
Liquid-liquid transition in supercooled aqueous solution involving a low-temperature phase similar to low-density amorphous water * * # # Sander Woutersen , Michiel Hilbers , Zuofeng Zhao and C. Austen Angell * Van 't Hoff Institute for Molecular Sciences, University of Amsterdam, Science Park 904,1098 XH Amsterdam, The Netherlands # School of Molecular Sciences, Arizona State University, Tempe, AZ, 85287-1604, USA The striking anomalies in physical properties of supercooled water that were discovered in the 1960-70s, remain incompletely understood and so provide both a source of controversy amongst theoreticians1-5, and a stimulus to experimentalists and simulators to find new ways of penetrating the "crystallization curtain" that effectively shields the problem from solution6,7. Recently a new door on the problem was opened by showing that, in ideal solutions, made using ionic liquid solutes, water anomalies are not destroyed as earlier found for common salt and most molecular solutes, but instead are enhanced to the point of precipitating an apparently first order liquid-liquid transition (LLT)8. The evidence was a spike in apparent heat capacity during cooling that could be fully reversed during reheating before any sign of ice crystallization appeared. Here, we use decoupled-oscillator infrared spectroscopy to define the structural character of this phenomenon using similar down and upscan rates as in the calorimetric study. Thin-film samples also permit slow scans (1 Kmin-1) in which the transition has a width of less than 1 K, and is fully reversible. The OH spectrum changes discontinuously at the phase- transition temperature, indicating a discrete change in hydrogen-bond structure. -
Application of Supercritical Fluids Review Yoshiaki Fukushima
1 Application of Supercritical Fluids Review Yoshiaki Fukushima Abstract Many advantages of supercritical fluids come Supercritical water is expected to be useful in from their interesting or unusual properties which waste treatment. Although they show high liquid solvents and gas carriers do not possess. solubility solutes and molecular catalyses, solvent Such properties and possible applications of molecules under supercritical conditions gently supercritical fluids are reviewed. As these fluids solvate solute molecules and have little influence never condense at above their critical on the activities of the solutes and catalysts. This temperatures, supercritical drying is useful to property would be attributed to the local density prepare dry-gel. The solubility and other fluctuations around each molecule due to high important parameters as a solvent can be adjusted molecular mobility. The fluctuations in the continuously. Supercritical fluids show supercritical fluids would produce heterogeneity advantages as solvents for extraction, coating or that would provide novel chemical reactions with chemical reactions thanks to these properties. molecular catalyses, heterogenous solid catalyses, Supercritical water shows a high organic matter enzymes or solid adsorbents. solubility and a strong hydrolyzing ability. Supercritical fluid, Supercritical water, Solubility, Solvation, Waste treatment, Keywords Coating, Organic reaction applications development reached the initial peak 1. Introduction during the period from the second half of the 1960s There has been rising concern in recent years over to the 1970s followed by the secondary peak about supercritical fluids for organic waste treatment and 15 years later. The initial peak was for the other applications. The discovery of the presence of separation and extraction technique as represented 1) critical point dates back to 1822. -
Navier-Stokes Equations Some Background
Navier-Stokes Equations Some background: Claude-Louis Navier was a French engineer and physicist who specialized in mechanics Navier formulated the general theory of elasticity in a mathematically usable form (1821), making it available to the field of construction with sufficient accuracy for the first time. In 1819 he succeeded in determining the zero line of mechanical stress, finally correcting Galileo Galilei's incorrect results, and in 1826 he established the elastic modulus as a property of materials independent of the second moment of area. Navier is therefore often considered to be the founder of modern structural analysis. His major contribution however remains the Navier–Stokes equations (1822), central to fluid mechanics. His name is one of the 72 names inscribed on the Eiffel Tower Sir George Gabriel Stokes was an Irish physicist and mathematician. Born in Ireland, Stokes spent all of his career at the University of Cambridge, where he served as Lucasian Professor of Mathematics from 1849 until his death in 1903. In physics, Stokes made seminal contributions to fluid dynamics (including the Navier–Stokes equations) and to physical optics. In mathematics he formulated the first version of what is now known as Stokes's theorem and contributed to the theory of asymptotic expansions. He served as secretary, then president, of the Royal Society of London The stokes, a unit of kinematic viscosity, is named after him. Navier Stokes Equation: the simplest form, where is the fluid velocity vector, is the fluid pressure, and is the fluid density, is the kinematic viscosity, and ∇2 is the Laplacian operator. -
Using Supercritical Fluid Technology As a Green Alternative During the Preparation of Drug Delivery Systems
pharmaceutics Review Using Supercritical Fluid Technology as a Green Alternative During the Preparation of Drug Delivery Systems Paroma Chakravarty 1, Amin Famili 2, Karthik Nagapudi 1 and Mohammad A. Al-Sayah 2,* 1 Small Molecule Pharmaceutics, Genentech, Inc. So. San Francisco, CA 94080, USA; [email protected] (P.C.); [email protected] (K.N.) 2 Small Molecule Analytical Chemistry, Genentech, Inc. So. San Francisco, CA 94080, USA; [email protected] * Correspondence: [email protected]; Tel.: +650-467-3810 Received: 3 October 2019; Accepted: 18 November 2019; Published: 25 November 2019 Abstract: Micro- and nano-carrier formulations have been developed as drug delivery systems for active pharmaceutical ingredients (APIs) that suffer from poor physico-chemical, pharmacokinetic, and pharmacodynamic properties. Encapsulating the APIs in such systems can help improve their stability by protecting them from harsh conditions such as light, oxygen, temperature, pH, enzymes, and others. Consequently, the API’s dissolution rate and bioavailability are tremendously improved. Conventional techniques used in the production of these drug carrier formulations have several drawbacks, including thermal and chemical stability of the APIs, excessive use of organic solvents, high residual solvent levels, difficult particle size control and distributions, drug loading-related challenges, and time and energy consumption. This review illustrates how supercritical fluid (SCF) technologies can be superior in controlling the morphology of API particles and in the production of drug carriers due to SCF’s non-toxic, inert, economical, and environmentally friendly properties. The SCF’s advantages, benefits, and various preparation methods are discussed. Drug carrier formulations discussed in this review include microparticles, nanoparticles, polymeric membranes, aerogels, microporous foams, solid lipid nanoparticles, and liposomes.