Artykuły w czasopismach: „Gas-liquid equilibrium”

1

Stringari, S., M. Barranco, A. Polls, P. J. Nacher i F. Laloë. "Spin-polarized 3He : liquid gas equilibrium". Journal de Physique 48, nr 8 (1987): 1337–50. http://dx.doi.org/10.1051/jphys:019870048080133700.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

2

YAMAMOTO, Takayuki, Norizumi MOTOOKA, Osamu MORI i Yoshihiro KISHINO. "Gas-Liquid Equilibrium Thruster of IKAROS". TRANSACTIONS OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES, AEROSPACE TECHNOLOGY JAPAN 12, ists29 (2014): Tf_13—Tf_18. http://dx.doi.org/10.2322/tastj.12.tf_13.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

3

Librovich, Bronislav V., Andrzej F. Nowakowski, Issa Chaer i Savvas Tassou. "Non-equilibrium gas-liquid transition model". PAMM 7, nr 1 (grudzień 2007): 2100029–30. http://dx.doi.org/10.1002/pamm.200700233.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

4

Xu, Hui. "The Research on SO₂ Desorption Equilibrium Mechanism of Sodium Alkali Desulfurization Regeneration Solution". Advanced Materials Research 898 (luty 2014): 461–64. http://dx.doi.org/10.4028/www.scientific.net/amr.898.461.

Pełny tekst źródła

Streszczenie:

Sodium alkali flue gas desulfurization (FGD) is one of the most promising renewable FGD technologies, and the SO2 gases desorption in desulfurization regeneration solution is very important to directly affect its application. Based on the gas-liquid equilibrium relationships, this paper researched the equilibrium mechanism of SO2 desorption in the sodium alkali desulfurization regeneration solution. The results showed that SO2 desorption process is a mass transfer process that SO2 transfer from liquid phase to gas phase essentially, and SO2 desorption limit capacity depend mainly on the gas-liquid equilibrium relationship. Moreover, the formula of SO2 desorption limit capacity at equilibrium condition was deduced through analyzing desorption equilibrium relationships, and the main factors are also discussed.

Style APA, Harvard, Vancouver, ISO itp.

5

Percus, Jerome K. "Classical liquid-gas interface in thermal equilibrium". Journal of Statistical Physics 78, nr 3-4 (luty 1995): 1165–69. http://dx.doi.org/10.1007/bf02183709.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

6

Clarke, Colin W., i David N. Glew. "Aqueous nonelectrolyte solutions. Part XV. The deuterium sulfide - deuterium oxide system and the deuterium sulfide D-hydrate". Canadian Journal of Chemistry 76, nr 8 (1.08.1998): 1119–29. http://dx.doi.org/10.1139/v98-133.

Pełny tekst źródła

Streszczenie:

The univariant (l1l2g) saturation vapor pressure of liquid deuterium oxide (phase l1) with liquid deuterium sulfide (phase l2) in equilibrium with a gas phase (g) has been measured in a stirred titanium reaction vessel at 19 temperatures from 33.003 to 18.905°C and at total pressures from 2.4500 to 1.7428 MPa. The univariant (hl1g) saturation vapor pressure of deuterium sulfide D-hydrate (phase h) in equilibrium with liquid deuterium oxide and a gas phase has been measured at 58 temperatures from 30.666 to 2.798°C and at pressures from 2.2959 to 0.11629 MPa. The maximum temperature for deuterium sulfide D-hydrate with a gas phase, the invariant quadruple point Q(hl1l2g), has been determined from the cut of the (hl1g) and the (l1l2g) curves at temperature 30.770°C with standard error 0.0043°C and at pressure 2.3263 MPa with standard error 0.00018 MPa. The univariant (s1l1g) equilibrium of D-ice (phase s1) with liquid deuterium oxide and a gas phase containing deuterium sulfide has been measured at 11 temperatures from 3.8061 to 3.4540°C and at pressures between 0.00242 and 0.10542 MPa. The lowest temperature for stability of deuterium sulfide D-hydrate with liquid deuterium oxide, the invariant quadruple point Q(hs1l1g), has been determined directly at 3.3917°C with standard error 0.0009°C and at pressure 0.12364 MPa with standard error 0.000011 MPa. This quadruple point Q(hs1l1g) has also been defined by the cut of the (hl1g) and the (s1l1g) curves at temperature 3.3912°C with standard error 0.0006°C and at pressure 0.12363 MPa with standard error 0.000002 MPa. The deuterium sulfide - deuterium oxide gas mixture, represented by a Redlich-Kwong equation of state, has been used to evaluate the fugacities and compositions of the gaseous and liquid deuterium oxide phases for all equilibria. Raoult's law using fugacities has been used to evaluate the saturation mole fraction of deuterium oxide in liquid deuterium sulfide and the Henry's law constant for deuterium oxide solubility in liquid deuterium sulfide between 33.003 and 18.905°C. Data for the (l1l2g) and (s1l1g) equilibria have been accurately represented by simple two-parameter equations. Data for the (hl1g) equilibrium have required a model with seven significant parameters for proper representation betweem 30.666 and 2.798°C.Key words: deuterium sulfide - deuterium oxide system, clathrate D-hydrate of deuterium sulfide, deuterium sulfide D-hydrate stability, freezing of deuterium oxide - deuterium sulfide, phase equilibria of deuterium sulfide - deuterium oxide.

Style APA, Harvard, Vancouver, ISO itp.

7

Chen, Panpan, Guoen Li, Hongfei Guo i Ji Lin Cao. "Phase Equilibrium Study on the Quaternary System H₂O-Na₂SO₄-MgSO₄-C₃H₈ at 0°C and Pressure". Advanced Materials Research 550-553 (lipiec 2012): 2690–94. http://dx.doi.org/10.4028/www.scientific.net/amr.550-553.2690.

Pełny tekst źródła

Streszczenie:

In order to develop a new technology for separating the bloedite by the method of gas hydrate formation, the phase equilibrium of the H2O-Na2SO4-MgSO4-C3H8 system and its subsystems was studied at 0°C and pressure.The equilibrium pressure and the composition of solid and liquid above system were investigated.It was found that equilibrium pressure of gas hydrate formation was increasing with the increase of the Na2SO4( or MgSO4) concentration. The addition of anionic surfactant SDS helped to lower the equilibrium pressure of gas hydrate formation. The mother liquor amount entrained in the gas hydrate after liquid separation by sinking was very high when surfactants was not added. But the equilibrium pressure of gas hydrate formation and the mother liquor amount entrained in gas hydrate were decreased when surfactant was added to the system.

Style APA, Harvard, Vancouver, ISO itp.

8

Mathis, Hélène. "A thermodynamically consistent model of a liquid-vapor fluid with a gas". ESAIM: Mathematical Modelling and Numerical Analysis 53, nr 1 (styczeń 2019): 63–84. http://dx.doi.org/10.1051/m2an/2018044.

Pełny tekst źródła

Streszczenie:

This work is devoted to the consistent modeling of a three-phase mixture of a gas, a liquid and its vapor. Since the gas and the vapor are miscible, the mixture is subjected to a non-symmetric constraint on the volume. Adopting the Gibbs formalism, the study of the extensive equilibrium entropy of the system allows to recover the Dalton’s law between the two gaseous phases. In addition, we distinguish whether phase transition occurs or not between the liquid and its vapor. The thermodynamical equilibria are described both in extensive and intensive variables. In the latter case, we focus on the geometrical properties of equilibrium entropy. The consistent characterization of the thermodynamics of the three-phase mixture is used to introduce two Homogeneous Equilibrium Models (HEM) depending on mass transfer is taking into account or not. Hyperbolicity is investigated while analyzing the entropy structure of the systems. Finally we propose two Homogeneous Relaxation Models (HRM) for the three-phase mixtures with and without phase transition. Supplementary equations on mass, volume and energy fractions are considered with appropriate source terms which model the relaxation towards the thermodynamical equilibrium, in agreement with entropy growth criterion.

Style APA, Harvard, Vancouver, ISO itp.

9

CHUJO, Toshihiro, Norizumi MOTOOKA, Takayuki YAMAMOTO i Osamu MORI. "Development of Bipropellant Gas-Liquid Equilibrium Propulsion System". TRANSACTIONS OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES, AEROSPACE TECHNOLOGY JAPAN 14 (2016): 9–14. http://dx.doi.org/10.2322/tastj.14.9.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

10

Mitrovic, J. "Upon equilibrium of gas bubble in infinite liquid". Chemical Engineering Science 55, nr 12 (czerwiec 2000): 2265–70. http://dx.doi.org/10.1016/s0009-2509(99)00475-3.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

11

Wang, Xiao-Ping, i Xinfu Chen. "Phase Transition Near a Liquid-Gas Coexistence Equilibrium". SIAM Journal on Applied Mathematics 61, nr 2 (styczeń 2000): 454–71. http://dx.doi.org/10.1137/s0036139999354285.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

12

SASAHIRA, Akira, i Fumio KAWAMURA. "Formation Rate and Gas-Liquid Equilibrium of RuO4". Journal of Nuclear Science and Technology 25, nr 5 (maj 1988): 472–78. http://dx.doi.org/10.1080/18811248.1988.9733615.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

13

Ryltsev, R. E., L. D. Son i K. Yu Shunyaev. "Liquid–Gas Equilibrium in Nanoparticle Network-Forming Systems". JETP Letters 108, nr 9 (listopad 2018): 627–32. http://dx.doi.org/10.1134/s0021364018210129.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

14

Ping, Wang, i Tang Shao-qiang. "Liquid-gas coexistence equilibrium in a relaxation model". Applied Mathematics and Mechanics 26, nr 6 (czerwiec 2005): 767–73. http://dx.doi.org/10.1007/bf02465428.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

15

Dahms, Rainer N., i Joseph C. Oefelein. "Non-equilibrium gas–liquid interface dynamics in high-pressure liquid injection systems". Proceedings of the Combustion Institute 35, nr 2 (2015): 1587–94. http://dx.doi.org/10.1016/j.proci.2014.05.155.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

16

Santos, J. E., i U. C. Täuber. "Non-equilibrium behavior at a liquid-gas critical point". European Physical Journal B 28, nr 4 (sierpień 2002): 423–40. http://dx.doi.org/10.1140/epjb/e2002-00246-2.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

17

LeMartelot, S., R. Saurel i O. Le Métayer. "Steady one-dimensional nozzle flow solutions of liquid–gas mixtures". Journal of Fluid Mechanics 737 (20.11.2013): 146–75. http://dx.doi.org/10.1017/jfm.2013.550.

Pełny tekst źródła

Streszczenie:

AbstractExact compressible one-dimensional nozzle flow solutions at steady state are determined in various limit situations of two-phase liquid–gas mixtures. First, the exact solution for a pure liquid nozzle flow is determined in the context of fluids governed by the compressible Euler equations and the ‘stiffened gas’ equation of state. It is an extension of the well-known ideal-gas steady nozzle flow solution. Various two-phase flow models are then addressed, all corresponding to limit situations of partial equilibrium among the phases. The first limit situation corresponds to the two-phase flow model of Kapila et al. (Phys. Fluids, vol. 13, 2001, pp. 3002–3024), where both phases evolve in mechanical equilibrium only. This model contains two entropies, two temperatures and non-conventional shock relations. The second one corresponds to a two-phase model where the phases evolve in both mechanical and thermal equilibrium. The last one corresponds to a model describing a liquid–vapour mixture in thermodynamic equilibrium. They all correspond to two-phase mixtures where the various relaxation effects are either stiff or absent. In all instances, the various flow regimes (subsonic, subsonic–supersonic, and supersonic with shock) are unambiguously determined, as well as various nozzle solution profiles.

Style APA, Harvard, Vancouver, ISO itp.

18

Woodcock, Leslie V. "Thermodynamics of Gas–Liquid Colloidal Equilibrium States: Hetero-Phase Fluctuations". Entropy 21, nr 12 (3.12.2019): 1189. http://dx.doi.org/10.3390/e21121189.

Pełny tekst źródła

Streszczenie:

Following on from two previous JETC (Joint European Thermodynamics Conference) presentations, we present a preliminary report of further advances towards the thermodynamic description of critical behavior and a supercritical gas-liquid coexistence with a supercritical fluid mesophase defined by percolation loci. The experimental data along supercritical constant temperature isotherms (T ≥ Tc) are consistent with the existence of a two-state mesophase, with constant change in pressure with density, rigidity, (dp/dρ) T, and linear thermodynamic state-functions of density. The supercritical mesophase is bounded by 3rd-order phase transitions at percolation thresholds. Here we present the evidence that these percolation transitions of both gaseous and liquid states along any isotherm are preceded by pre-percolation hetero-phase fluctuations that can explain the thermodynamic properties in the mesophase and its vicinity. Hetero-phase fluctuations give rise to one-component colloidal-dispersion states; a single Gibbs phase retaining 2 degrees of freedom in which both gas and liquid states with different densities percolate the phase volume. In order to describe the thermodynamic properties of two-state critical and supercritical coexistence, we introduce the concept of a hypothetical homo-phase of both gas and liquid, defined as extrapolated equilibrium states in the pre-percolation vicinity, with the hetero-phase fractions subtracted. We observe that there can be no difference in chemical potential between homo-phase liquid and gaseous states along the critical isotherm in mid-critical isochoric experiments when the meniscus disappears at T = Tc. For T > Tc, thermodynamic states comprise equal mole fractions of the homo-phase gas and liquid, both percolating the total phase volume, at the same temperature, pressure, and with a uniform chemical potential, stabilised by a positive finite interfacial surface tension.

Style APA, Harvard, Vancouver, ISO itp.

19

Toikka, M. A., A. A. Samarov, A. A. Sadaev, A. A. Senina i O. L. Lobacheva. "CHEMICAL EQUILIBRIUM IN THE PROPIONIC ACID - ETHANOL - ETHYL PROPIONATE - WATER SYSTEM AND EXTRACTION PROCESSES WITH PARTICIPATION OF DEEP EUTECTIC SOLVENTS". Fine Chemical Technologies 14, nr 1 (28.02.2019): 47–58. http://dx.doi.org/10.32362/2410-6593-2019-14-1-47-58.

Pełny tekst źródła

Streszczenie:

New experimental data on the chemical equilibrium in the propionic acid - ethanol - ethyl propionate - water system at 293.15 K and atmospheric pressure are presented. Chemically equilibrium compositions corresponding to the liquid-liquid equilibrium were obtained by gas chromatographic analysis. Using the method of nuclear magnetic resonance, homogeneous chemically equilibrium compositions were determined and the concentration equilibrium constant is calculated. The surface of chemical equilibrium and the region of splitting chemically equilibrium compositions are represented in the square of the transformed concentration variables. Comparison of the data obtained in the work with the literature was carried out at 303.15 and 313.15 K. It was found that the region of such compositions decreases with increasing temperature, while the surface of chemical equilibrium does not change the shape and position in the concentration space in the temperature range 293.15-313.15 K and atmospheric pressure. Liquid-liquid equilibrium compositions have also been obtained by gas chromatographic analysis for ethanol and ethyl propionate in the pseudo-ternary system using deep eutectic solvents (DES) based on choline chloride and glycerol / urea in whole range of concentration. The analysis of the extraction properties of DES showed the highest efficiency of DES based on choline chloride and urea. Experimental data on phase equilibrium are processed using Othmer-Tobias and Hand models. The calculated correlation coefficient (more than 0.99) indicates a high internal consistency of the experimental data obtained in this work.

Style APA, Harvard, Vancouver, ISO itp.

20

Pereira, Antonio, i Serafim Kalliadasis. "Equilibrium gas–liquid–solid contact angle from density-functional theory". Journal of Fluid Mechanics 692 (15.12.2011): 53–77. http://dx.doi.org/10.1017/jfm.2011.496.

Pełny tekst źródła

Streszczenie:

AbstractWe investigate the equilibrium of a fluid in contact with a solid boundary through a density-functional theory. Depending on the conditions, the fluid can be in one phase, gas or liquid, or two phases, while the wall induces an external field acting on the fluid particles. We first examine the case of a liquid film in contact with the wall. We construct bifurcation diagrams for the film thickness as a function of the chemical potential. At a specific value of the chemical potential, two equally stable films, a thin one and a thick one, can coexist. As saturation is approached, the thickness of the thick film tends to infinity. This allows the construction of a liquid–gas interface that forms a well-defined contact angle with the wall.

Style APA, Harvard, Vancouver, ISO itp.

21

Luo, T., i A. Yu Chirkov. "Thermodynamic Property Calculation in Vapor-Liquid Equilibrium for Multicomponent Mixtures using Highly Accurate Helmholtz Free Energy Equation of State". Herald of the Bauman Moscow State Technical University. Series Mechanical Engineering, nr 3 (138) (wrzesień 2021): 108–21. http://dx.doi.org/10.18698/0236-3941-2021-3-108-121.

Pełny tekst źródła

Streszczenie:

Thermodynamic properties of multicomponent mixtures in phase equilibrium were studied. The tangent plane criterion was used for stability analysis, and the Gibbs energy minimization was employed for phase equilibrium calculation when the successive substitution didn't converge. Thermodynamic properties of a 12-component natural gas mixture in vapor-liquid equilibrium were calculated with highly accurate Helmholtz free energy equation of state GERG--2008, simplified GERG--2008 and common cubic Peng --- Robinson (PR) equation of state. Results show that in vapor-liquid equilibrium, GERG--2008 has high accuracy and works better than simplified GERG--2008 and PR-equation of state. Simplified GERG--2008 and PR-equation of state both work unsatisfactorily in vapor-liquid equilibrium calculation, especially near the saturation zone. The deviation function in GERG--2008 can significantly affect the accuracy of GERG--2008 when calculating thermodynamic properties of mixtures in vapor-liquid equilibrium

Style APA, Harvard, Vancouver, ISO itp.

22

Zuend, A., C. Marcolli, T. Peter i J. H. Seinfeld. "Computation of liquid-liquid equilibria and phase stabilities: implications for RH-dependent gas/particle partitioning of organic-inorganic aerosols". Atmospheric Chemistry and Physics Discussions 10, nr 5 (12.05.2010): 12497–561. http://dx.doi.org/10.5194/acpd-10-12497-2010.

Pełny tekst źródła

Streszczenie:

Abstract. Semivolatile organic and inorganic aerosol species partition between the gas and aerosol particle phases to maintain thermodynamic equilibrium. Liquid-liquid phase separation into an organic-rich and an aqueous electrolyte phase can occur in the aerosol as a result of the salting-out effect. Such liquid-liquid equilibria (LLE) affect the gas/particle partitioning of the different semivolatile compounds and might significantly alter both particle mass and composition as compared to a one-phase particle. We present a new liquid-liquid equilibrium and gas/particle partitioning model, using as a basis the group-contribution model AIOMFAC (Zuend et al., 2008). This model allows the reliable computation of the liquid-liquid coexistence curve (binodal), corresponding tie-lines, the limit of stability/metastability (spinodal), and further thermodynamic properties of the phase diagram. Calculations for ternary and multicomponent alcohol/polyol-water-salt mixtures suggest that LLE are a prevalent feature of organic-inorganic aerosol systems. A six-component polyol-water-ammonium sulphate system is used to simulate effects of relative humidity (RH) and the presence of liquid-liquid phase separation on the gas/particle partitioning. RH, salt concentration, and hydrophilicity (water-solubility) are identified as key features in defining the region of a miscibility gap and govern the extent to which compound partitioning is affected by changes in RH. The model predicts that liquid-liquid phase separation can lead to either an increase or decrease in total particulate mass, depending on the overall composition of a system and the particle water content, which is related to the hydrophilicity of the different organic and inorganic compounds. Neglecting non-ideality and liquid-liquid phase separations by assuming an ideal mixture leads to an overestimation of the total particulate mass by up to 30% for the composition and RH range considered in the six-component system simulation. For simplified partitioning parametrizations, we suggest a modified definition of the effective saturation concentration, C*j, by including water and other inorganics in the absorbing phase. Such a C*j definition reduces the RH-dependency of the gas/particle partitioning of semivolatile organics in organic-inorganic aerosols by an order of magnitude as compared to the currently accepted definition, which considers the organic species only.

Style APA, Harvard, Vancouver, ISO itp.

23

Zuend, A., C. Marcolli, T. Peter i J. H. Seinfeld. "Computation of liquid-liquid equilibria and phase stabilities: implications for RH-dependent gas/particle partitioning of organic-inorganic aerosols". Atmospheric Chemistry and Physics 10, nr 16 (24.08.2010): 7795–820. http://dx.doi.org/10.5194/acp-10-7795-2010.

Pełny tekst źródła

Streszczenie:

Abstract. Semivolatile organic and inorganic aerosol species partition between the gas and aerosol particle phases to maintain thermodynamic equilibrium. Liquid-liquid phase separation into an organic-rich and an aqueous electrolyte phase can occur in the aerosol as a result of the salting-out effect. Such liquid-liquid equilibria (LLE) affect the gas/particle partitioning of the different semivolatile compounds and might significantly alter both particle mass and composition as compared to a one-phase particle. We present a new liquid-liquid equilibrium and gas/particle partitioning model, using as a basis the group-contribution model AIOMFAC (Zuend et al., 2008). This model allows the reliable computation of the liquid-liquid coexistence curve (binodal), corresponding tie-lines, the limit of stability/metastability (spinodal), and further thermodynamic properties of multicomponent systems. Calculations for ternary and multicomponent alcohol/polyol-water-salt mixtures suggest that LLE are a prevalent feature of organic-inorganic aerosol systems. A six-component polyol-water-ammonium sulphate system is used to simulate effects of relative humidity (RH) and the presence of liquid-liquid phase separation on the gas/particle partitioning. RH, salt concentration, and hydrophilicity (water-solubility) are identified as key features in defining the region of a miscibility gap and govern the extent to which compound partitioning is affected by changes in RH. The model predicts that liquid-liquid phase separation can lead to either an increase or decrease in total particulate mass, depending on the overall composition of a system and the particle water content, which is related to the hydrophilicity of the different organic and inorganic compounds. Neglecting non-ideality and liquid-liquid phase separations by assuming an ideal mixture leads to an overestimation of the total particulate mass by up to 30% for the composition and RH range considered in the six-component system simulation. For simplified partitioning parametrizations, we suggest a modified definition of the effective saturation concentration, Cj*, by including water and other inorganics in the absorbing phase. Such a Cj* definition reduces the RH-dependency of the gas/particle partitioning of semivolatile organics in organic-inorganic aerosols by an order of magnitude as compared to the currently accepted definition, which considers the organic species only.

Style APA, Harvard, Vancouver, ISO itp.

24

Schwarzmeier, Christoph, i Ulrich Rüde. "Comparison of refilling schemes in the free-surface lattice Boltzmann method". AIP Advances 12, nr 11 (1.11.2022): 115324. http://dx.doi.org/10.1063/5.0131159.

Pełny tekst źródła

Streszczenie:

Simulating mobile liquid–gas interfaces with the free-surface lattice Boltzmann method (FSLBM) requires frequent re-initialization of fluid flow information in computational cells that convert from gas to liquid. The corresponding algorithm, here referred to as the refilling scheme, is crucial for the successful application of the FSLBM in terms of accuracy and numerical stability. This study compares five refilling schemes that extract information from the surrounding liquid and interface cells by averaging, extrapolating, or assuming one of the three different equilibrium states. Six numerical experiments were performed, covering a broad spectrum of possible scenarios. These include a standing gravity wave, a rectangular and cylindrical dam break, a Taylor bubble, a drop impact into liquid, and a bubbly plane Poiseuille flow. In some simulations, the averaging, extrapolation, and one equilibrium-based scheme were numerically unstable. Overall, the results have shown that the simplest equilibrium-based scheme should be preferred in terms of numerical stability, computational cost, accuracy, and ease of implementation.

Style APA, Harvard, Vancouver, ISO itp.

25

Ndukwe, Obineche Charles, i Chukwudi Christian Ezuru. "Measurement and Correlation of the Liquid-Liquid Equilibria of Tertiary-Butyl Alcohol – Water – Benzene System at 30°C and 1 Atmosphere Pressure". Saudi Journal of Engineering and Technology 7, nr 8 (25.09.2022): 485–94. http://dx.doi.org/10.36348/sjet.2022.v07i08.009.

Pełny tekst źródła

Streszczenie:

The Liquid-Liquid equilibria of Tertiary-Butyl Alcohol – Water – Benzene System were measured experimentally at 30°C and 1atm pressure. The experimental binodal curve compositions were obtained using the cloud point method. The compositions of the two equilibrium phases were analysed using Agilent 7820A series Gas Chromatograph. The consistency of the experimental data was determined using the Hand, Othmer-Tobias and Bachman- Brown correlation equations while the plate point was determined using the Treybal’s method. The effectiveness of the solvent in the extraction was determined by calculating the distribution coefficients and separation factors. The experimental tie-line data were correlated with the Universal Quasi-Chemical (UNIQUAC) and Non-Random Two Liquid (NRTL) activity coefficient models. Also, the deviation between the experimental and calculated equilibrium compositions were calculated using the root mean squared deviation equation. The UNIQUAC predicted data gave a closer resemblance to the experimental.

Style APA, Harvard, Vancouver, ISO itp.

26

Kamilov, Ibraghimkhan, Gennadiy Stepanov, Larisa Malysheva, Anvar Rasulov, Suleyman Rasulov i Kurban Shakhbanov. "Phase equilibrium curves and critical lines of n-hexane--water: liquid-liquid and liquid-gas". High Temperatures-High Pressures 29, nr 4 (1997): 491–95. http://dx.doi.org/10.1068/htec310.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

27

Wang, XingJian, Patrick Lafon, Dilip Sundaram i Vigor Yang. "Liquid vaporization under thermodynamic phase non-equilibrium condition at the gas-liquid interface". Science China Technological Sciences 63, nr 12 (9.11.2020): 2649–56. http://dx.doi.org/10.1007/s11431-020-1732-5.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

28

Duan, Runze, Ziwei Feng, Hongbin Duan, Huiru Qu, Liting Tian, Wenqi Jia, Jakov Baleta, Enyu Wang, Liansheng Liu i Liang Tian. "Energy equilibrium analysis in the effervescent atomization". Open Physics 18, nr 1 (6.12.2020): 925–32. http://dx.doi.org/10.1515/phys-2020-0214.

Pełny tekst źródła

Streszczenie:

Abstract In this paper, the flow characteristics and energy equilibrium analysis of the effervescent atomization had been investigated theoretically and experimentally. The effect of the gas–liquid rate (GLR from 0.04 to 0.15) on the atomization stability was revealed. When the GLR was small, the atomization was unstable. The atomization was gradually stable with an increase in the GLR. The optimal atomization region can be obtained. The Sauter mean diameter (SMD) of the droplets was measured by the phase Doppler analyzer. The SMD decreases with an increase in the GLR. The energy equilibrium analysis was investigated for the swirl atomizer theoretically and experimentally. The results show that the energy dissipation terms are mainly compressed gas expansion, liquid viscosity dissipation, and resistance losses. However, the ratio of the spray kinetic energy and the surface tension energy to the total energy is small.

Style APA, Harvard, Vancouver, ISO itp.

29

Nakagawa, Naoko, i Shin-ichi Sasa. "Global Thermodynamics for Heat Conduction Systems". Journal of Statistical Physics 177, nr 5 (8.10.2019): 825–88. http://dx.doi.org/10.1007/s10955-019-02393-2.

Pełny tekst źródła

Streszczenie:

Abstract We propose the concept of global temperature for spatially non-uniform heat conduction systems. With this novel quantity, we present an extended framework of thermodynamics for the whole system such that the fundamental relation of thermodynamics holds, which we call “global thermodynamics” for heat conduction systems. Associated with this global thermodynamics, we formulate a variational principle for determining thermodynamic properties of the liquid-gas phase coexistence in heat conduction, which corresponds to the natural extension of the Maxwell construction for equilibrium systems. We quantitatively predict that the temperature of the liquid–gas interface deviates from the equilibrium transition temperature. This result indicates that a super-cooled gas stably appears near the interface.

Style APA, Harvard, Vancouver, ISO itp.

30

Shagapov, V. Sh, i A. V. Yalaev. "ON THE THEORY OF THE BULK FOAM-FORMATION OF GAS-SATURATED LIQUID DURING THE DEPRESSURIZING OF CONTAINER". Vestnik of Samara University. Natural Science Series 19, nr 6 (2.06.2017): 126–32. http://dx.doi.org/10.18287/2541-7525-2013-19-6-126-132.

Pełny tekst źródła

Streszczenie:

The problem of depressurizing in the gas-saturated liquid is considered. It is found out that the smaller is the initial radius of original germ of gas, the more pressure drops as compared with equilibrium pressure. The solution of the system that describes the transition from the metastable state to the equilibrium two-phase state is found. It is found that the characteristic time of exit from the metastable state depends on the initial number of gas germ.

Style APA, Harvard, Vancouver, ISO itp.

31

Ma, Ai Lin, i Peng Yun Song. "The Liquid Condensation Conditions in the Dry Gas Seal System". Applied Mechanics and Materials 752-753 (kwiecień 2015): 199–204. http://dx.doi.org/10.4028/www.scientific.net/amm.752-753.199.

Pełny tekst źródła

Streszczenie:

Dry gas seal is often used as the seal devices in centrifugal compressor and other high-speed rotating equipment, which requires seal gas clean and dry. If there is some liquid in the seal gas, the dry gas seal will rapidly fail. When the seal gas flows through the filters, valves, orifices, seal faces and so on, the gas temperature will decrease resulted from the Joule- Thomson effect. If the gas temperature is lower than the corresponding dew point, there will be liquid condensation in dry gas seal system. Wet air is taken as an example to show how to calculate the pressure and temperature relationship when it is adiabatic expansion. Dew point lines at different conditions are calculated by considering the vapor-liquid equilibrium. Liquid condensation conditions are acquired by comparing expansion lines and dew point lines, and the factors of influencing liquid condensation were analyzed. The results shows that decreasing gas humidity, increasing the gas temperature can effectively reduce the liquid condensation.

Style APA, Harvard, Vancouver, ISO itp.

32

Xiong, Wenjie, Xiaohui Chen, Quanyong Wang, Min Gao, Danxing Zheng, Yuliang Mai i Wei Hu. "Heterogeneous Phases Reaction Equilibrium in an Oxy-Thermal Carbide Furnace". ChemEngineering 4, nr 1 (3.01.2020): 2. http://dx.doi.org/10.3390/chemengineering4010002.

Pełny tekst źródła

Streszczenie:

This work focuses on revealing the chemical reaction equilibrium behaviors of gas–liquid–solid heterogeneous phases in an oxy-thermal carbide furnace. From a CaC2 formation mechanism investigation, it was determined that a one-step mechanism occurs when there is an excess of C and a high CO partial pressure, which inhibits the formation of Ca in the system, and a two-step mechanism occurs when there is insufficient C and a low CO partial pressure, which promotes the formation of Ca. Based on the calculated results of the equilibrium compositions at 100 kPa and different temperature conditions, the chemical reaction equilibrium behaviors of gas–liquid–solid heterogeneous phases in an oxy-thermal carbide furnace were analyzed at conditions of excess C and insufficient C.

Style APA, Harvard, Vancouver, ISO itp.

33

Ismailov, G. G., R. A. Ismailov, H. N. Babirov i Kh Т. Jahangirova. "Studying the dynamics of sedimentation of liquid particles during gas separation". Azerbaijan Oil Industry, nr 01 (15.01.2024): 34–37. http://dx.doi.org/10.37474/0365-8554/2024-01-34-37.

Pełny tekst źródła

Streszczenie:

Analysis of separation devices shows that it is not always possible to achieve effective separation of liquid particles. Traditional methods for determining the sedimentation rate of particles in separators are based on the thermodynamic equilibrium of the main parameters (pressure, density) of the incoming gas flow. At the same time, well production, in particular condensing gases, is a non-equilibrium system, which is characterized by some delay (relaxation times) in changing parameters. As a result of this delay, the settling rate of particles in the separator does not have time to reach the steady-state Stokes regime, corresponding to effective separation. The work proposes a non-equilibrium model for the settling rate of particles and establishes that for effective separation of liquid particles in a gravitational separator, the relaxation time for the settling rate of particles should not exceed 10 seconds.

Style APA, Harvard, Vancouver, ISO itp.

34

WANG, Ke. "Model for Drop Entrainment in Equilibrium Gas-liquid Churn Flow". Journal of Mechanical Engineering 49, nr 12 (2013): 147. http://dx.doi.org/10.3901/jme.2013.12.147.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

35

Wang, Y. N., Y. W. Li, L. Bai, Y. L. Zhao i B. J. Zhang. "Correlation for gas–liquid equilibrium prediction in Fischer–Tropsch synthesis". Fuel 78, nr 8 (czerwiec 1999): 911–17. http://dx.doi.org/10.1016/s0016-2361(99)00020-4.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

36

Weidner, E., V. Wiesmet, Ž. Knez i M. Škerget. "Phase equilibrium (solid-liquid-gas) in polyethyleneglycol-carbon dioxide systems". Journal of Supercritical Fluids 10, nr 3 (sierpień 1997): 139–47. http://dx.doi.org/10.1016/s0896-8446(97)00016-8.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

37

Nikolaidis, Ilias K., Varvara S. Samoili, Epaminondas C. Voutsas i Ioannis G. Economou. "Solid–Liquid–Gas Equilibrium of Methane–n-Alkane Binary Mixtures". Industrial & Engineering Chemistry Research 57, nr 25 (4.06.2018): 8566–83. http://dx.doi.org/10.1021/acs.iecr.8b01339.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

38

YAMAMOTO, Takayuki, Osamu MORI i Jun'ichiro KAWAGUCHI. "New Thruster System for Small Satellite : Gas-Liquid Equilibrium Thruster". TRANSACTIONS OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES, SPACE TECHNOLOGY JAPAN 7, ists26 (2009): Tb_29—Tb_33. http://dx.doi.org/10.2322/tstj.7.tb_29.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

39

Pisoni, C., C. Schenone i L. A. Tagliafico. "Non equilibrium gas-liquid flows in variable cross section ducts". Heat and Mass Transfer 30, nr 3 (luty 1995): 135–41. http://dx.doi.org/10.1007/bf01476521.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

40

Romero, L. E., i D. Cantero. "Mathematical model for liquid-gas equilibrium in acetic acid fermentations". Biotechnology and Bioengineering 59, nr 3 (5.08.1998): 310–17. http://dx.doi.org/10.1002/(sici)1097-0290(19980805)59:3<310::aid-bit7>3.0.co;2-e.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

41

Ilčin, Michal, Martin Michalík, Klára Kováčiková, Lenka Káziková i Vladimír Lukeš. "Water liquid-vapor equilibrium by molecular dynamics: Alternative equilibrium pressure estimation". Acta Chimica Slovaca 9, nr 1 (1.04.2016): 36–43. http://dx.doi.org/10.1515/acs-2016-0007.

Pełny tekst źródła

Streszczenie:

Abstract The molecular dynamics simulations of the liquid-vapor equilibrium of water including both water phases — liquid and vapor — in one simulation are presented. Such approach is preferred if equilibrium curve data are to be collected instead of the two distinct simulations for each phase separately. Then the liquid phase is not restricted, e.g. by insufficient volume resulting in too high pressures, and can spread into its natural volume ruled by chosen force field and by the contact with vapor phase as vaporized molecules are colliding with phase interface. Averaged strongly fluctuating virial pressure values gave untrustworthy or even unreal results, so need for an alternative method arisen. The idea was inspired with the presence of vapor phase and by previous experiences in gaseous phase simulations with small fluctuations of pressure, almost matching the ideal gas value. In presented simulations, the first idea how to calculate pressure only from the vapor phase part of simulation box were applied. This resulted into very simple method based only on averaging molecules count in the vapor phase subspace of known volume. Such simple approach provided more reliable pressure estimation than statistical output of the simulation program. Contrary, also drawbacks are present in longer initial thermostatization time or more laborious estimation of the vaporization heat. What more, such heat of vaporization suffers with border effect inaccuracy slowly decreasing with the thickness of liquid phase. For more efficient and more accurate vaporization heat estimation the two distinct simulations for each phase separately should be preferred.

Style APA, Harvard, Vancouver, ISO itp.

42

OH, YOOL KWON, DONG PYO SEO i HO DONG YANG. "VISUALIZATION ON THERMAL AND DYNAMIC CHARACTERISTICS OF TWO PHASE FLOW". International Journal of Modern Physics B 20, nr 25n27 (30.10.2006): 4347–52. http://dx.doi.org/10.1142/s0217979206041331.

Pełny tekst źródła

Streszczenie:

This paper was visually studied the thermal and dynamic characteristics of two phase flow by vertical upward bubbles in the liquid. Air-water model in a ladle was visually studied with a particle image velocimetry (PIV) and a thermo vision camera. Once gas was injected into the liquid, bubbles-liquid plume started to form and then circulations was caused by bubbles' behavior helped to reach temperature equilibrium and remove impurities in the liquid. The experimental results showed that temperature equilibrium between water and gas could be achieved in a short time. High speed CCD camera and argon illumination laser were used for the visualization of test section. Liquid circulation was repeated in the local or whole liquid region and accelerated the mixing rate. Visualization of qualitative descriptions such as velocity vectors, turbulent intensity and kinetic energy in the flow field presents useful information on thermal and dynamic characteristics of two phase flow.

Style APA, Harvard, Vancouver, ISO itp.

43

Tamson, J., M. Mair i S. Grohmann. "Vapor-liquid equilibrium of the nitrogen-argon system at 100 K". IOP Conference Series: Materials Science and Engineering 1240, nr 1 (1.05.2022): 012159. http://dx.doi.org/10.1088/1757-899x/1240/1/012159.

Pełny tekst źródła

Streszczenie:

Abstract Mixed-refrigerant cycles (MRC) are state-of-the-art for efficient LNG production. The development of cryogenic mixed-refrigerant cycles (CMRC) at temperatures below 100 K relies on physical property data of cryogenic mixtures such as vapor-liquid equilibria and enthalpies. This data is insufficient for some binary mixtures and unavailable for most multi-component systems. The cryogenic phase equilibria test stand CryoPHAEQTS provides precise physical property data of cryogenic fluid mixtures at temperatures from 15 K to 300K and at pressures up to 150 bar. Contrary to previous apparatus in the literature, CryoPHAEQTS uses cooling of the equilibrium cell by a pulse-tube cryocooler. Temperature is measured by two CERNOX® sensors directly immersed in the liquid/vapor phase. Pressure is measured through a capillary and a differential pressure sensor connected to a secondary system containing three high precision sensors. Up to three occurring phases can be sampled directly from the cell and analyzed by gas chromatography. Measurement uncertainties are ±13mK in temperature, ±1 mbar in pressure and ±1% in composition. Prior to publishing new phase equilibrium data, the test stand is benchmarked against available vapor-liquid equilibrium data of the widely investigated nitrogen-argon system. In this paper, we report on the first measurement results of cryogenic mixtures in CryoPHAEQTS and compare them against the literature data.

Style APA, Harvard, Vancouver, ISO itp.

44

Shishatskii, Y. I., A. A. Derkanosova i S. A. Tolstov. "Thermodynamics of phase equilibrium in solid-liquid and solid-gas systems". Proceedings of the Voronezh State University of Engineering Technologies 83, nr 1 (3.06.2021): 30–35. http://dx.doi.org/10.20914/2310-1202-2021-1-30-35.

Pełny tekst źródła

Streszczenie:

The thermodynamic equilibrium of a two-phase system is described by the Gibbs equation, which includes state parameters. On the basis of the Gibbs equation and the combined equation of the first and second laws of thermodynamics, thermodynamic potentials are written: internal energy, enthalpy and Gibbs free energy. If the two phases are in equilibrium, then the temperatures, pressures and chemical potentials of these phases are equal to each other. Equalities express the conditions of thermal and mechanical equilibrium, as well as the condition for the absence of a driving force for the transfer of a component across the interface. For a two-phase system, the Gibbs-Duhem equation connects the volume and entropy of 1 mole of the mixture, the content of any component, expressed in mole fractions. Extraction from lupine particles with cheese whey (solid-liquid system) is considered. The driving force of the extraction process in the solid-liquid system is the difference between the concentration of the solvent at the surface of the solid C and its average concentration C0 in the bulk of the solution. The concentration at the interface is usually taken to be equal to the concentration of a saturated solution of Cn, since equilibrium is established rather quickly near the surface of a solid. Then the driving force of the process is expressed as Cn – C0. A curve for the extraction of extractives from lupine with cheese whey was plotted by superimposing low-frequency mechanical vibrations.

Style APA, Harvard, Vancouver, ISO itp.

45

Zhao, Sha, Yu-Dong Ding, Qiang Liao, Xun Zhu i Yun Huang. "Experimental and theoretical study on dissolution of a single mixed gas bubble in a microalgae suspension". RSC Advances 5, nr 41 (2015): 32615–25. http://dx.doi.org/10.1039/c5ra03905c.

Pełny tekst źródła

Streszczenie:

Visualization experiments using a promoted bubble grafting method were carried out and the non-equilibrium theory at the gas–liquid interface was adopted to predict the dissolution and transmission process of CO₂ gas.

Style APA, Harvard, Vancouver, ISO itp.

46

Shin, Hun Yong, i Jin Ho Kim. "Vapor Liquid Equilibrium of Aqueous Diethanolamine Solution for Carbon Dioxide Capture Processes". Journal of Korean Society of Environmental Engineers 45, nr 2 (28.02.2023): 119–26. http://dx.doi.org/10.4491/ksee.2023.45.2.119.

Pełny tekst źródła

Streszczenie:

Objectives : Acid gases such as carbon dioxide (CO<sub>2</sub>) and hydrogen sulfide (H<sub>2</sub>S) that cause global warming are mainly generated in chemical processes. As a technology for reducing acid gas, the post-combustion capture process is representative. Aqueous alkanolamine solution, which is mainly used in the carbon dioxide absorption process, is used as the most representative chemical absorbent. Thermodynamic data of vapor-liquid equilibrium are important for the economics of process design and operation. In this study, vapor-liquid equilibrium data of water + DEA are measured so that DEA, a secondary amine, can be used in the carbon dioxide absorption process, so that it can be used for designing a new carbon dioxide absorption process.Methods : Vapor-liquid equilibrium data of a mixture of water + DEA (diethanolamine) were measured under isothermal conditions of 393.15 K using HSGC (Headspace Gas Chromatography).Results and Discussion : The measured vapor-liquid equilibrium data were correlated using NRTL, an activity coefficient model. In addition, as additional thermodynamic data of the absorbent mixture, the density of the DEA aqueous mixture was measured at a temperature of 303.15 K to 333.15 K using a density meter (Anton Paar DMA4500). The measured density data of the mixture was converted into excess volume, and the excess volume data was correlated using the Redilchi-Kister-Muggianu equation. Using the measured water+DEA vapor-liquid equilibrium data, it is expected to reducing the design cost and operating cost of the carbon dioxide absorption processes.

Style APA, Harvard, Vancouver, ISO itp.

47

Holubets, Taras. "Investigation of an equilibrium state of water and two-component gas mixture of dry air and water vapor at the separation surface of phases in the conditions of phase transition Part I". Physico-mathematical modelling and informational technologies, nr 25 (25.05.2017): 51–71. http://dx.doi.org/10.15407/fmmit2017.25.051.

Pełny tekst źródła

Streszczenie:

In this part of the publication from the point of view the macroscopically and microscopically description of the properties of phase transition the conditions of stationary thermodynamic state (equilibrium) at the separation surface between the liquid and gas phases under uniform heating or cooling from the side of the thermal reservoir (thermostat) are reviewed and formulated. The basic methods of investigations of the equilibrium state of a two-component gas mixture (dry air and water vapor) in contact with a liquid phase under conditions of phase transformation are described. In the framework of the quasi-classical approximation, the macroscopic equations of the balance of pressures at the interfacial phase surface are defined, according to which the effective molar characteristics of the gas (binary) mixture in the conditions of fluctuation mixing with the ideal liquid into the superfacial layer are determined under certain diffusion approximations. According to macroscopic (mechanical) and microscopic (probabilistic) considerations, an equation of state of a nonideal gas mixture in the case of evaporation or condensation during phase transition under stationary conditions is obtained.

Style APA, Harvard, Vancouver, ISO itp.

48

Pradhan, Sushobhan, i Prem Kumar Bikkina. "An Analytical Method to Estimate Supersaturation in Gas–Liquid Systems as a Function of Pressure-Reduction Step and Waiting Time". Eng 3, nr 1 (21.02.2022): 116–23. http://dx.doi.org/10.3390/eng3010010.

Pełny tekst źródła

Streszczenie:

When the concentration of a gas exceeds the equilibrium concentration in a liquid, the gas–liquid system is referred as a supersaturated system. The supersaturation can be achieved by either changing the pressure and/or temperature of the system. The gas from a supersaturated liquid escapes either through bubble nucleation that usually occurs on solid surface and/or gas diffusion through the gas–liquid interface. The bubble nucleation requires a minimum threshold supersaturation. A waiting time is required to observe whether the applied supersaturation is sufficient to initiate bubble nucleation. When the supersaturation is not sufficient to cause bubble nucleation, some or all of the supersaturated gas may diffuse out from the liquid through the gas–liquid interface before further reducing the pressure in order to increase the supersaturation. In this article, using Fick’s second law of diffusion and Henry’s law, an analytical method is proposed to estimate the level of supersaturations generated in three gas–liquid systems at different step-down pressures. Characteristic times of the gas–liquid systems were estimated to validate whether the waiting times used in this study are in accordance with the semi-infinite diffusion model used to estimate the supersaturations generated.

Style APA, Harvard, Vancouver, ISO itp.

49

Gao, Yu Ming, Ji Lin Cao, Panpan Chen, Hong Fei Guo i Zhao Yang Tan. "Equilibrium Studies on the System H₂O-H₂O₂-CO(NH₂)₂-C₃H₈". Advanced Materials Research 233-235 (maj 2011): 1690–93. http://dx.doi.org/10.4028/www.scientific.net/amr.233-235.1690.

Pełny tekst źródła

Streszczenie:

The phase equilibrium of the quaternary system H2O-H2O2-CO(NH2)2-C3H8 with gas hydrate formation had been studied at high pressure and low temperature. The temperature and pressure of gas hydrate formed from different hydrogen peroxide concentration aqueous were determined at adding surfactants and no surfactants separately. It was concluded that the equilibrium pressure of gas hydrate formation was increasing with the increase of the hydrogen peroxide concentration, the urea concentration and the temperature, the mother liquor amount entrained in the gas hydrate after liquid separation by sinking was very high when surfactants was not added, but the equilibrium pressure of gas hydrate formation was decreased and the mother liquor amount entrained in gas hydrate was also decreased when surfactants was added to the system. In addition, the equilibrium pressure of gas hydrate formation in the quaternary system H2O-H2O2-CO(NH2)2-C3H8 was calculated according to Chen-Guo thermodynamic model, improved UNIFAC mathematical equation and Aasberg-Peterson fugacity coefficient model. The calculated data was in agreement with the experiment data.

Style APA, Harvard, Vancouver, ISO itp.

50

Miller, R. S., K. Harstad i J. Bellan. "Evaluation of equilibrium and non-equilibrium evaporation models for many-droplet gas-liquid flow simulations". International Journal of Multiphase Flow 24, nr 6 (wrzesień 1998): 1025–55. http://dx.doi.org/10.1016/s0301-9322(98)00028-7.

Pełny tekst źródła

Style APA, Harvard, Vancouver, ISO itp.

Artykuły w czasopismach na temat „Gas-liquid equilibrium”

Utwórz poprawne odniesienie w stylach APA, MLA, Chicago, Harvard i wielu innych