1
|
Crossover Residual Entropy Scaling of the Viscosity and Thermal Conductivity of Carbon Dioxide. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.120799] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
|
2
|
Abdulagatov IM, Skripov PV. Thermodynamic and Transport Properties of Supercritical Fluids. Part 2: Review of Transport Properties. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B 2022. [DOI: 10.1134/s1990793121070022] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
|
3
|
Das SK. A scaling investigation of pattern in the spread of COVID-19: universality in real data and a predictive analytical description. Proc Math Phys Eng Sci 2021; 477:20200689. [PMID: 35153541 PMCID: PMC8317978 DOI: 10.1098/rspa.2020.0689] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2020] [Accepted: 01/05/2021] [Indexed: 12/16/2022] Open
Abstract
We analyse the spread of COVID-19, a disease caused by a novel coronavirus, in various countries by proposing a model that exploits the scaling and other important concepts of statistical physics. Quite expectedly, for each of the considered countries, we observe that the spread at early times occurs exponentially fast. We show how the countries can be classified into groups, like universality classes in the literature of phase transitions, based on the rates of infections during late times. This method brings a new angle to the understanding of disease spread and is useful in obtaining a country-wise comparative picture of the effectiveness of lockdown-like social measures. Strong similarity, during both natural and lockdown periods, emerges in the spreads within countries having varying geographical locations, climatic conditions, population densities and economic parameters. We derive accurate mathematical forms for the corresponding scaling functions and show how the model can be used as a predictive tool, with instruction even for future waves, and, thus, as a guide for optimizing social measures and medical facilities. The model is expected to be of general relevance in the studies of epidemics.
Collapse
Affiliation(s)
- Subir K Das
- Theoretical Sciences Unit and School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur PO, Bangalore 560064, India
| |
Collapse
|
4
|
Hopp M, Gross J. Thermal Conductivity from Entropy Scaling: A Group-Contribution Method. Ind Eng Chem Res 2019. [DOI: 10.1021/acs.iecr.9b04289] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Madlen Hopp
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, 70569 Stuttgart, Germany
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, 70569 Stuttgart, Germany
| |
Collapse
|
5
|
Model development for sc-drying kinetics of aerogels: Part 1. Monoliths and single particles. J Supercrit Fluids 2018. [DOI: 10.1016/j.supflu.2018.07.002] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
|
6
|
Tsolakidou CM, Assael MJ, Huber ML, Perkins RA. Correlations for the Viscosity and Thermal Conductivity of Ethyl Fluoride (R161). JOURNAL OF PHYSICAL AND CHEMICAL REFERENCE DATA 2017; 46:023103. [PMID: 28785120 PMCID: PMC5544035 DOI: 10.1063/1.4983027] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
This paper presents new wide-ranging correlations for the viscosity and thermal conductivity of ethyl fluoride (R161) based on critically evaluated experimental data. The correlations are designed to be used with a recently published equation of state that is valid from 130 K to 450 K, at pressures up to 100 MPa. The estimated uncertainty at a 95% confidence level is 2% for the viscosity of low-density gas (pressures below 0.5 MPa), and 3% for the viscosity of the liquid over the temperature range from 243 K to 363 K at pressures up to 30 MPa. The estimated uncertainty is 3% for the thermal conductivity of the low-density gas, and 3% for the liquid over the temperature range from 234 K to 374 K at pressures up to 20 MPa. Both correlations may be used over the full range of the equation of state, but the uncertainties will be larger, especially in the critical region.
Collapse
Affiliation(s)
- Ch. M. Tsolakidou
- Laboratory of Thermophysical Properties and Environmental Processes, Chemical Engineering Department, Aristotle University, Thessaloniki 54636, Greece
| | - M. J. Assael
- Laboratory of Thermophysical Properties and Environmental Processes, Chemical Engineering Department, Aristotle University, Thessaloniki 54636, Greece
| | - M. L. Huber
- Applied Chemicals and Materials Division, National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, USA
| | - R. A. Perkins
- Applied Chemicals and Materials Division, National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, USA
| |
Collapse
|
7
|
Hopp M, Gross J. Thermal Conductivity of Real Substances from Excess Entropy Scaling Using PCP-SAFT. Ind Eng Chem Res 2017. [DOI: 10.1021/acs.iecr.6b04289] [Citation(s) in RCA: 63] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Madlen Hopp
- Institute of Thermodynamics
and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring
9, 70569 Stuttgart, Germany
| | - Joachim Gross
- Institute of Thermodynamics
and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring
9, 70569 Stuttgart, Germany
| |
Collapse
|
8
|
Midya J, Das SK. Finite-size scaling study of dynamic critical phenomena in a vapor-liquid transition. J Chem Phys 2017; 146:044503. [PMID: 28147549 DOI: 10.1063/1.4974506] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Via a combination of molecular dynamics (MD) simulations and finite-size scaling (FSS) analysis, we study dynamic critical phenomena for the vapor-liquid transition in a three dimensional Lennard-Jones system. The phase behavior of the model has been obtained via the Monte Carlo simulations. The transport properties, viz., the bulk viscosity and the thermal conductivity, are calculated via the Green-Kubo relations, by taking inputs from the MD simulations in the microcanonical ensemble. The critical singularities of these quantities are estimated via the FSS method. The results thus obtained are in nice agreement with the predictions of the dynamic renormalization group and mode-coupling theories.
Collapse
Affiliation(s)
- Jiarul Midya
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
| | - Subir K Das
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
| |
Collapse
|
9
|
Ryzhkov II, Kozlova SV. Stationary and transient Soret separation in a binary mixture with a consolute critical point. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2016; 39:130. [PMID: 28004276 DOI: 10.1140/epje/i2016-16130-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2016] [Accepted: 11/25/2016] [Indexed: 06/06/2023]
Abstract
The stationary and transient Soret separation in a binary mixture with a consolute critical point is studied theoretically. The mixture is placed between two parallel plates kept at different temperatures. A polymer blend is used as a model system. Analytical solutions are constructed to describe the stationary separation in a binary mixture with variable Soret coefficient. The latter strongly depends on temperature and concentration and enhances near a consolute critical point due to reduced diffusion. As a result, a large concentration gradient is observed locally, while much smaller concentration variations are found in the rest of the layer. It is shown that complete separation can be obtained by applying a small temperature difference first, waiting for the establishment of stationary state, and then increasing this difference again. In this case, the critical temperature lies between hot and cold wall temperatures, while the mixture still remains in the one-phase region. When the initial (mean) temperature or concentration are shifted away from the near-critical values, the separation decreases. The analysis of transient behavior shows that the Soret separation occurs much faster than diffusion to the homogeneous state when the initial concentration is close to the critical one. It happens due to the decrease (increase) of the local relaxation time during the Soret (Diffusion) steps. The transient times of these steps become comparable for small temperature differences or off-critical initial concentrations. An unusual (non-exponential) separation dynamics is observed when the separation starts in the off-critical domain, and then enhances greatly when the system enters into the near-critical region. It is also found that the transient time decreases with increasing the applied temperature difference.
Collapse
Affiliation(s)
- Ilya I Ryzhkov
- Institute of Computational Modelling SB RAS, Akademgorodok, 660036, Krasnoyarsk, Russia.
- Siberian Federal University, Svobodny 79, 660041, Krasnoyarsk, Russia.
| | - Sofia V Kozlova
- Institute of Computational Modelling SB RAS, Akademgorodok, 660036, Krasnoyarsk, Russia
| |
Collapse
|
10
|
Roy S, Das SK. Study of critical dynamics in fluids via molecular dynamics in canonical ensemble. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2015; 38:132. [PMID: 26687057 DOI: 10.1140/epje/i2015-15132-2] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/21/2015] [Accepted: 11/30/2015] [Indexed: 06/05/2023]
Abstract
With the objective of understanding the usefulness of thermostats in the study of dynamic critical phenomena in fluids, we present results for transport properties in a binary Lennard-Jones fluid that exhibits liquid-liquid phase transition. Various collective transport properties, calculated from the molecular dynamics (MD) simulations in canonical ensemble, with different thermostats, are compared with those obtained from MD simulations in microcanonical ensemble. It is observed that the Nosé-Hoover and dissipative particle dynamics thermostats are useful for the calculations of mutual diffusivity and shear viscosity. The Nosé-Hoover thermostat, however, as opposed to the latter, appears inadequate for the study of bulk viscosity.
Collapse
Affiliation(s)
- Sutapa Roy
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O, 560064, Bangalore, India
| | - Subir K Das
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O, 560064, Bangalore, India.
| |
Collapse
|
11
|
Roy S, Das SK. Simulation of transport around the coexistence region of a binary fluid. J Chem Phys 2014; 139:064505. [PMID: 23947869 DOI: 10.1063/1.4817777] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We use Monte Carlo and molecular dynamics simulations to study phase behavior and transport properties in a symmetric binary fluid where particles interact via Lennard-Jones potential. Our results for the critical behavior of collective transport properties, with particular emphasis on bulk viscosity, is understood via appropriate application of finite-size scaling technique. It appears that the critical enhancements in these quantities are visible far above the critical point. This result is consistent with an earlier report from computer simulations where, however, the authors do not quantify the critical singularity.
Collapse
Affiliation(s)
- Sutapa Roy
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
| | | |
Collapse
|
12
|
Llovell F, Marcos RM, Vega LF. Free-Volume Theory Coupled with Soft-SAFT for Viscosity Calculations: Comparison with Molecular Simulation and Experimental Data. J Phys Chem B 2013; 117:8159-71. [DOI: 10.1021/jp401307t] [Citation(s) in RCA: 86] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- F. Llovell
- MATGAS Research Center, Campus de la UAB, 08193 Bellaterra, Barcelona, Spain
| | - R. M. Marcos
- Departament d’Enginyeria
Mecànica, ETSE, Universitat Rovira i Virgili, 43007 Tarragona, Spain
| | - L. F. Vega
- MATGAS Research Center, Campus de la UAB, 08193 Bellaterra, Barcelona, Spain
- Carburos Metálicos/Air Products Group, C/Aragón, 300, 08009 Barcelona,
Spain
| |
Collapse
|
13
|
Biddle JW, Holten V, Sengers JV, Anisimov MA. Thermal conductivity of supercooled water. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:042302. [PMID: 23679409 DOI: 10.1103/physreve.87.042302] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/25/2013] [Indexed: 06/02/2023]
Abstract
The heat capacity of supercooled water, measured down to -37°C, shows an anomalous increase as temperature decreases. The thermal diffusivity, i.e., the ratio of the thermal conductivity and the heat capacity per unit volume, shows a decrease. These anomalies may be associated with a hypothesized liquid-liquid critical point in supercooled water below the line of homogeneous nucleation. However, while the thermal conductivity is known to diverge at the vapor-liquid critical point due to critical density fluctuations, the thermal conductivity of supercooled water, calculated as the product of thermal diffusivity and heat capacity, does not show any sign of such an anomaly. We have used mode-coupling theory to investigate the possible effect of critical fluctuations on the thermal conductivity of supercooled water and found that indeed any critical thermal-conductivity enhancement would be too small to be measurable at experimentally accessible temperatures. Moreover, the behavior of thermal conductivity can be explained by the observed anomalies of the thermodynamic properties. In particular, we show that thermal conductivity should go through a minimum when temperature is decreased, as Kumar and Stanley observed in the TIP5P model of water. We discuss physical reasons for the striking difference between the behavior of thermal conductivity in water near the vapor-liquid and liquid-liquid critical points.
Collapse
Affiliation(s)
- John W Biddle
- Institute for Physical Science and Technology and Department of Chemical and Biomolecular Engineering, University of Maryland, College Park, Maryland 20742, USA
| | | | | | | |
Collapse
|
14
|
Oprisan A, Oprisan SA, Bayley B, Hegseth JJ, Garrabos Y, Lecoutre-Chabot C, Beysens D. Dynamic structure factor of density fluctuations from direct imaging very near (both above and below) the critical point of SF(6). PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:061501. [PMID: 23367952 DOI: 10.1103/physreve.86.061501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2012] [Revised: 10/02/2012] [Indexed: 06/01/2023]
Abstract
Large density fluctuations were observed by illuminating a cylindrical cell filled with sulfur hexafluoride (SF(6)), very near its liquid-gas critical point (|T-T(c)|< 300 μK) and recorded using a microscope with 3 μm spatial resolution. Using a dynamic structure factor algorithm, we determined from the recorded images the structure factor (SF), which measures the spatial distribution of fluctuations at different moments, and the correlation time of fluctuations. This method authorizes local measurements in contrast to the classical scattering techniques that average fluctuations over the illuminating beam. We found that during the very early stages of phase separation the SF scales with the wave vector q according to the Lorentzian q(-2), which shows that the liquid and vapor domains are just emerging. The critical wave number, which is related to the characteristic length of fluctuations, steadily decreases over time, supporting a sustained increase in the spatial scale of the fluctuating domains. The scaled evolution of the critical wave number obeys the universal evolution for the interconnected domains at high volume fraction with an apparent power law exponent of -0.35 ± 0.02. We also determined the correlation time of the fluctuations and inferred values for thermal diffusivity coefficient very near the critical point, above and below. The values were used to pinpoint the crossing of T(c) within 13 μK.
Collapse
Affiliation(s)
- Ana Oprisan
- Department of Physics and Astronomy, College of Charleston, 66 George Street, Charleston, South Carolina 29424, USA
| | | | | | | | | | | | | |
Collapse
|
15
|
Gross M, Varnik F. Critical dynamics of an isothermal compressible nonideal fluid. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:061119. [PMID: 23367905 DOI: 10.1103/physreve.86.061119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2012] [Revised: 08/23/2012] [Indexed: 06/01/2023]
Abstract
A pure fluid at its critical point shows a dramatic slow-down in its dynamics, due to a divergence of the order-parameter susceptibility and the coefficient of heat transport. Under isothermal conditions, however, sound waves provide the only possible relaxation mechanism for order-parameter fluctuations. Here we study the critical dynamics of an isothermal, compressible nonideal fluid via scaling arguments and computer simulations of the corresponding fluctuating hydrodynamics equations. We show that, below a critical dimension of 4, the order-parameter dynamics of an isothermal fluid effectively reduces to "model A," characterized by overdamped sound waves and a divergent bulk viscosity. In contrast, the shear viscosity remains finite above two dimensions. Possible applications of the model are discussed.
Collapse
Affiliation(s)
- Markus Gross
- Interdisciplinary Centre for Advanced Materials Simulation, Ruhr-Universität Bochum, Universitätsstr 90a, 44789 Bochum, Germany.
| | | |
Collapse
|
16
|
|
17
|
Mclure IA, Clements PJ. Shear Viscosity of Hexane+Tetradecafluorohexane near the Upper Critical Endpoint. ACTA ACUST UNITED AC 2010. [DOI: 10.1002/bbpc.19971010115] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
|
18
|
Zausch J, Virnau P, Binder K, Horbach J, Vink RL. Statics and dynamics of colloid-polymer mixtures near their critical point of phase separation: A computer simulation study of a continuous Asakura–Oosawa model. J Chem Phys 2009; 130:064906. [DOI: 10.1063/1.3071197] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
19
|
Das SK, Sengers JV, Fisher ME. Simulating critical dynamics in liquid mixtures: Short-range and long-range contributions. J Chem Phys 2007; 127:144506. [DOI: 10.1063/1.2770736] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
20
|
Kostko AF, Anisimov MA, Sengers JV. Dynamics of critical fluctuations in polymer solutions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:021804. [PMID: 17930058 DOI: 10.1103/physreve.76.021804] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2007] [Indexed: 05/25/2023]
Abstract
Using dynamic light scattering we have investigated the time dependence of fluctuations near the critical point of phase separation in solutions of polystyrene in cyclohexane with polymer molecular weights ranging from 196,000 to 11.4 x 10(6) g mol(-1). At the lowest polymer molecular weight the dynamic correlation function follows a single-exponential decay with a decay rate that can be represented by the mode-coupling theory of critical dynamics but with a mesoscopic viscosity that characterizes the hydrodynamic environment of the polymers in the solution. At all higher polymer molecular weights two distinct dynamic modes are observed, a slow and a fast mode, that originate from a coupling of the critical concentration fluctuations with viscoelastic relaxation of the polymer chain in solutions. This coupling causes an additional slowing down of the fluctuations on top of the well-known critical slowing down expected in the absence of a coupling between the two modes. From an analysis of the time dependence of the experimental dynamic correlation functions in terms of a theory of coupling of dynamic modes we are able to determine the viscoelastic properties of the polymers in the solution. These viscoelastic properties diverge in the theta-point limit of infinite polymer molecular weight.
Collapse
Affiliation(s)
- A F Kostko
- Chemical and Life Sciences Engineering, School of Engineering, Virginia Commonwealth University, Richmond, Virginia 23284, USA
| | | | | |
Collapse
|
21
|
Das SK, Horbach J, Binder K, Fisher ME, Sengers JV. Static and dynamic critical behavior of a symmetrical binary fluid: A computer simulation. J Chem Phys 2006; 125:24506. [PMID: 16848591 DOI: 10.1063/1.2215613] [Citation(s) in RCA: 75] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A symmetrical binary, A+B Lennard-Jones mixture is studied by a combination of semi-grand-canonical Monte Carlo (SGMC) and molecular dynamics (MD) methods near a liquid-liquid critical temperature T(c). Choosing equal chemical potentials for the two species, the SGMC switches identities (A-->B-->A) to generate well-equilibrated configurations of the system on the coexistence curve for T<T(c) and at the critical concentration, x(c)=12, for T>T(c). A finite-size scaling analysis of the concentration susceptibility above T(c) and of the order parameter below T(c) is performed, varying the number of particles from N=400 to 12 800. The data are fully compatible with the expected critical exponents of the three-dimensional Ising universality class. The equilibrium configurations from the SGMC runs are used as initial states for microcanonical MD runs, from which transport coefficients are extracted. Self-diffusion coefficients are obtained from the Einstein relation, while the interdiffusion coefficient and the shear viscosity are estimated from Green-Kubo expressions. As expected, the self-diffusion constant does not display a detectable critical anomaly. With appropriate finite-size scaling analysis, we show that the simulation data for the shear viscosity and the mutual diffusion constant are quite consistent both with the theoretically predicted behavior, including the critical exponents and amplitudes, and with the most accurate experimental evidence.
Collapse
Affiliation(s)
- Subir K Das
- Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA
| | | | | | | | | |
Collapse
|
22
|
Das SK, Fisher ME, Sengers JV, Horbach J, Binder K. Critical dynamics in a binary fluid: simulations and finite-size scaling. PHYSICAL REVIEW LETTERS 2006; 97:025702. [PMID: 16907461 DOI: 10.1103/physrevlett.97.025702] [Citation(s) in RCA: 52] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2006] [Indexed: 05/11/2023]
Abstract
We report comprehensive simulations of the critical dynamics of a symmetric binary Lennard-Jones mixture near its consolute point. The self-diffusion coefficient exhibits no detectable anomaly. The data for the shear viscosity and the mutual-diffusion coefficient are fully consistent with the asymptotic power laws and amplitudes predicted by renormalization-group and mode-coupling theories provided finite-size effects and the background contribution to the relevant Onsager coefficient are suitably accounted for. This resolves a controversy raised by recent molecular simulations.
Collapse
Affiliation(s)
- Subir K Das
- Institute for Physical Science and Technology, University of Maryland, College Park, 20742, USA
| | | | | | | | | |
Collapse
|
23
|
|
24
|
Haller J, Behrends R, Kaatze U. Critical fluctuations of the micellar triethylene glycol monoheptyl ether-water system. J Chem Phys 2006; 124:124910. [PMID: 16599728 DOI: 10.1063/1.2179424] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Using the equal volume criterion and also the pseudospinodal conception the critical demixing point of the triethylene glycol monoheptyl ether/water system (C7E3H2O) has been determined as Ycrit=0.1 and Tcrit=296.46 K (Y, mass fraction of surfactant). From density measurements the critical micelle concentration (cmc) followed as Ycmc=0.007 at 288.15 K and Ycmc=0.0066 at 298.15 K. The (static) shear viscosity etas and the mutual diffusion coefficient D of the C7E3H2O mixture of critical composition have been evaluated to yield their singular and background parts. From a combined treatment of both quantities the relaxation rate Gamma of order parameter fluctuations has been derived. Gamma follows power law with universal critical exponent and amplitude Gamma0=3.1 x 10(9) s(-1). Broadband ultrasonic spectra of C7E3H2O mixtures exhibit a noncritical relaxation, reflecting the monomer exchange between micelles and the suspending phase, and a critical term due to concentration fluctuations. The former is subject to a relaxation time distribution that broadens when approaching the critical temperature. The latter can be well represented with the aid of the dynamic scaling model by Bhattacharjee and Ferrell (BF) [Phys. Rev. A. 31, 1788 (1985)]. The half-attenuation frequency in the scaling function of the latter model is noticeably smaller (Omega12 (BF) approximately 1) than the theoretically predicted value Omega12 (BF)=2.1. This result has been taken as an indication of a coupling between the fluctuations in the local concentration and the kinetics of micelle formation, in correspondence with the idea of a fluctuation controlled monomer exchange [T. Telgmann and U. Kaatze, Langmuir 18, 3068 (2002)].
Collapse
Affiliation(s)
- J Haller
- Drittes Physikalisches Institut, Georg-August-Universität, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | | | | |
Collapse
|
25
|
Iwanowski I, Leluk K, Rudowski M, Kaatze U. Critical Dynamics of the Binary System Nitroethane/3-Methylpentane: Relaxation Rate and Scaling Function. J Phys Chem A 2006; 110:4313-9. [PMID: 16571033 DOI: 10.1021/jp0569584] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Shear viscosity and dynamic light scattering measurements as well as ultrasonic spectrometry studies of the nitroethane/3-methylpentane mixture of critical composition have been performed at various temperatures near the critical temperature, T(c). A combined evaluation of the shear viscosity and mutual diffusion coefficient data yielded the amplitude, xi(0), of the fluctuation correlation length, xi, assumed to follow power law, and the relaxation rate, Gamma, or order parameter fluctuations. The latter was found to follow power law with the theoretical universal exponent. The amplitudes xi(0) = 0.23 +/- 0.02 nm and Gamma(0) = (125 +/- 5) x 10(9) s(-1) nicely agree with literature values. Using the relaxation rates resulting from the viscosity and diffusion coefficient data, the scaling function has been calculated assuming the ultrasonic spectra to be composed of a critical part and a noncritical background contribution. The experimental scaling function fits well to the predictions of the Bhattacharjee-Ferrell dynamic scaling model with scaled half-attenuation frequency, Omega(BF)1/2= 2.1. The amplitude of the sonic spectra yields the amount |g| = 0.26 of the adiabatic coupling constant, g, in fair agreement with -0.29 from another thermodynamic relation.
Collapse
Affiliation(s)
- I Iwanowski
- Drittes Physikalisches Institut, Georg-August-Universität, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | | | | | | |
Collapse
|
26
|
Onuki A, Kanatani K. Droplet motion with phase change in a temperature gradient. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:066304. [PMID: 16486056 DOI: 10.1103/physreve.72.066304] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2005] [Indexed: 05/06/2023]
Abstract
We examine the droplet motion in one-component fluids in a small temperature gradient by solving linearized hydrodynamic equations supplemented with appropriate surface boundary conditions. We show that the velocity field and the temperature around the droplet are strongly influenced by first-order phase transition taking place at the interface. Latent heat released or absorbed at the interface drastically changes the hydrodynamic flow around the droplet. As a result, the temperature becomes almost homogeneous inside the droplet and the Marangoni effect arising from the surface tension gradient is much suppressed. The droplet velocity is also much decelerated.
Collapse
Affiliation(s)
- Akira Onuki
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
| | | |
Collapse
|
27
|
Jagannathan K, Yethiraj A. Dynamics of fluids near the consolute critical point: A molecular-dynamics study of the Widom–Rowlinson mixture. J Chem Phys 2005; 122:244506. [PMID: 16035781 DOI: 10.1063/1.1940053] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Molecular-dynamics simulations are presented for the dynamic behavior of the Widom-Rowlinson mixture [B. Widom, and J. S. Rowlinson, J. Chem. Phys. 52, 1670 (1970)] at its critical point. This model consists of two components where like species do not interact and unlike species interact via a hard-core potential. Critical exponents are obtained from a finite-size scaling analysis. The self-diffusion coefficient shows no anomalous behavior near the critical point. The shear viscosity and thermal conductivity show no divergent behavior for the system sizes considered, although there is a significant critical enhancement. The mutual diffusion coefficient, D(AB), vanishes as D(AB) approximately xi(-1.26 +/- 0.08), where xi is the correlation length. This is different from the renormalization-group (D(AB) approximately xi(-1.065)) mode coupling theory (D(AB) approximately xi(-1)) predictions. The theories and simulations can be reconciled if we assume that logarithmic corrections to scaling are important.
Collapse
|
28
|
Behrends R, Iwanowski I, Kosmowska M, Szala A, Kaatze U. Sound attenuation, shear viscosity, and mutual diffusivity behavior in the nitroethane-cyclohexane critical mixture. J Chem Phys 2004; 121:5929-34. [PMID: 15367021 DOI: 10.1063/1.1781614] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The shear viscosity eta(s), mutual diffusion coefficient D, and ultrasonic attenuation spectra of the nitroethane-cyclohexane mixture of critical composition have been measured at various temperatures near the critical temperature T(c). The relaxation rate of order parameter fluctuations resulting from a combined evaluation of the eta(s) and D data follows power law behavior with the theoretical exponent and with the large amplitude Gamma(o)=(156+/-2)x10(9) s(-1). The ultrasonic spectra have been evaluated in terms of a critical contribution and a noncritical background contribution. The amplitude of the former exhibits a temperature dependence, in conformity with a temperature dependence in the adiabatic coupling constant (|g| = 0.064 near T(c) and 0.1 at T-T(c)=3 K). If the variation of the critical amplitude with T is taken into account the experimental attenuation coefficient data display a scaling function which nicely fits to the theoretical prediction from the Bhattacharjee-Ferrell dynamic scaling model [R. A. Ferrell and J. K. Bhattacharjee, Phys. Rev. A 31, 1788 (1985)].
Collapse
Affiliation(s)
- R Behrends
- Drittes Physikalisches Institut, Georg-August-Universität, Bürgerstrasse 42-44, 37073 Göttingen, Germany
| | | | | | | | | |
Collapse
|
29
|
Iwanowski I, Behrends R, Kaatze U. Critical fluctuations near the consolute point of n-pentanol-nitromethane. An ultrasonic spectrometry, dynamic light scattering, and shear viscosity study. J Chem Phys 2004; 120:9192-8. [PMID: 15267856 DOI: 10.1063/1.1703524] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Ultrasonic attenuation spectra, the shear viscosity, and the mutual diffusion coefficient of the n-pentanol-nitromethane mixture of critical composition have been measured at different temperatures near the critical temperature. The noncritical background contribution, proportional to frequency, to the acoustical attenuation-per-wavelength spectra has been determined and subtracted from the total attenuation to yield the critical contribution. When plotted versus the reduced frequency, with the relaxation rate of order-parameter fluctuations from the shear viscosity and diffusion coefficient measurements, the critical part in the sonic attenuation coefficient displays a scaling function which nicely fits to the data for the critical system 3-methylpentane-nitromethane and also to the empirical scaling function of the Bhattacharjee-Ferrell dynamic scaling theory. The scaled half-attenuation frequency follows from the experimental data as Omega(1/2)emp= 1.8+/-0.1. The relaxation rate of order-parameter fluctuation shows power-law behavior with the theoretically predicted universal exponent and the extraordinary high amplitude Gammao= (187+/-2) x 10(9) s(-1). The amount of the adiabatic coupling constant /g/= 0.03, as estimated from the amplitude of the critical contribution to the acoustical spectra, is unusually small.
Collapse
Affiliation(s)
- I Iwanowski
- Drittes Physikalisches Institut, Georg-August-Universität, Burgerstrasse 42-44, D-37073 Göttingen, Germany
| | | | | |
Collapse
|
30
|
Huber ML, Laesecke A, Perkins RA. Model for the Viscosity and Thermal Conductivity of Refrigerants, Including a New Correlation for the Viscosity of R134a. Ind Eng Chem Res 2003. [DOI: 10.1021/ie0300880] [Citation(s) in RCA: 106] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
|
31
|
|
32
|
Cherayil BJ. Anomalies in the self-diffusion coefficient near the critical point. J Chem Phys 2002. [DOI: 10.1063/1.1471549] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
33
|
Drozd-Rzoska A. Shear viscosity studies above and below the critical consolute point in a nitrobenzene-decane mixture. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:8071-8075. [PMID: 11138091 DOI: 10.1103/physreve.62.8071] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/1999] [Revised: 06/01/2000] [Indexed: 05/23/2023]
Abstract
The shear viscosity has been studied in a nitrobenzene-decane critical mixture above the critical consolute temperature T(C), in the homogeneous phase, and below T(C), in coexisting phases. The form of background viscosity for coexisting phases has been postulated. The same value of the critical exponent straight phi has been obtained in the lower (L), upper (U), and homogeneous (H) phases. The pretransitional amplitudes (A(L,U)) in coexisting phases are approximately the same, whereas A(L,U)/A(H) approximately 0.965. In the homogeneous phase the possibility of the appearance of the quasinematic, field-induced structure of critical fluctuations has been discussed.
Collapse
Affiliation(s)
- A Drozd-Rzoska
- August Chelkowski" Institute of Physics, Silesian University, ulica Uniwersytecka 4 40-007 Katowice, Poland
| |
Collapse
|
34
|
Flossmann G, Folk R. Critical light scattering in liquids. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:2460-70. [PMID: 11088725 DOI: 10.1103/physreve.62.2460] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2000] [Indexed: 11/07/2022]
Abstract
We compare theoretical results for the characteristic frequency of the Rayleigh peak calculated in one-loop order within the field theoretical method of the renormalization group theory with experiments and other theoretical results. Our expressions describe the nonasymptotic crossover in temperature, density, and wave vector. In addition we discuss the frequency dependent shear viscosity evaluated within the same model and compare our theoretical results with recent experiments in microgravity.
Collapse
Affiliation(s)
- G Flossmann
- Institute for Theoretical Physics, University of Linz, A-4040 Linz, Austria
| | | |
Collapse
|
35
|
Berg RF, Moldover MR, Zimmerli GA. Frequency-dependent viscosity of xenon near the critical point. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:4079-98. [PMID: 11970244 DOI: 10.1103/physreve.60.4079] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/1999] [Indexed: 04/18/2023]
Abstract
We used a novel, overdamped oscillator aboard the Space Shuttle to measure the viscosity eta of xenon near its critical density rho(c) and temperature Tc. In microgravity, useful data were obtained within 0.1 mK of Tc, corresponding to a reduced temperature t=(T-Tc)/Tc=3 x 10(-7). Because they avoid the detrimental effects of gravity at temperatures two decades closer to T(c) than the best ground measurements, the data directly reveal the expected power-law behavior eta proportional, variant t(-nuz(eta)). Here nu is the correlation length exponent, and our result for the viscosity exponent is z(eta)=0.0690+/-0.0006. (All uncertainties are one standard uncertainty.) Our value for z(eta) depends only weakly on the form of the viscosity crossover function, and it agrees with the value 0.067+/-0.002 obtained from a recent two-loop perturbation expansion [H. Hao, R.A. Ferrell, and J.K. Bhattacharjee, (unpublished)]. The measurements spanned the frequency range 2 Hz< or = f < or =12 Hz and revealed viscoelasticity when t < or = 10(-5), further from Tc than predicted. The viscoelasticity's frequency dependence scales as Aftau, where tau is the fluctuation-decay time. The fitted value of the viscoelastic time-scale parameter A is 2.0+/-0.3 times the result of a one-loop perturbation calculation. Near Tc, the xenon's calculated time constant for thermal diffusion exceeded days. Nevertheless, the viscosity results were independent of the xenon's temperature history, indicating that the density was kept near rho(c) by judicious choices of the temperature versus time program. Deliberately bad choices led to large density inhomogeneities. At t>10(-5), the xenon approached equilibrium much faster than expected, suggesting that convection driven by microgravity and by electric fields slowly stirred the sample.
Collapse
Affiliation(s)
- R F Berg
- Physical and Chemical Properties Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8380, USA
| | | | | |
Collapse
|
36
|
Flossmann G, Folk R, Moser G. Frequency-dependent shear viscosity, sound velocity, and sound attenuation near the critical point in liquids. III. The shear viscosity. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:779-91. [PMID: 11969819 DOI: 10.1103/physreve.60.779] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/1998] [Indexed: 04/18/2023]
Abstract
We compare theoretical results for the shear viscosity calculated in one-loop order within the field-theoretical method of the renormalization-group theory with experiments. Our expressions describe the nonasymptotic crossover in both temperature and density, and allow us to consider effects of finite gravitation and finite frequency at which the experiments are performed. In doing so we treat the critical exponent x(eta) of the shear viscosity as an independent parameter, keeping the one-loop value of the Kawasaki amplitude fixed. Within our model we also consider the temperature and density dependence of the thermal diffusion including gravitational effects.
Collapse
Affiliation(s)
- G Flossmann
- Institute for Theoretical Physics, University of Linz, Linz, Austria
| | | | | |
Collapse
|
37
|
Sakonidou EP, van den Berg HR, ten Seldam CA, Sengers JV. The thermal conductivity of an equimolar methane–ethane mixture in the critical region. J Chem Phys 1998. [DOI: 10.1063/1.476611] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
38
|
Sakonidou EP, van den Berg HR, ten Seldam CA, Sengers JV. The thermal conductivity of methane in the critical region. J Chem Phys 1996. [DOI: 10.1063/1.472943] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
39
|
Luettmer‐Strathmann J, Sengers JV. The transport properties of fluid mixtures near the vapor–liquid critical line. J Chem Phys 1996. [DOI: 10.1063/1.471070] [Citation(s) in RCA: 44] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|