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21 pages, 337 KiB

Open AccessArticle

Thermodynamic Explanation of Landau Damping by Reduction to Hydrodynamics

by Michal Pavelka, Václav Klika and Miroslav Grmela

Entropy 2018, 20(6), 457; https://doi.org/10.3390/e20060457 - 12 Jun 2018

Cited by 5 | Viewed by 3366

Landau damping is the tendency of solutions to the Vlasov equation towards spatially homogeneous distribution functions. The distribution functions, however, approach the spatially homogeneous manifold only weakly, and Boltzmann entropy is not changed by the Vlasov equation. On the other hand, density and [...] Read more.

Landau damping is the tendency of solutions to the Vlasov equation towards spatially homogeneous distribution functions. The distribution functions, however, approach the spatially homogeneous manifold only weakly, and Boltzmann entropy is not changed by the Vlasov equation. On the other hand, density and kinetic energy density, which are integrals of the distribution function, approach spatially homogeneous states strongly, which is accompanied by growth of the hydrodynamic entropy. Such a behavior can be seen when the Vlasov equation is reduced to the evolution equations for density and kinetic energy density by means of the Ehrenfest reduction. Full article

(This article belongs to the Special Issue Mesoscopic Thermodynamics and Dynamics)

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27 pages, 961 KiB

Open AccessArticle

Thermoelectricity and Thermodiffusion in Magnetic Nanofluids: Entropic Analysis

by Thomas J. Salez, Sawako Nakamae, Régine Perzynski, Guillaume Mériguet, Andrejs Cebers and Michel Roger

Entropy 2018, 20(6), 405; https://doi.org/10.3390/e20060405 - 24 May 2018

Cited by 21 | Viewed by 4609

Abstract

An analytical model describing the thermoelectric potential production in magnetic nanofluids (dispersions of magnetic and charged colloidal particles in liquid media) is presented. The two major entropy sources, the thermogalvanic and thermodiffusion processes are considered. The thermodiffusion term is described in terms of [...] Read more.

An analytical model describing the thermoelectric potential production in magnetic nanofluids (dispersions of magnetic and charged colloidal particles in liquid media) is presented. The two major entropy sources, the thermogalvanic and thermodiffusion processes are considered. The thermodiffusion term is described in terms of three physical parameters; the diffusion coefficient, the Eastman entropy of transfer and the electrophoretic charge number of colloidal particles, which all depend on the particle concentration and the applied magnetic field strength and direction. The results are combined with well-known formulation of thermoelectric potential in thermogalvanic cells and compared to the recent observation of Seebeck coefficient enhancement/diminution in magnetic nanofluids in polar media. Full article

(This article belongs to the Special Issue Mesoscopic Thermodynamics and Dynamics)

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18 pages, 1403 KiB

Open AccessArticle

Thermoelectric Efficiency of a Topological Nano-Junction

by Manuel Álamo and Enrique Muñoz

Entropy 2018, 20(5), 366; https://doi.org/10.3390/e20050366 - 14 May 2018

Cited by 2 | Viewed by 3174

Abstract

We studied the non-equilibrium current, transport coefficients and thermoelectric performance of a nano-junction, composed by a quantum dot connected to a normal superconductor and a topological superconductor leads, respectively. We considered a one-dimensional topological superconductor, which hosts two Majorana fermion states at its [...] Read more.

We studied the non-equilibrium current, transport coefficients and thermoelectric performance of a nano-junction, composed by a quantum dot connected to a normal superconductor and a topological superconductor leads, respectively. We considered a one-dimensional topological superconductor, which hosts two Majorana fermion states at its edges. Our results show that the electric and thermal currents across the junction are highly mediated by multiple Andreev reflections between the quantum dot and the leads, thus leading to a strong nonlinear dependence of the current on the applied bias voltage. Remarkably, we find that our system reaches a sharp maximum of its thermoelectric efficiency at a finite bias, when an external magnetic field is imposed upon the junction. We propose that this feature can be used for accurate temperature sensing at the nanoscale. Full article

(This article belongs to the Special Issue Mesoscopic Thermodynamics and Dynamics)

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11 pages, 422 KiB

Open AccessArticle

Thermodynamics at Solid–Liquid Interfaces

by Michael Frank and Dimitris Drikakis

Entropy 2018, 20(5), 362; https://doi.org/10.3390/e20050362 - 12 May 2018

Cited by 22 | Viewed by 5405

Abstract

The variation of the liquid properties in the vicinity of a solid surface complicates the description of heat transfer along solid–liquid interfaces. Using Molecular Dynamics simulations, this investigation aims to understand how the material properties, particularly the strength of the solid–liquid interaction, affect [...] Read more.

The variation of the liquid properties in the vicinity of a solid surface complicates the description of heat transfer along solid–liquid interfaces. Using Molecular Dynamics simulations, this investigation aims to understand how the material properties, particularly the strength of the solid–liquid interaction, affect the thermal conductivity of the liquid at the interface. The molecular model consists of liquid argon confined by two parallel, smooth, solid walls, separated by a distance of 6.58 σ. We find that the component of the thermal conductivity parallel to the surface increases with the affinity of the solid and liquid. Full article

(This article belongs to the Special Issue Mesoscopic Thermodynamics and Dynamics)

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14 pages, 6284 KiB

Open AccessArticle

Numerical Study on Entropy Generation in Thermal Convection with Differentially Discrete Heat Boundary Conditions

by Zhengdao Wang, Yikun Wei and Yuehong Qian

Entropy 2018, 20(5), 351; https://doi.org/10.3390/e20050351 - 08 May 2018

Cited by 13 | Viewed by 3517

Abstract

Entropy generation in thermal convection with differentially discrete heat boundary conditions at various Rayleigh numbers (Ra) are numerically investigated using the lattice Boltzmann method. We mainly focused on the effects of Ra and discrete heat boundary conditions on entropy generation in [...] Read more.

Entropy generation in thermal convection with differentially discrete heat boundary conditions at various Rayleigh numbers (Ra) are numerically investigated using the lattice Boltzmann method. We mainly focused on the effects of Ra and discrete heat boundary conditions on entropy generation in thermal convection according to the minimal entropy generation principle. The results showed that the presence of the discrete heat source at the bottom boundary promotes the transition to a substantial convection, and the viscous entropy generation rate (S_u) generally increases in magnitude at the central region of the channel with increasing Ra. Total entropy generation rate (S) and thermal entropy generation rate (S_θ) are larger in magnitude in the region with the largest temperature gradient in the channel. Our results also indicated that the thermal entropy generation, viscous entropy generation, and total entropy generation increase exponentially with the increase of Rayleigh number. It is noted that lower percentage of single heat source area in the bottom boundary increases the intensities of viscous entropy generation, thermal entropy generation and total entropy generation. Comparing with the classical homogeneous thermal convection, the thermal entropy generation, viscous entropy generation, and total entropy generation are improved by the presence of discrete heat sources at the bottom boundary. Full article

(This article belongs to the Special Issue Mesoscopic Thermodynamics and Dynamics)

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20 pages, 402 KiB

Open AccessFeature PaperArticle

Extended Thermodynamics of Rarefied Polyatomic Gases: 15-Field Theory Incorporating Relaxation Processes of Molecular Rotation and Vibration

by Takashi Arima, Tommaso Ruggeri and Masaru Sugiyama

Entropy 2018, 20(4), 301; https://doi.org/10.3390/e20040301 - 20 Apr 2018

Cited by 24 | Viewed by 3532

Abstract

After summarizing the present status of Rational Extended Thermodynamics (RET) of gases, which is an endeavor to generalize the Navier–Stokes and Fourier (NSF) theory of viscous heat-conducting fluids, we develop the molecular RET theory of rarefied polyatomic gases with 15 independent fields. The [...] Read more.

After summarizing the present status of Rational Extended Thermodynamics (RET) of gases, which is an endeavor to generalize the Navier–Stokes and Fourier (NSF) theory of viscous heat-conducting fluids, we develop the molecular RET theory of rarefied polyatomic gases with 15 independent fields. The theory is justified, at mesoscopic level, by a generalized Boltzmann equation in which the distribution function depends on two internal variables that take into account the energy exchange among the different molecular modes of a gas, that is, translational, rotational, and vibrational modes. By adopting the generalized Bhatnagar, Gross and Krook (BGK)-type collision term, we derive explicitly the closed system of field equations with the use of the Maximum Entropy Principle (MEP). The NSF theory is derived from the RET theory as a limiting case of small relaxation times via the Maxwellian iteration. The relaxation times introduced in the theory are shown to be related to the shear and bulk viscosities and heat conductivity. Full article

(This article belongs to the Special Issue Mesoscopic Thermodynamics and Dynamics)

8 pages, 1460 KiB

Open AccessArticle

Modeling of the Atomic Diffusion Coefficient in Nanostructured Materials

by Zhiqing Hu, Zhuo Li, Kai Tang, Zi Wen and Yongfu Zhu

Entropy 2018, 20(4), 252; https://doi.org/10.3390/e20040252 - 05 Apr 2018

Cited by 3 | Viewed by 3245

Abstract

A formula has been established, which is based on the size-dependence of a metal’s melting point, to elucidate the atomic diffusion coefficient of nanostructured materials by considering the role of grain-boundary energy. When grain size is decreased, a decrease in the atomic diffusion [...] Read more.

A formula has been established, which is based on the size-dependence of a metal’s melting point, to elucidate the atomic diffusion coefficient of nanostructured materials by considering the role of grain-boundary energy. When grain size is decreased, a decrease in the atomic diffusion activation energy and an increase in the corresponding diffusion coefficient can be observed. Interestingly, variations in the atomic diffusion activation energy of nanostructured materials are small relative to nanoparticles, depending on the size of the grain boundary energy. Our theoretical prediction is in accord with the computer simulation and experimental results of the metals described. Full article

(This article belongs to the Special Issue Mesoscopic Thermodynamics and Dynamics)

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12 pages, 280 KiB

Open AccessArticle

Fluid-Fluid Interfaces of Multi-Component Mixtures in Local Equilibrium

by Dick Bedeaux and Signe Kjelstrup

Entropy 2018, 20(4), 250; https://doi.org/10.3390/e20040250 - 04 Apr 2018

Cited by 7 | Viewed by 3256

Abstract

We derive in a new way that the intensive properties of a fluid-fluid Gibbs interface are independent of the location of the dividing surface. When the system is out of global equilibrium, this finding is not trivial: In a one-component fluid, it can [...] Read more.

We derive in a new way that the intensive properties of a fluid-fluid Gibbs interface are independent of the location of the dividing surface. When the system is out of global equilibrium, this finding is not trivial: In a one-component fluid, it can be used to obtain the interface temperature from the surface tension. In other words, the surface equation of state can serve as a thermometer for the liquid-vapor interface in a one-component fluid. In a multi-component fluid, one needs the surface tension and the relative adsorptions to obtain the interface temperature and chemical potentials. A consistent set of thermodynamic properties of multi-component surfaces are presented. They can be used to construct fluid-fluid boundary conditions during transport. These boundary conditions have a bearing on all thermodynamic modeling on transport related to phase transitions. Full article

(This article belongs to the Special Issue Mesoscopic Thermodynamics and Dynamics)

13 pages, 2490 KiB

Open AccessArticle

Fractional Time Fluctuations in Viscoelasticity: A Comparative Study of Correlations and Elastic Moduli

by Rosalío F. Rodríguez, Elizabeth Salinas-Rodríguez and Jorge Fujioka

Entropy 2018, 20(1), 28; https://doi.org/10.3390/e20010028 - 11 Jan 2018

Cited by 6 | Viewed by 3849

Abstract

We calculate the transverse velocity fluctuations correlation function of a linear and homogeneous viscoelastic liquid by using a generalized Langevin equation (GLE) approach. We consider a long-ranged (power-law) viscoelastic memory and a noise with a long-range (power-law) auto-correlation. We first evaluate [...] Read more.

We calculate the transverse velocity fluctuations correlation function of a linear and homogeneous viscoelastic liquid by using a generalized Langevin equation (GLE) approach. We consider a long-ranged (power-law) viscoelastic memory and a noise with a long-range (power-law) auto-correlation. We first evaluate the transverse velocity fluctuations correlation function for conventional time derivatives

{\hat{C}}_{N F} (\vec{k}, t)

and then introduce time fractional derivatives in their equations of motion and calculate the corresponding fractional correlation function. We find that the magnitude of the fractional correlation

{\hat{C}}_{F} (\vec{k}, t)

is always lower than the non-fractional one and decays more rapidly. The relationship between the fractional loss modulus

G_{F}^{″} (ω)

and

{\hat{C}}_{F} (\vec{k}, t)

is also calculated analytically. The difference between the values of

G^{″} (ω)

for two specific viscoelastic fluids is quantified. Our model calculation shows that the fractional effects on this measurable quantity may be three times as large as compared with its non-fractional value. The fact that the dynamic shear modulus is related to the light scattering spectrum suggests that the measurement of this property might be used as a suitable test to assess the effects of temporal fractional derivatives on a measurable property. Finally, we summarize the main results of our approach and emphasize that the eventual validity of our model calculations can only come from experimentation. Full article

(This article belongs to the Special Issue Mesoscopic Thermodynamics and Dynamics)

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2736 KiB

Open AccessArticle

Surface Interaction of Nanoscale Water Film with SDS from Computational Simulation and Film Thermodynamics

by Tiefeng Peng, Qibin Li, Longhua Xu, Chao He and Liqun Luo

Entropy 2017, 19(11), 620; https://doi.org/10.3390/e19110620 - 18 Nov 2017

Cited by 10 | Viewed by 5364

Abstract

Foam systems have been attracting extensive attention due to their importance in a variety of applications, e.g., in the cleaning industry, and in bubble flotation. In the context of flotation chemistry, flotation performance is strongly affected by bubble coalescence, which in turn relies [...] Read more.

Foam systems have been attracting extensive attention due to their importance in a variety of applications, e.g., in the cleaning industry, and in bubble flotation. In the context of flotation chemistry, flotation performance is strongly affected by bubble coalescence, which in turn relies significantly on the surface forces upon the liquid film between bubbles. Conventionally, unusual short-range strongly repulsive surface interactions for Newton black films (NBF) between two interfaces with thickness of less than 5 nm were not able to be incorporated into the available classical Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory. The non-DLVO interaction would increase exponentially with the decrease of film thickness, as it plays a crucial role in determining liquid film stability. However, its mechanism and origin are still unclear. In the present work, we investigate the surface interaction of free-standing sodium dodecyl-sulfate (SDS) nanoscale black films in terms of disjoining pressure using the molecular simulation method. The aqueous nanoscale film, consisting of a water coating with SDS surfactants, and with disjoining pressure and film tension of SDS-NBF as a function of film thickness, were quantitatively determined by a post-processing technique derived from film thermodynamics. Full article

(This article belongs to the Special Issue Mesoscopic Thermodynamics and Dynamics)

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Review

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23 pages, 5735 KiB

Open AccessEditor’s ChoiceReview

Levitated Nanoparticles for Microscopic Thermodynamics—A Review

by Jan Gieseler and James Millen

Entropy 2018, 20(5), 326; https://doi.org/10.3390/e20050326 - 28 Apr 2018

Cited by 67 | Viewed by 9166

Abstract

Levitated Nanoparticles have received much attention for their potential to perform quantum mechanical experiments even at room temperature. However, even in the regime where the particle dynamics are purely classical, there is a lot of interesting physics that can be explored. Here we [...] Read more.

Levitated Nanoparticles have received much attention for their potential to perform quantum mechanical experiments even at room temperature. However, even in the regime where the particle dynamics are purely classical, there is a lot of interesting physics that can be explored. Here we review the application of levitated nanoparticles as a new experimental platform to explore stochastic thermodynamics in small systems. Full article

(This article belongs to the Special Issue Mesoscopic Thermodynamics and Dynamics)

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