Maxwell times in higher-order generalized hydrodynamics: Classical fluids, and carriers and phonons in semiconductors

Rodrigues, Clóves Gonçalves; Silva, Carlos A. B.; Ramos, J. Galvão; Luzzi, Roberto

doi:10.1103/physreve.95.022104

Cited by 7 publications

(3 citation statements)

References 33 publications

(35 reference statements)

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“…As already stated this technoindustrial process provides a good illustration of the working of MHT, with a, say, visual characterization of the question of contraction of description in MHT [67], as well as the important role of Maxwell time for determining the character of the motion [68].…”

Section: Summary Of Some Applicationsmentioning

confidence: 99%

Higher-order generalized hydrodynamics: Foundations within a nonequilibrium statistical ensemble formalism

et al. 2015

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Construction, in the framework of a nonequilibrium statistical ensemble formalism, of a higher-order generalized hydrodynamics, also referred to as mesoscopic hydrothermodynamics, that is, covering phenomena involving motion of fluids displaying variations short in space and fast in time-unrestricted values of Knudsen numbers, is presented. In that way, an approach is provided enabling the coupling and simultaneous treatment of the kinetics and hydrodynamic levels of descriptions. It is based on a complete thermostatistical approach in terms of the densities of matter and energy and their fluxes of all orders covering systems arbitrarily driven away from equilibrium. The set of coupled nonlinear integrodifferential hydrodynamic equations is derived. They are the evolution equations of the Gradlike moments of all orders, derived from a generalized kinetic equation built in the framework of the nonequilibrium statistical ensemble formalism. For illustration, the case of a system of particles embedded in a fluid acting as a thermal bath is fully described. The resulting enormous set of coupled evolution equations is of unmanageable proportions, thus requiring in practice to introduce an appropriate description using the smallest possible number of variables. We have obtained a hierarchy of Maxwell times, associated to the set of all the higher-order fluxes, which have a particular relevance in the process of providing criteria for establishing the contraction of description.

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Section: Summary Of Some Applicationsmentioning

confidence: 99%

Higher-order generalized hydrodynamics: Foundations within a nonequilibrium statistical ensemble formalism

et al. 2015

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“…The construction of the nonlinear higher-order thermohydrodynamics here presented is based, as noticed, in a nonequilibrium statistical ensemble formalism (NESEF). 41,54,55 and for the sake of completeness, we here very briefly review its foundations. For such purpose, first it needs be noticed that for systems away from equilibrium, several important points need be carefully taken into account in each case under consideration:…”

Section: Appendix A: Kinetic Foundations Of a Generalized Hydrodynamicsmentioning

confidence: 99%

Nonlinear higher-order hydrodynamics: Fluids under driven flow and shear pressure

et al. 2021

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In the context of a nonequilibrium statistical thermodynamics-based on a nonequilibrium statistical ensemble formalism-a generalized hydrodynamics of fluids under driven flow and shear stress is derived. At the thermodynamic level, the nonequilibrium equations of state are derived, which are coupled to the evolution of the basic variables that describe the hydrodynamic motion in such a system. Generalized diffusion-advection and Maxwell-Cattaneo advection equations are obtained in appropriate limiting situations. This nonlinear higher-order hydrodynamics is applied, in an illustration, to the case of a dilute solution of Brownian particles in nonequilibrium conditions and flowing in a solvent acting as a thermal bath. This is done in the framework of such generalized hydrodynamics but truncated up to a second order.

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“…As shown elsewhere [42], a general contraction criterion can be conjectured, namely, a truncation of order r (keeping the densities and their fluxes to order r) can be introduced, once we show that in the spectrum of wavelengths, the motion predominates over the "frontier" motion, λ 2 (r,r+1) = v 2 θ r θ r+1 , where v is of the order of the thermal velocity, and θ r and θ r+1 are the corresponding Maxwell times associated with the r-and r + 1-fluxes [38,46,47]. We recall that the Maxwell time was originally introduced by Maxwell in his fundamental article of 1867 [48] on the dynamical theory of gases in what was related to viscoelasticity.…”

Section: Contraction Of Descriptionmentioning

confidence: 99%

Statistical Mesoscopic Hydro-thermodynamics: the Description of Kinetics and Hydrodynamics of Nonequilibrium Processes in Single Liquids

et al. 2019

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Hydrodynamics, a term apparently introduced by Daniel Bernoulli (1700-1783) to comprise hydrostatic and hydraulics, has a long history with several theoretical approaches. Here, after a descriptive introduction, we present so-called mesoscopic hydro-thermodynamics, which is also referred to as higher-order generalized hydrodynamics, built within the framework of a mechanicalstatistical formalism. It consists of a description of the material and heat motion of fluids in terms of the corresponding densities and their associated fluxes of all orders. In this way, movements are characterized in terms of intermediate to short wavelengths and intermediate to high frequencies.The fluxes have associated Maxwell-like times, which play an important role in determining the appropriate contraction of the description (of the enormous set of fluxes of all orders) necessary to address the characterization of the motion in each experimental setup. This study is an extension of a preliminary article: Physical Review E 91, 063011 (2015).

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Maxwell times in higher-order generalized hydrodynamics: Classical fluids, and carriers and phonons in semiconductors

Cited by 7 publications

References 33 publications

Higher-order generalized hydrodynamics: Foundations within a nonequilibrium statistical ensemble formalism

Higher-order generalized hydrodynamics: Foundations within a nonequilibrium statistical ensemble formalism

Nonlinear higher-order hydrodynamics: Fluids under driven flow and shear pressure

Statistical Mesoscopic Hydro-thermodynamics: the Description of Kinetics and Hydrodynamics of Nonequilibrium Processes in Single Liquids

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