Mechanical approach to chemical transport

Nonequilibrium thermodynamics describes the rates of transport phenomena with the aid of various thermodynamic forces, but often the phenomenological transport coefficients are not known, and the description is not easily connected with equilibrium relations. We present a simple and intuitive model to address these issues. Our model is based on Lagrangian dynamics for chemical systems with dissipation, so one may think of the model as physicochemical mechanics. Using one main equation, the model allows a systematic derivation of all transport and equilibrium equations, subject to the limitation that heat generated or absorbed in the system must be small for the model to be valid. A table with all major examples of transport and equilibrium processes described using physicochemical mechanics is given. In equilibrium, physicochemical mechanics reduces to standard thermodynamics and the Gibbs–Duhem relation, and we show that the First and Second Laws of thermodynamics are satisfied for our system plus bath model. Out of equilibrium, our model provides relationships between transport coefficients and describes system evolution in the presence of several simultaneous external fields. The model also leads to an extension of the Onsager–Casimir reciprocal relations for properties simultaneously transported by many components.

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A Derivation of the Main Relations of Nonequilibrium Thermodynamics

ISRN Thermodynamics ◽

10.1155/2013/906136 ◽

2013 ◽

Vol 2013 ◽

pp. 1-9 ◽

Cited By ~ 3

Author(s):

Vladimir N. Pokrovskii

Keyword(s):

Nonequilibrium Thermodynamics ◽

Second Law Of Thermodynamics ◽

Thermodynamic System ◽

Internal Variables ◽

Second Law ◽

Basic Principles ◽

First Law Of Thermodynamics ◽

Sum Of Products ◽

Thermodynamic Forces ◽

Production Of Entropy

The principles of nonequilibrium thermodynamics are discussed, using the concept of internal variables that describe deviations of a thermodynamic system from the equilibrium state. While considering the first law of thermodynamics, work of internal variables is taken into account. It is shown that the requirement that the thermodynamic system cannot fulfil any work via internal variables is equivalent to the conventional formulation of the second law of thermodynamics. These statements, in line with the axioms introducing internal variables can be considered as basic principles of nonequilibrium thermodynamics. While considering stationary nonequilibrium situations close to equilibrium, it is shown that known linear parities between thermodynamic forces and fluxes and also the production of entropy, as a sum of products of thermodynamic forces and fluxes, are consequences of fundamental principles of thermodynamics.

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Nonequilibrium thermodynamics in field theory: Transport coefficients

Annals of Physics ◽

10.1016/0003-4916(84)90144-1 ◽

1984 ◽

Vol 154 (1) ◽

pp. 229-252 ◽

Cited By ~ 144

Author(s):

Akio Hosoya ◽

Masa-aki Sakagami ◽

Masaru Takao

Keyword(s):

Field Theory ◽

Nonequilibrium Thermodynamics ◽

Transport Coefficients

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Nonequilibrium thermodynamics in field theory: Transport coefficients

Annals of Physics ◽

10.1016/0003-4916(84)90032-0 ◽

1984 ◽

Vol 153 (2) ◽

pp. 447

Keyword(s):

Field Theory ◽

Nonequilibrium Thermodynamics ◽

Transport Coefficients

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Corrosion-Fatigue Structural Integrity Assessment Using a Thermodynamic Entropy Based Damage Approach

Volume 14: Emerging Technologies; Safety Engineering and Risk Analysis; Materials: Genetics to Structures ◽

10.1115/imece2015-53452 ◽

2015 ◽

Author(s):

Anahita Imanian ◽

Mohammad Modarres

Keyword(s):

Entropy Generation ◽

Corrosion Fatigue ◽

Structural Integrity ◽

Degradation Mechanism ◽

Health Assessment ◽

Irreversible Thermodynamics ◽

Integrity Assessment ◽

Thermodynamic Entropy ◽

Equilibrium Processes ◽

Thermodynamic Forces

Using fundamentals of irreversible thermodynamics, with specific focus on entropy generation, this paper studies the structural integrity of degraded materials. All damage mechanisms share a common feature namely energy dissipation. Dissipation, as a fundamental measure for irreversibility in a thermodynamic treatment of non-equilibrium processes, is quantified by entropy generation. Based on the theoretical relationship between entropy generation and generalized thermodynamic forces and fluxes, the entropic damage is measured during a corrosion-fatigue degradation experiment. Life estimation of components, which were subject to complex corrosion-fatigue degradation mechanism, was then estimated through a proposed entropic-based prognostic framework. The performance of predictions was evaluated and compared with previous predictions in terms of the influence of additional features on components health assessment.

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Nonequilibrium thermodynamics and continued fraction expansions of transport coefficients

Physics Letters A ◽

10.1016/0375-9601(89)90358-7 ◽

1989 ◽

Vol 134 (7) ◽

pp. 400-404 ◽

Cited By ~ 9

Author(s):

D. Jou ◽

M. Ferrer

Keyword(s):

Continued Fraction ◽

Nonequilibrium Thermodynamics ◽

Transport Coefficients ◽

Continued Fraction Expansions

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Transport Phenomena

10.1093/oso/9780199592357.003.0004 ◽

2018 ◽

Author(s):

Sauro Succi

Keyword(s):

Distribution Function ◽

Transport Phenomena ◽

Transport Coefficients ◽

Mean Free Path ◽

Microscopic Scale ◽

Equilibrium Processes ◽

Intimate Relation ◽

Non Equilibrium

The previous Chapter presented a discussion of the notion of local and global equilibria and shown that these equilibria represent the special forms taken by the distribution function once direct and inverse collisions come into balance. This Chapter provides an elementary introduction to transport phenomena and discusses their intimate relation to non-equilibrium processes at the microscopic scale. In particular it shall deal with the connection between the transport coefficients, such as mass, momentum and energy diffusivity with the molecular mean free path, namely the distance traveled by a representative molecules between two subsequent collisions. The discussion also highlights the fundamental role of inhomogeneity in fueling non-equilibrium processes.

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SOLUTION OF THE MAIN DIFFERENTIAL EQUATION OF DEFORMATIONS OF THE CASING IN A CURVED WELL

Scientific Bulletin of Ivano-Frankivsk National Technical University of Oil and Gas ◽

10.31471/1993-9965-2019-1(46)-25-34 ◽

2019 ◽

pp. 25-34

Author(s):

I. I. Paliichuk

Keyword(s):

Differential Equation ◽

First Integral ◽

Partial Solution ◽

Variable Coefficients ◽

Elastic Rod ◽

Equilibrium Equations ◽

Inhomogeneous Differential Equation ◽

Main Requirement ◽

Main Equation ◽

External Forces

In a curvilinear well, the casing functions as a long continuous rod. It is installed on the supports-centralizers and replicates the complex profile of the well, as a result of which it receives large deformations. To describe them, a system of differential equilibrium equations of internal and external forces and moments was composed, which was supplemented to a closed form with a differential equation of curvature. It is non-uniform, because it takes into account the own distributed weight of the rod. Two ways are proposed to solve the problem: by the method of mathematical compression of the system equations into a complex inhomogeneous differential equation or by projecting the equilibrium equations of forces on the global (vertical-horizontal) and on the local (tangent-normal) coordinate systems. It is shown that the first integral of the system can also be found from the equilibrium equations of a portion of a curved rod of finite length. This integral has the form of a second-order inhomogeneous differential equation with variable coefficients and is the main equation that describes the deformation of a long elastic rod under the action of the longitudinal and transverse components of the forces of distributed weight. The main requirement of the technology is the installation of a pipes column on the centering supports, the purpose of which is to ensure the coaxiality of the pipes and the borehole walls and the creation between them a cement ring of the same thickness and strength. Accounting for this requirement allowed us to linearize the main equation. Its solution is the clue to the formulas of deflections, angular slopes, internal bending moments and transverse forces in the rod with the arbitrary arrangement of supports and boundary conditions in their intersections. The solution of the main differential equation of angular deformations of a long bar is found in the form of a linear combination of Airy and Scorer’s functions and in the form of three linearly independent polynomial series in the sum with a partial solution. The obtained formulas of flexure and power parameters allow us to calculate stress and strain in the pipes column during the process of casing the borehole of an arbitrary profile which increases the reliability and durability of the well.

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