CRYSTAL GROWTH AND THE THERMODYNAMICS OF IRREVERSIBLE PROCESSES

1959 ◽  
Vol 37 (6) ◽  
pp. 739-754 ◽  
Author(s):  
J. S. Kirkaldy
Keyword(s):  
Free Energy ◽  
Steady State ◽  
Entropy Production ◽  
Dendritic Growth ◽  
Transport Processes ◽  
Irreversible Processes ◽  
Interface Morphology ◽  
Crystal Face ◽  
Thermodynamics Of Irreversible Processes ◽  
Alloy Crystal

The principle of minimum rate of entropy production is applied to steady-state transport processes in the neighborhood of an alloy crystal face growing into its melt. The procedure gives a satisfactory rationale of observed interface morphology. It is noted that segregation, which occurs in cellular or dendritic growth of alloys, is a direct manifestation of the system's attempt to minimize entropy production by conserving free energy. The general problems of growth of pure and impure single crystals from the melt and vapor are discussed.

scholarly journals Crystal Growth and Solute Trapping

1983 ◽  
Vol 23 ◽  
Author(s):  
Michael J. Aziz
Keyword(s):  
Free Energy ◽  
Steady State ◽  
Laser Annealing ◽  
Solute Drag ◽  
Irreversible Processes ◽  
Maximum Speed ◽  
Growth Speed ◽  
Solute Trapping ◽  
Order Of Magnitude ◽  
Energy Dissipated

ABSTRACTA simple model for solute trapping during rapid solidification is presented in terms of a single unknown parameter, the interfacial diffusivity Di. A transition from equilibrium segregation to complete solute trapping occurs over roughly an order of magnitude in growth speed, as the interface speed surpasses the maximum speed with which solute atoms can diffuse across the interface to remain ahead of the growing crystal. This diffusive speed is given by Di/λ, where λ is the interatomic spacing, and is typically of the order 10 meters per second. Comparison is made with experiment. The steady–state speed of a planar interface is predicted by calculating the free energy dissipated by irreversible processes at the interface and equating it to the available driving free energy. A solute drag term and an intrinsic interfacial mobility term are included in the dissipation calculations. Steady–state solutions are presented for Bi–doped Si during pulsed laser annealing.

scholarly journals Minimization of a free-energy-like potential for non-equilibrium flow systems at steady state

2010 ◽  
Vol 365 (1545) ◽  
pp. 1323-1331 ◽  
Author(s):  
Robert K. Niven
Keyword(s):  
Free Energy ◽  
Steady State ◽  
Entropy Production ◽  
Equilibrium Thermodynamics ◽  
Turbulent Fluid Flow ◽  
System A ◽  
Flow Heat ◽  
Observed Behaviour ◽  
New Formulation ◽  
Non Equilibrium

This study examines a new formulation of non-equilibrium thermodynamics, which gives a conditional derivation of the ‘maximum entropy production’ (MEP) principle for flow and/or chemical reaction systems at steady state. The analysis uses a dimensionless potential function ϕ st for non-equilibrium systems, analogous to the free energy concept of equilibrium thermodynamics. Spontaneous reductions in ϕ st arise from increases in the ‘flux entropy’ of the system—a measure of the variability of the fluxes—or in the local entropy production; conditionally, depending on the behaviour of the flux entropy, the formulation reduces to the MEP principle. The inferred steady state is also shown to exhibit high variability in its instantaneous fluxes and rates, consistent with the observed behaviour of turbulent fluid flow, heat convection and biological systems; one consequence is the coexistence of energy producers and consumers in ecological systems. The different paths for attaining steady state are also classified.

Thermodynamics of the relaxation of a temperature anisotropy in a collisionless plasma

1972 ◽  
Vol 7 (1) ◽  
pp. 67-79 ◽  
Author(s):  
C. Montes ◽  
J. Peyraud
Keyword(s):  
Free Energy ◽  
Linear Problem ◽  
Collisionless Plasma ◽  
New Method ◽  
Linear Relaxation ◽  
Irreversible Processes ◽  
Unstable System ◽  
Temperature Anisotropy ◽  
Thermodynamics Of Irreversible Processes ◽  
Onsager Relations

A new method for dealing with a typical quasi-linear problem is presented. The quasi-linear relaxation of the temperature anisotropy of a collisionless plasma is completely described within the framework of the thermodynamics of irreversible processes. This is obtained by means of generalized Onsager relations applied to the weakly unstable system. Free energy of the system is analyzed in detail, to study the net work involved in the process.

scholarly journals Entropy Production and the Maximum Entropy of the Universe

Proceedings ◽  
2019 ◽  
Vol 46 (1) ◽  
pp. 11
Author(s):  
V. M. Patel ◽  
C. H. Lineweaver
Keyword(s):  
Free Energy ◽  
Entropy Production ◽  
Maximum Entropy ◽  
Time Dependent ◽  
Irreversible Processes ◽  
Observable Universe ◽  
Upper Limits ◽  
The Universe ◽  
Entropy Growth ◽  
Entropy Of The Universe

The entropy of the observable universe has been calculated as Suni ~ 10104 k and is dominated by the entropy of supermassive black holes. Irreversible processes in the universe can only happen if there is an entropy gap ΔS between the entropy of the observable universe Suni and its maximum entropy Smax: ΔS = Smax − Suni. Thus, the entropy gap ΔS is a measure of the remaining potentially available free energy in the observable universe. To compute ΔS, one needs to know the value of Smax. There is no consensus on whether Smax is a constant or is time-dependent. A time-dependent Smax(t) has been used to represent instantaneous upper limits on entropy growth. However, if we define Smax as a constant equal to the final entropy of the observable universe at its heat death, Smax ≡ Smax,HD, we can interpret T ΔS as a measure of the remaining potentially available (but not instantaneously available) free energy of the observable universe. The time-dependent slope dSuni/dt(t) then becomes the best estimate of current entropy production and T dSuni/dt(t) is the upper limit to free energy extraction.

scholarly journals Numerical simulation of corneal transport processes

2005 ◽  
Vol 3 (7) ◽  
pp. 303-310 ◽  
Author(s):  
Long-yuan Li ◽  
Brian Tighe
Keyword(s):  
Numerical Study ◽  
Corneal Stroma ◽  
Ionic Species ◽  
Transport Processes ◽  
Irreversible Processes ◽  
Thermodynamics Of Irreversible Processes ◽  
Ionic Solution ◽  
Numerical Examples ◽  
Corneal Hydration ◽  
Transport Of Ions

This paper presents a numerical study on the transport of ions and ionic solution in human corneas and the corresponding influences on corneal hydration. The transport equations for each ionic species and ionic solution within the corneal stroma are derived based on the transport processes developed for electrolytic solutions, whereas the transport across epithelial and endothelial membranes is modelled by using phenomenological equations derived from the thermodynamics of irreversible processes. Numerical examples are provided for both human and rabbit corneas, from which some important features are highlighted.

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