On the thermodynamics of volume/mass diffusion in fluids (original) (raw)
Related papers
Second law of thermodynamics in volume diffusion hydrodynamics in multicomponent gas mixtures
Physics Letters A, 2012
We presented the thermodynamic structure of a new continuum flow model for multicomponent gas mixtures. The continuum model is based on a volume diffusion concept involving specific species. It is independent of the observer's reference frame and enables a straightforward tracking of a selected species within a mixture composed of a large number of constituents. A method to derive the second law and constitutive equations accompanying the model is presented. Using the configuration of a rotating fluid we illustrated an example of non-classical flow physics predicted by new contributions in the entropy and constitutive equations.
A continuum model of gas flows with localized density variations
Physica A: Statistical Mechanics and its Applications, 2008
We discuss the kinetic representation of gases and the derivation of macroscopic equations governing the thermomechanical behavior of a dilute gas viewed at the macroscopic level as a continuous medium. We introduce an approach to kinetic theory where spatial distributions of the molecules are incorporated through a meanfree-volume argument. The new kinetic equation derived contains an extra term involving the evolution of this volume, which we attribute to changes in the thermodynamic properties of the medium. Our kinetic equation leads to a macroscopic set of continuum equations in which the gradients of thermodynamic properties, in particular density gradients, impact on diffusive fluxes. New transport terms bearing both convective and diffusive natures arise and are interpreted as purely macroscopic expansion or compression. Our new model is useful for describing gas flows that display non-local-thermodynamic-equilibrium (rarefied gas flows), flows with relatively large variations of macroscopic properties, and/or highly compressible fluid flows.
Mechanics and thermodynamics of diffusion
The relation between diffusive forces and fluxes is sometimes chosen on the basis of the entropy inequality. Since the form of the entropy inequality is influenced by the form of the thermal energy equation, a precise understanding of the latter is necessary when the matter of forces and fluxes is explored. Often the form of the thermal energy equation for multicomponent systems is developed on an intuitive basis, and this leads to uncertainty in the form of the entropy inequality. A detailed analysis of the thermal energy equation leads to an entropy transport equation which indicates that the use of the gradient of the chemical potential as a driving force for the diffusive flux is not justified.
Diffusion, drift and their interrelation through volume density
Philosophical Magazine, 2009
The evolution of the understanding of the mass transport phenomena in solids and liquids allows for the unification of phenomenological models. We consider the central Darken problem of the choice of the coordinate axes for diffusion. Namely, the definition of this mode of motion and the method how diffusion displacement is defined and measured. In our analysis we extensively use the Euler's and Liouville theorems. We derive the formula of volume density conservation, i.e., the volume continuity equation. This fundamental formula defines the volume-fixed frame of reference in the multicomponent, solid, gas and liquid solutions. The volume fixed frame of reference is self-consistent with the foundations of linear irreversible thermodynamics except recognizing the need to add volume density to the usual list of extensive physical properties undergoing transport in every continuum. Proposed modifications are selfconsistent with the literature dating back to Onsager, the experiments of Kirkendall, their interpretation by Darken and recent generalized formulations. It will be shown that the method can be used in mechano-chemistry and electromechano-chemistry.
On the Relationship between Molecular and Macroscopic Diffusion in Ideal Gases
ForsChem Research Reports, 2019
In this report, two different models of multicomponent diffusion in ideal gases are presented. The first model, introduced in a previous report, is derived from the probabilistic observation of individual molecules colliding with a specific molecular neighborhood. The second model is based on the macroscopic motion of a large number of molecules in one direction (molecular flux). Since both diffusion models are consistent with Fick's laws of diffusion, it is proposed that the macroscopic diffusion coefficient is proportional to the molecular diffusion coefficient. It is also assumed that during the self-diffusion of a pure ideal gas, the symmetry of the collisions and the indistinguishability of individual molecules result in the equivalence between molecular and macroscopic diffusion coefficients. For multicomponent mixtures of ideal gases with different masses and sizes, the specific composition of the neighborhood influences both the molecular and macroscopic diffusion coefficients in different ways. It is also shown that each species has its own diffusion coefficients (macroscopic and molecular), which are a function of the composition of the mixture and the environmental conditions (e.g. pressure and temperature). Overall macroscopic diffusion coefficients of multicomponent systems can be obtained as a molar fraction weighted-average of the macroscopic diffusion coefficients for each species in the mixture. Significant differences with respect to conventional expressions used to estimate macroscopic diffusion coefficients of pure ideal gases and mixtures are found. However, some experimental results seem to be consistent with the proposed model of diffusion.
Kinetic theory of dense fluids. IV. Entropy balance equation and irreversible thermodynamics
Annals of Physics, 1979
By making use of the kinetic equation and the global entropy formula reported in the first paper of this series, we have derived the entropy balance equation and the accompanying molecular formulas for local entropy density, entropy flux and entropy production for real fluids at an arbitrary density. We have thereby obtained an extension to real fluids of the Boltzmannian irreversible thermodynamics which is based on the Boltzmann equation for ideal fluids. The theory presented provides us with a molecular basis for the continuum mechanics formulation of irreversible thermodynamics by Coleman, Noll, Gurtin and their coworkers: The macroscopic constitutive functionals in their theory can now be calculated from the various molecular formulas for the relevant quantities in our theory. * Work supported by the grants from the Natural Sciences and Engineering Research Council of Canada.
The continuum mechanical theory of multicomponent diffusion in fluid mixtures
Chemical Engineering Science, 2010
The continuum mechanical approach for deriving the generalized equations of multicomponent diffusion in fluids is described here in detail, which is based on application of the principle of linear momentum balance to a species in a mixture, resulting in the complete set of diffusion driving forces. When combined with the usual constitutive equations including the continuum friction treatment of diffusion, the result is a very complete and clear exposition of multicomponent diffusion that unifies previous work and includes all of the various possible driving forces as well as the generalized Maxwell-Stefan form of the constitutive equations, with reciprocal diffusion coefficients resulting from Newton's third law applied to individual molecular encounters. This intuitively appealing and rigorous approach, first proposed over 50 years ago, has been virtually ignored in the chemical engineering literature, although it has a considerable following in the mechanical engineering literature, where the focus, naturally, has been physical properties of multiphase fluid and solid mixtures. The described approach has the advantages of transparency over the conventional approach of non-equilibrium thermodynamics and of simplicity over those based on statistical mechanical or kinetic theory of gases or liquids. We provide the general derivation along with some new results in order to call attention of chemical engineers to this comprehensive, attractive, and accessible theory of multicomponent diffusion in fluids.
A volume-based description of gas flows with localised mass-density variations
2006
We reconsider some fundamental aspects of the fluid mechanics model, and the derivation of continuum flow equations from gas kinetic theory. Two topologies for fluid representation are presented, and a set of macroscopic equations are derived through a modified version of the classical Boltzmann kinetic equation for monatomic gases. The free volumes around the gaseous molecules are introduced into the set of kinetic microscopic parameters. Our new description comprises four, rather than three, conservation equations; the classical continuity equation, which conflates actual mass-density and number-density in a single equation, has been split into a conservation equation of mass (which involves only the classical numberdensity of the gaseous particles) and an evolution equation purely of the massdensity (mass divided by the actual volume of the fluid). We propose this model as a better description of gas flows displaying non-local-thermodynamic-equilibrium (rarefied flows), flows with relatively large variations of macroscopic properties, and/or highly compressible fluids/flows.
The Journal of Physical Chemistry B, 2005
In this paper, we apply the Matteoli-Mansoori empirical formula for the pair correlation function of simple fluids obeying the Lennard-Jones potential to calculate reduced self-diffusion coefficients on the basis of the modified free volume theory. The self-diffusion coefficient thus computed as functions of temperature and density is compared with the molecular dynamics simulation data and the self-diffusion coefficient obtained by the modified free volume theory implemented with the Monte Carlo simulation method for the pair correlation function. We show that the Matteoli-Mansoori empirical formula yields sufficiently accurate self-diffusion coefficients in the supercritical regime, provided that the minimum free volume activating diffusion is estimated with the classical turning point of binary collision at the mean relative kinetic energy 3k B T/2, where k B is the Boltzmann constant and T is the temperature. In the subcritical regime, the empirical formula yields qualitatively correct, but lower values for the self-diffusion coefficients compared with computer simulation values and those from the modified free volume theory implemented with the Monte Carlo simulations for the pair correlation function. However, with a slightly modified critical free volume, the results can be made quite acceptable.
Gas diffusion into viscous and non-Newtonian liquids
Chemical Engineering Science, 1992
A quiescent technique has been developed to determine the diffusion coefficients of carbon dioxide in water and viscous and non-Newtonian liquids. The rate of gas absorption was measured accurately as the pressure change of a fixed volume of gas by a micromanometer. Gas penetration analysis suggests that a plot of gas absorption rate against the square root of contact time should be linear. The plot revealed a distinct initial phase of molecular diffusion lasting for about 100 seconds when water was instantaneously exposed to carbon dioxide. This was followed by non-linear behaviour in which natural convection is driven by density gradients. The diffusion coefficient of carbon dioxide in water was found to agree well with the values reported in the literature. Mass transfer coefficients, k , were detennincd for the interface in the convective regime. Diffusion without natural convection of C?Oz into viscous and pseudoplastic aqueous solutions appeared to be prolonged and proceeded at a slower rate. The onset of convection was suppressed considerably depending on the (apparent) viscosity of the solutions. A critical Rayleigh number was computed to characterise the onset of linear instability leading to natural convection. The critical times for stable diffusion were predicted from this critical Rayleigh number. Agreement with observed values is fair. KEYWORDS Diffision coefficients; non-Newtonian liquids; linear instability; critical Rayleigh number. critical times. INTRODUCIION In this paper we first describe experiments to measure the diffusion coefficients of COz into water and aqueous solutions of car-boxy methyl cellulose (CMC). In the experiments we observed a time of stable molecular diffusion which was followed by natural convection. The second part of the paper deals with the latter phenomenon. Diffusion coefficients (0) am fundamental constants in gas-liquid mass transfer and am used in associated correlations to calculate mass transfer coefficients. In most cases, the transfer coefficients are found to be proportional to D to the power q, where q is between 0.2 to 1.