2,865 research outputs found
Quasichemical Models of Multicomponent Nonlinear Diffusion
Diffusion preserves the positivity of concentrations, therefore,
multicomponent diffusion should be nonlinear if there exist non-diagonal terms.
The vast variety of nonlinear multicomponent diffusion equations should be
ordered and special tools are needed to provide the systematic construction of
the nonlinear diffusion equations for multicomponent mixtures with significant
interaction between components. We develop an approach to nonlinear
multicomponent diffusion based on the idea of the reaction mechanism borrowed
from chemical kinetics.
Chemical kinetics gave rise to very seminal tools for the modeling of
processes. This is the stoichiometric algebra supplemented by the simple
kinetic law. The results of this invention are now applied in many areas of
science, from particle physics to sociology. In our work we extend the area of
applications onto nonlinear multicomponent diffusion.
We demonstrate, how the mechanism based approach to multicomponent diffusion
can be included into the general thermodynamic framework, and prove the
corresponding dissipation inequalities. To satisfy thermodynamic restrictions,
the kinetic law of an elementary process cannot have an arbitrary form. For the
general kinetic law (the generalized Mass Action Law), additional conditions
are proved. The cell--jump formalism gives an intuitively clear representation
of the elementary transport processes and, at the same time, produces kinetic
finite elements, a tool for numerical simulation.Comment: 81 pages, Bibliography 118 references, a review paper (v4: the final
published version
Solutions for models of chemically reacting mixtures
International audienceThe mathematical modeling of chemically reacting mixtures is investigated. The governing equations, that may be split between conservation equations, thermochemistry and transport fluxes, are presented as well as typical simplifications often encountered in the literature. The hyperbolic-parabolic structure of the resulting system of partial differential equations is analyzed using symmetrizing variables. The Cauchy problem is discussed for the full system derived from the kinetic theory of gases as well as relaxation towards chemical equilibrium fluids in the fast chemistry limit. The situations of traveling waves and reaction-diffusion systems is also addressed
Fluctuation-enhanced electric conductivity in electrolyte solutions
In this letter we analyze the effects of an externally applied electric field
on thermal fluctuations for a fluid containing charged species. We show in
particular that the fluctuating Poisson-Nernst-Planck equations for charged
multispecies diffusion coupled with the fluctuating fluid momentum equation,
result in enhanced charge transport. Although this transport is advective in
nature, it can macroscopically be represented as electrodiffusion with
renormalized electric conductivity. We calculate the renormalized electric
conductivity by deriving and integrating the structure factor coefficients of
the fluctuating quantities and show that the renormalized electric conductivity
and diffusion coefficients are consistent although they originate from
different noise terms. In addition, the fluctuating hydrodynamics approach
recovers the electrophoretic and relaxation corrections obtained by
Debye-Huckel-Onsager theory, and provides a quantitative theory that predicts a
non-zero cross-diffusion Maxwell-Stefan coefficient that agrees well with
experimental measurements. Finally, we show that strong applied electric fields
result in anisotropically enhanced velocity fluctuations and reduced
fluctuations of salt concentrations.Comment: 12 pages, 1 figur
Linear-nonequilibrium thermodynamics theory for coupled heat and mass transport
Linear-nonequilibrium thermodynamics (LNET) has been used to express the entropy generation and dissipation functions representing the true forces and flows for heat and mass transport in a multicomponent fluid. These forces and flows are introduced into the phenomenological equations to formulate the coupling phenomenon between heat and mass flows. The degree of the coupling is also discussed. In the literature such coupling has been formulated incompletely and sometimes in a confusing manner. The reason for this is the lack of a proper combination of LNET theory with the phenomenological theory. The LNET theory involves identifying the conjugated flows and forces that are related to each other with the phenomenological coefficients that obey the Onsager relations. In doing so, the theory utilizes the dissipation function or the entropy generation equation derived from the Gibbs relation. This derivation assumes that local thermodynamic equilibrium holds for processes not far away from the equilibrium. With this assumption we have used the phenomenological equations relating the conjugated flows and forces defined by the dissipation function of the irreversible transport and rate process. We have expressed the phenomenological equations with the resistance coefficients that are capable of reflecting the extent of the interactions between heat and mass flows. We call this the dissipation-phenomenological equation (DPE) approach, which leads to correct expression for coupled processes, and for the second law analysis
Irreversible thermodynamics of creep in crystalline solids
We develop an irreversible thermodynamics framework for the description of
creep deformation in crystalline solids by mechanisms that involve vacancy
diffusion and lattice site generation and annihilation. The material undergoing
the creep deformation is treated as a non-hydrostatically stressed
multi-component solid medium with non-conserved lattice sites and
inhomogeneities handled by employing gradient thermodynamics. Phase fields
describe microstructure evolution which gives rise to redistribution of vacancy
sinks and sources in the material during the creep process. We derive a general
expression for the entropy production rate and use it to identify of the
relevant fluxes and driving forces and to formulate phenomenological relations
among them taking into account symmetry properties of the material. As a simple
application, we analyze a one-dimensional model of a bicrystal in which the
grain boundary acts as a sink and source of vacancies. The kinetic equations of
the model describe a creep deformation process accompanied by grain boundary
migration and relative rigid translations of the grains. They also demonstrate
the effect of grain boundary migration induced by a vacancy concentration
gradient across the boundary
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