Quasichemical Models of Multicomponent Nonlinear Diffusion

@article{Gorban2010QuasichemicalMO,
  title={Quasichemical Models of Multicomponent Nonlinear Diffusion},
  author={Alexander N Gorban and Heghine Sargsyan and Hafiz Abdul Wahab},
  journal={Mathematical Modelling of Natural Phenomena},
  year={2010},
  volume={6},
  pages={184-262}
}
Diffusion preserves the positivity of concentrations, therefore, multicomponent diffu- sion should be nonlinear if there exist non-diagonal terms. The vast variety of nonlinear multicom- ponent 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 in- teraction between components. We develop an approach to nonlinear multicomponent diffusion based on the idea of… 

Figures from this paper

On the Value Method of Determining a Dominant Mechanism of Nonlinear Multicomponent Diffusion

Abstract The work is devoted to the problem of analyzing the mechanisms of nonlinear multicomponent diffusion in complex systems. A new method is proposed for determining the stoichiometric

Nonlinear diffusion in multicomponent liquid solutions.

Mutual diffusion in multicomponent liquids is studied and taking into account molecular complex formation allows one to explain the experimental dependence of diffusion coefficients on the composition (components concentration).

Manifestation of Onsager’s off-diagonal fluxes in diffusion of coadsorbed particles

Quasisolitons in self-diffusive excitable systems, or Why asymmetric diffusivity obeys the Second Law

It is demonstrated that quasi-solitons can be robustly observed in excitable systems with excitable kinetics and with self-diffusion only, and a reduction procedure can be used for the search of complicated wave regimes in multi-component, stiff systems by studying simplified, soft systems.

Chemical reaction-diffusion networks: convergence of the method of lines

We show that solutions of the chemical reaction-diffusion system associated to $$A+B\rightleftharpoons C$$A+B⇌C in one spatial dimension can be approximated in $$L^2$$L2 on any finite time interval

The robust finite-volume schemes for modeling nonclassical surface reactions

A coupled system of nonlinear parabolic PDEs arising in modeling of surface reactions with piecewise continuous kinetic data is studied. The nonclassic conjugation conditions are used at the surface

Description of Nonlinear Diffusion in Non-Ideal Multicomponent Systems. Approach of Variable Stochiometric Vectors

  • H. Sargsyan
  • Materials Science
    Journal of Contemporary Physics (Armenian Academy of Sciences)
  • 2021
Abstract A new formal kinetic approach to the description of diffusion in nonideal multi-component systems is proposed. For special cases, an approach of variable stoichiometric vectors has been
...

References

SHOWING 1-10 OF 164 REFERENCES

Multicomponent diffusion theory and its applications to polymer‐solvent systems

Recent publications by Zielinski and Hanley and by Alsoy and Duda have proposed relationships between self- and mutual-diffusion coefficients in multicomponent systems that can be derived from

Constraints in nonequilibrium thermodynamics : General framework and application to multicomponent diffusiona)

We elaborate how holonomic constraints can be incorporated into the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) framework of nonequilibrium thermodynamics.

Spinodal Decomposition for Multicomponent Cahn–Hilliard Systems

We consider the initial-stage phase separation process in multicomponent Cahn–Hilliard systems through spinodal decomposition. Relying on recent work of Maier-Paape and Wanner, we establish the

Colloquium: Role of the H theorem in lattice Boltzmann hydrodynamic simulations

In the last decade, minimal kinetic models, and primarily the lattice Boltzmann equation, have met with significant success in the simulation of complex hydrodynamic phenomena, ranging from slow

General mass action kinetics

The principal result of this work shows that there exists a simply identifiable class of kinetic expressions, including the familiar detailed balanced kinetics as a proper subclass, which ensure consistency with the extended thermodynamic conditions.

The Porous Medium Equation: Mathematical Theory

The Heat Equation is one of the three classical linear partial differential equations of second order that form the basis of any elementary introduction to the area of PDEs, and only recently has it

Stochastic simulation of chemical kinetics.

  • D. Gillespie
  • Chemistry
    Annual review of physical chemistry
  • 2007
Some recent advances in methods for using that theory to make numerical simulations include improvements to the exact stochastic simulation algorithm (SSA) and the approximate explicit tau-leaping procedure, as well as the development of two approximate strategies for simulating systems that are dynamically stiff.

Dynamics and thermodynamics of complex fluids. I. Development of a general formalism

We recognize some universal features of macroscopic dynamics describing the approach of a well-established level of description (that is, successfully tested by experimental observations) to

Energetics of the Kirkendall effect

The purpose of this article is to explore what a rational framework might be if one were to analyse the Kirkendall effect from a dynamical perspective, and the extent to which such ideas may have relevance to diffusion in solids.

Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism

For a number of well-known time-evolution equations for nonequilibrium systems we extract a common structure from these equations, referred to as a general equation for the nonequilibrium
...