# 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… Expand

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#### References

SHOWING 1-10 OF 219 REFERENCES

Multicomponent diffusion theory and its applications to polymer‐solvent systems

- Chemistry
- 2003

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… Expand

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

- Physics
- 2009

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

Constraints in nonequilibrium thermodynamics: General framework and application to multicomponent diffusion.

- Medicine
- The Journal of chemical physics
- 2009

As a consequence of its more elaborate and restrictive structure, GENERIC removes the ambiguities occurring in the classical thermodynamics of irreversible processes when one works with redundant variables. Expand

Spinodal Decomposition for Multicomponent Cahn–Hilliard Systems

- Physics
- 2000

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… Expand

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

- Physics
- 2002

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… Expand

General mass action kinetics

- Mathematics
- 1972

SummaryThe familiar idea of mass action kinetics is extended to embrace situations more general than chemically reacting mixtures in closed vessels. Thus, for example, many reaction regions connected… Expand

The Porous Medium Equation: Mathematical Theory

- Mathematics
- 2006

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… Expand

Stochastic simulation of chemical kinetics.

- Computer Science, Medicine
- 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. Expand

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

- Physics
- 1997

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… Expand

Energetics of the Kirkendall effect

- Biology
- 2007

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. Expand