publication . Other literature type . Article . Preprint . 2011

Quasichemical Models of Multicomponent Nonlinear Diffusion

Gorban, A. N.; Sargsyan, H. P.; Wahab, H. A.;
  • Published: 10 Aug 2011
  • Publisher: EDP Sciences
Abstract
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 supple...
Subjects
free text keywords: Modelling and Simulation, Finite element method, Computer simulation, Detailed balance, Convection–diffusion equation, Dissipation, Entropy production, Nonlinear system, Statistical physics, Mathematical analysis, Mathematics, Mass action law, Condensed Matter - Materials Science, Physics - Chemical Physics
Related Organizations
38 references, page 1 of 3

1. Introduction 4 1.1. Linear Diffusion: from Graham and Fick to Einstein, Onsager and Teorell . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.1. Fick's Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.2. Einstein's Mobility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.3. Teorell Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.4. Onsager's Linear Phenomenology . . . . . . . . . . . . . . . . . . . . . . 6 1.2. Mechanisms of Nonlinear Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.1. Jumps on the Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.2. Diffusion in Solids as Reaction: from Frenkel to Eyring . . . . . . . . . . 10 1.2.3. Ginzburg-Landau Free energy and Cahn-Hilliard equation . . . . . . . . . 11 1.2.4. Teorell Formula for Non-perfect Systems . . . . . . . . . . . . . . . . . . 12 1.3. Main Ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3.1. Mechanisms as Collections of Elementary Processes . . . . . . . . . . . . 13 1.3.2. Discrete Kinetic Models and Lattice Automata . . . . . . . . . . . . . . . 14 1.3.3. Thermodynamics and Intermediate Complexes . . . . . . . . . . . . . . . 24

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publication . Other literature type . Article . Preprint . 2011

Quasichemical Models of Multicomponent Nonlinear Diffusion

Gorban, A. N.; Sargsyan, H. P.; Wahab, H. A.;