عنوان

Quasichemical models of multicomponent nonlinear diffusion

Number

TLets809444

Title Proper

Quasichemical models of multicomponent nonlinear diffusion

General Material Designation

[Thesis]

First Statement of Responsibility

Wahab, Hafiz Abdul

Subsequent Statement of Responsibility

Gorban, Alexander

Name of Publisher, Distributor, etc.

University of Leicester

Date of Publication, Distribution, etc.

2011

Dissertation or thesis details and type of degree

Thesis (Ph.D.)

Text preceding or following the note

2011

Text of Note

Diffusion preserves 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 necessary to provide 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 reaction mechanism borrowed from chemical kinetics. Chemical kinetics gave rise to the very seminal tools for the modelling 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 the 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.

University of Leicester

Gorban, Alexander

University of Leicester

Electronic name

p

[Thesis]

276903

a

Y