Syllabus
1. Continuum theory of mixtures: Motivation, basic applications, assumption of co-occupancy, kinematics
2. Measures and relations between them, balance of mass, momentum, angular momentum, energy and entropy for the mixture components and for the mixture as a whole, definition of mixture velocity, mixture classes I,II,III,IV
3. Class I mixtures, derivation of Fick’s law and Fick-Navier-Stokes-Fourier (Fick-NSF) model
4. Fick-NSF model with boundary conditions
5. Quasi-incompressible approximations, quasi-incompressible variants of the Fick-NSF model
6. Derivation of the Cahn-Hilliard-NSF model
7. Chemical reactions - introduction, stoichiometry
8. Chemical reactions - mixture of ideal gasses, chemical potential, chemical equilibrium, mass action law, chemical kinetics
9. Derivation of the Allen-Cahn-NSF model
10. Mechanical interaction between the phases, basic mechanical analogues of the interaction mechanisms in mixtures, drag, lift, Magnus force, virtual mass effect
11. Class II mixtures, derivation of the Darcy law and other simplified models for flows through porous media (Forchheimer, Brinkman)
12. A thermodynamic framework for the mixture of two liquids
13. Balance equations at interfaces, generalized interface conditions
14. Multi-phase mixture theory: formalism, averaging, balance equations, structure of the interaction terms
Annotation
The goal of the course is to present several approaches to modelling of multi-component materials in the framework of mechanics and thermodynamics of continua. The general theory will be presented together with derivation of simplified models.