Syllabus
1. Small window to the endless universe of mixtures
- water, salt and a an ocean of questions;
- saturated zone groundwater flow, as a mixture of water and a rigid (or elastic) porous media;
- unsaturated zone, as a mixture of water, soil and air;
- solutes in water (groundwater);
- solute polymers, blood cells in blood plasma;
- evaporation and condensation, snow, ice, melting and freezing, etc... 2. Little on interactions
- flow around bodies, flow through a fracture or pipe;
- flow stability, turbulence, and turbulent viscosity;
- surfaces tension, adhesion, cohesion and capillary forces;
- diffusion and dispersion. 3. Multicomponent mixture
- the concept of co-existence and the representative elementary volume;
- conservation laws in bulk (how many velocities can a point contain?);
- mixture descriptions hierarchy (according to Hutter);
- class I: from Fick's law to advection-(reaction-)diffusion equation;
- compressibility and quasi-compressibility (is a mixture of two incompressible fluids incompressible itself?);
- class II: Darcy, Forchheimer and Brinkmann, and the groundwater flow;
- Richardson and Richards, and the motion of groundwater and air;
- and other very different classes...
Annotation
This follow-up course to Language of Continuum Mechanics for Applied Geology aims at expanding what was built up in the mechanics of single continua into the description of multi-component continuum. Practicals will consist of an individual research focused on a particular mixture model.
The lecture will be supplemented by examples of all kinds of behavior of various fluids and mixtures in different situations, the focus will remain with the basic theory and the mathematical description, rather than particular processes or practical acquaintance. The theory of mixtures comprises a great deal of nutrition, while we will bite off no more than a morsel; by examples such as the groundwater flow, viewed as a mixture of porous media, water
(and air, eventually). A bit carelessly, we will omit the heat and the most of heat-related issues.