Mixtures

Mixtures consist of different substances which keep their own properties. The individual molecules enjoy being near to each other so that, in the mathematical model, each point in the mixture may be occupied by all of the substances simultaneously. If the chemical structure of a substance changes when it enters the mixture then the mixture is said to be chemically reacting. The easiest mixtures to deal with are gaseous mixtures in which gases readily mix. Fluid mixtures may be formed from fluids or from a fluid and gases that dissolve in the fluid or from a fluid and solids that dissolve in the fluid. In most cases, a fluid is preponderant and hence is called the solvent while the remaining constituents are called solutes. Both fluid mixtures and solid mixtures are examined. The mixture is regarded as ideal in that the volumetric and energetic properties of the mixture are taken to be the linear combination of those of the constituents or species. The chapter provides a derivation of the balance equations by starting with global balances and allowing for interaction terms (growths and supplies). The second law is stated in terms of the constituents and is expressed by the non-negative value of the sum of the entropy productions. Details are given for the balance equations of the whole mixture as a single body; an analysis is given of the various forms of the second-law inequality (Gibbs equation) occurring in the literature. Diffusion is considered through various known models (Fick, Maxwell–Stefan, Cahn–Hilliard, Allen–Cahn). Moreover immiscible mixtures are investigated.