Theory of mixtures

Abstract

In developing the balance equations for a multicomponent flow, there are two approaches available. Some authors (Whitaker 1967, Slattery 1967) start from the equations of fluid mechanics, valid on the particle scale, and then integrate these equations in regions sufficiently large to contain a representative mass of all components. In case of multiphase particulate flow, those regions must be much greater than the size of the particles contained in the system. The spatially averaged properties then become field variables and the new balance equations constitute a set of local equations describing the flow of a multicomponent mixture. The second approach is the theory of mixtures which uses the concepts of continuum mechanics, considering all components as superimposed interacting continua (Bowen 1976, Truesdell 1984, Dobran 1985). The macroscopic balances are established as the fundamental equations and, from them, the local balances and jump conditions are deduced. The field variables in the continuum approach are equivalent to the averaged variables in the first approach, so that both methods give the same results (Drew 1983). In both cases the local variables cannot be experimentally measured and are not to be confused with the experimental variables of fluid mechanics. In the work that follows, we use the continuum approach of the theory of mixtures.