FLUID-DYNAMICS OF COARSE DISPERSIONS

Dispersions of identical spherical particles in a fluid are considered with allowance for random fluctuations that both, particles and the fluid, are involved in. The particles are assumed to be sufficiently large in the sense that the interparticle exchange by momentum and energy of the particle fluctuations is carried out mainly through direct collisions, and the role of interphase interaction in this process is negligible. Then the particles may be regarded as statistically independent, and the fluctuation energy is almost uniformly distributed over their translational degrees of freedom. Equations of mass and momentum conservation for flow of the dispersed phase as well as an equation of fluctuation energy transfer are stated similarly to those obtained by the classical method by Enskog in the kinetic theory of gases. The equations involve additional terms due to the interphase interaction and the energy dissipation by collisions. These equations, together with those of mass and momentum conservation of the continuous phase, constitute a complete set of equations which govern the macroscopic flow of disperse mixtures. A closure problem for this set is discussed in detail. It is reduced, in fact, to the determination of a single quantity characterizing the particle fluctuation intensity in a macroscopically homogeneous state of a disperse mixture.