Statistical hydromechanics of disperse systems. Part 3. Pseudo-turbulent structure of homogeneous suspensions

Abstract

The theory of concentrated two-phase mixtures developed in the previous parts of this paper is applied to analysis of the structure of the local random motion (pseudo-turbulence) occurring in flows of suspensions of small solid spheres. Suspensions under study are assumed to be locally homogeneous in the sense that large-scale agglomerates of many particles or voids filled with the pure liquid do not arise in their flows and particles can be approximately regarded as statistically independent units.

Coefficients of the particle diffusion caused by pseudo-turbulence are calculated without restrictions imposed on the value of the Reynolds number Re characterizing the fluid flow around one particle. Other pseudo-turbulent quantities (the r.m.s. pseudo-turbulent velocities of both phases, their effective pseudo-turbulent viscosities in a shear flow, etc.) are considered for small Re. In particular, a natural explanation is given to the known effect of the reduced hydraulic resistance of a fluidized bed as compared with that of a stationary particulate bed of the same porosity.

Additionally, some properties of the mean motion of a suspension influenced by pseudo-turbulence are discussed brifly. By way of example, two problems are considered: stability of the upward flow of a homogeneous suspension with respect to small perturbations depending upon the vertical co-ordinate and time, and the spatial distribution of particles suspended by the upward flow of a fluid under gravity.