INTERPHASE INTERACTION IN FINE SUSPENSION FLOW

A self-consistent model of moderately concentrated fine suspensions of identical spherical particles is developed. It provides for a completely closed fluid dynamic scheme of suspensions neglecting random particle fluctuations. Above all, it brings forward a set of conservation equations governing the mean flow of both phases of a suspension in the continuum approximation. The model allows also to obtain all constitutive theological relations (''equations of state'') which determine terms of those equations as functions of unknown variables and physical parameters. The theological relations are found in an explicit form for effective stresses and different constituents of the interphase interaction force in weakly unsteady flow of a moderately concentrated suspension. The stresses are shown to take shape as a result of a certain relaxation process. The force constituents are of the same origin and have basically the same meaning as those for a single particle in an unbounded fluid. In particular, the contents of the paper bring to an end a recent scholastic and rather fruitless debate as to how the drag and buoyancy constituents have to be singled out from the total force acting on a particle of a uniform fluidized bed at steady conditions. It is demonstrated in an unequivocal way that it is the density of the fluidized bed as a whole that must be used while expressing the buoyancy force, but not that of the fluidizing fluid alone.