The consolidation of concentrated suspensions. Part 1.—The theory of sedimentation

Abstract

The concentration or consolidation of suspensions of fine particles under the influence of a gravitational field has been analysed. The rate and extent of consolidation depends upon a balance of three forces, the gravitational driving force, the viscous drag force associated with flow of liquid in the sediment and a particle or network stress developed as a result of direct particle–particle interactions. In the case of colloidally stable suspensions, this particle stress is the osmotic pressure of the particles; in the case of flocculated or coagulated suspensions, it is the elastic stress developed in the network of particles. A constitutive equation is suggested for irreversibly flocculated suspensions undergoing consolidation which embodies the concept of a concentration-dependent yield stress P_y(ϕ). This is then used to analyse the sedimentation behaviour of flocculated sediments and to derive expressions for the initial sedimentation rate. The initial rate of change of sediment height with time in a uniform gravitational or centrifugal field is given approximately by: [graphic ommitted] where B=Δρgϕ₀H₀/P_y(ϕ₀), u₀ is the sedimentation rate of an isolated particle, ϕ₀ is the initial (uniform) volume fraction of solids, r(ϕ₀) is a dimensionless hydrodynamic interaction parameter, Δρ is the difference in density between solid and liquid, g is the gravitational or centrifugal acceleration and H₀ is the initial sediment height. The theory accounts correctly for the equilibrium consolidation behaviour of strongly flocculated suspensions, and preliminary experimental data suggest that it is not inconsistent with their dynamic behaviour. The estimation of the yield stress P_y(ϕ) from a batch centrifuge experiment is also described.