The theory of sediment volumes of compressible, particulate structures

Abstract

Specific sediment volume or its reciprocal, average volume fraction of solids, plays a significant role in determining the state of particle aggregation in a suspension. It is determined by the properties of the rising sediment (or cake) in a batch settling tube. A close relation exists between the sediment volume and sedimentation characteristics involved in design of thickeners and clarifiers. Qualitatively, the average porosity of a particulate bed is shown to be principally a function of particle size, shape, and state of aggregation. Slurry concentration, mechanical agitation, and vibration also affect the state of the sediment. Assuming that porosity is a function of the buoyed weight of solids (effective pressure) and the initial porosity of unstressed sediment, formulas are developed which give the average specific sediment volume as a function of height and bed compressibility. For highly compressible materials, the value of the specific sediment volume changes rapidly with height. The limiting value of the specific sediment volume for a cake with differential thickness or the value of the volume fraction of solids ε s0 for an unstressed bed is probably the best parameter for assessing the state of aggregation of a suspension. Two experimental methods are presented for its determination. In the first method, the volume of particulates is plotted as a function of thickness; and the limiting slope for a cake of zero thickness is obtained. In the second method, the initial rates of fall and rise, respectively, of the upper particle—supernatant boundary and the sediment are experimentally measured; and ε s0 is obtained through a material balance.