Powder Technology, 11 (1975) 75-84 @ Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands Sedimentation of Compressibl e Materials: Ana lysis of Batch Sedimentation Curve C.C. HARRIS, P. SOMASUNDARAN and R.R. JENSEN Henry Krumb School of Mines, Columbia University, New York, N. Y. 10021 (U.S.A.) (Received April 22, 1974; in revised form Auaust 6,1974) SUMMARY Batch sedimentation curves or dilute phos- phatic slimes o which small amounts of coarser particles were added to hasten settling are ana- lysed. The curves are marke dly reverse S-shaped, without a constant settling rate period, and with pronounced asymptotic behaviour ndica- ting compressible material; no flocculants were added but the slimes were observed o flocculate into small clu sters of particles which grouped nto aggregates. The system s compl icated and, as a pre- cursor to an analytical approach, an idealized model is proposed as a framework for future discussion. Several egions of the curve a re identified . Each region indicates a specific sedimentat ion mechanism which predominates over a con- centration range. Phenomenological models for the regions are proposed and expressed n their simplest mathematica l form. The result- ing equations consist of logistic, logarithmic, and exponential decay erms, and they fit data within experimenta l error. size fraction of hard regular particles - for example, clean unflocculate d glass pheres in the approx imate range 250 - 25 11m t a volume concentration about 10 - 25%. n this case, batch settling is characterized by a linear suspension height versus ime relationship termed "constant settl ing rate period". It is easily amenable o analysis along the lines of the modified Kozeny [26] model for flow through porous media. Data correlation can be handled by the dimensionless groups: resistance coefficient and modified Reynolds or Blake number [5,16,17]. Settling ends abruptly with little further decrease n height [18]; the material is said to be incomp ressible. In contrast, the sedimentat ion curve of di- lute suspensions f subsieve lay materials displays a reverse S-shape which is so cu rved that no region could be described as exhibiting a constant settling rate period [23]. Moreover, settling continues at an ever decreasing ate over an extremely long time period, suggesting that the material is compressible. In an earlier paper [23], stages n the sedi- mentation process of compressible limes con- taining substantial quantities of fibrous ma- terials [ 27] were briefly described; part of the curve was reported to ~e f itted approximate ly by a Weibull type equation [28]. The purpose of this note i s to propa8e a phenomenological model describing he entire sedimentati on process as a framework for more rigorous future treatment. It is based on the observation of the sedimentation systems and the analysis of the simplest plausible equations. INTRODUCTION * In some terminologies "sedimentation" refers to the upward growth of settled material; in the present usage, sedimentation" is synonymous wit h "..bsi- dence". As a suspension of fine particles n water settles under gravity, an interface forms be- tween the suspension and the supernatant water. A graph of the interface height versus time is known as J1e edimentation curve. Summaries of the pres ent state of research nto sedimentati on and thickening can be found in several publication s (1 - 25). The simplest sed imentation cu rve is pro- duced by a suspension onsisting of a narrow
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7/24/2019 Sedimentation of Compressible Materials ... Sedimentation Cu