Settling

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FM 304: BATCH SETTLING OF SOLID SLURRIES
Introduction: The behaviour of settling particles in slurry can be conveniently studied in small batch experiments. The data is then useful for designing large scale settling tanks which have a number of applications.(e.g. clarification of waste water) The main information required for design is the settling rate of the particles as a function of the system parameters such as particle size and shape , concentration, geometry of the system, etc. The effect of concentration on the settling slurry continuously increases with time. The effect of geometry of the system on the settling rate can be significant. When the cylinder is tilted, Boycott (1920) found that the settling rate increases due to shorter sedimentation path. This phenomenon is known as the boycott effect, and is used to enhance the rate of settling in some applications. Objectives: i) Vertical Cylinders: Obtain the batch settling data for the given calcium carbonate slurry (i.e. the settling rate versus concentration of slurry), and demarcate the different settling regimes. (‘free settling” and ‘hindered settling’) Tilted Cylinders: Obtain the batch settling data in the free settling regime for different angles. Observe the flow patterns during the settling.

ii)

Procedure: Vertical Cylinder: 1) Note the initial concentration of slurry. 2) After thoroughly mixing (so that the concentration of the slurry is uniform), recored the height of the slurry below the clear liquid versus time until a constatnt height is obtained. 3) Simultaneously carry out similar runs for second vertical cylinder. Tilted Cylinder: 1) Fix the angle of the cylinder to a particular value.(Figure 1) 2) Note the initial concentrating of slurry. 3) After thoroughly mixing (so that the concentration of the slurry is uniform). Record the height versus time (Figure 1) in the free settling regime. Observe the flow patterns of the solids and fluid. 4) Repeat for 3 different angles.

Theory and Analysis: (i) Vertical Cylinders: Depending on the concentration of the slurry, two regimes of settling are possible, free settling and hindered settling. As the name implies, in free settling, each particle is unaffected by the motion of the neighbouring ones and its terminal velocity is given by ⎛ 4 g ( ρp − ρ ) Dp ⎞ 2 ⎟ Ut = ⎜ ⎜ ⎟ 3C D ρ ⎝ ⎠ where ρp and ρ are the densities of the particle and the suspending medium respectively. Dp is the diameter of the particle and CD is the drag coefficient. In the hindered settling regime due to particle-particle interactions and up draft of liquid, the velocity of individual particles is considerably smaller. The settling velocity (u0) may be estimated by an empirical equation of the form. us = u t ε n where ε is the volume fraction of the fluid and n is a constant. From your data, plot the settling velocity which is given by us = −(dh dt ) versus concentration and hence estimate the concentration at which the settling crosses over from the free settling to the hindered regime. Assuming that the concentration is nearly uniform over the cylinder, the concentration at any time is given by
C 0 h0 h where C0 is the initial concentration and h0 is the initial height of the suspension-clear liquid interface. If acceleration of the particles during the start of their fall is neglected, the rate of change of height is simply given by C=
1

dh = −u t dt
Find the equivalent diameter of the particles using the free settling data (Ref. P. 139, Unit Operations of Chemical Engineering, McCabe, Smith and Harriot for C0. Using the equivalent diameter found by this method, calculate the exponent ‘n’ in the empirical equation for hindered settling. Compare with values in the literature.

ii) Tilted Cylinders:
The theory for an increased rate of the settling for inclined cylinders was proposed by Ponder-Nakamura and Kuroda (PNK) based on the increased projected area available for settling. The Volumetric rate of increase if the clear fluid (S) according to the PNK theory is given by

S= utW (b secθ + H tanθ) Where W = width of the cylinder. See Figure 1 for definition of θ, b and H. If δ (figure 1) is small, the rate of change of height with time is given by

dH ⎛ H ⎞ = −ut ⎜1 + sin θ ⎟ dt b ⎝ ⎠ Compare your data with the above expression. The flow patterns observed during sedimentation can be explained qualitatively if the suspension is treated as homogeneous fluid. (P.145 McCabe, Smith and Harriot). Once sedimentation starts, the system can be supposed to consist of two fluids, the clear liquid of density ρ and the suspension of density ρs = ρε + (1-ε)ρp Based on the densities, it is possible to decide whether a particular configuration of the two fluids is stable or unstable. Using this physical picture try and rationalize the flow patterns that you observe. A quantitative analysis of the problem has been carried out by Acrivos and Herbolzheimer(1979)
Points for Discussion: i) Vertical Cylinders:

1) Can you verify the diameter of the particles by an independent measurement? 2) What are some of the other parameters besides particle size which affect the sedimentation rate? 3) What would be the effect of the sedimentation, process if particles have a tendency to agglomerate? 4) Could you design a continuous settler based on the batch data?
ii)Tilted Cylinder:

1) Does the data taken agree with the PNK theory? If not what could be the possible causes for the deviation? 2) What would be the effect of concentration of suspension on the circulatory flow produced in the case of tilted cylinders? 3) Can you derive the PNK theory equations? 4) If we accept that a fine suspension behaves essentially as a homogeneous fluid, can you think of a way how it can be used to separate solids of different densities? (P. 889, McCabe, Smith and Harriot)
Reference:

Unit Operations of Chemical Engineering, McCabe, Smith and Harriot Boycott (1920), Nature, 104, 532.

Ponder (1925), Quart J. Exp. Physics, 15, 235 Nakamura and Kuroda (1937), Keijo J. Medicine, 8, 256. Acrivos and Herboizheimer (1979), J. Fluid Mech, 92, 435.

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