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ABSTRACT The main industrial purpose of gravitational sedimentation is to separate solids from a liquid for
purpose of obtaining a liquid or solid that may be of value, or separation before disposal. In this
experiment, the suspension height was recorded as time elapsed, for suspensions of different
mass concentrations. The effects of initial suspension concentration on sedimentation
characteristics were determined from sedimentation curves for different mass concentrations, and
mass settling rate in linear hindered settling against mass concentrations. Results showed that the
rate of fall of suspension height decreased linearly, in linear hindered settling region, with
increasing mass concentrations. The concentration at which mass settling rate of solids is a
minimum for the 2.5% mass concentration, and the corresponding settling velocity were
determined through graphical analysis of the sedimentation curve for the 2.5% concentration
suspension. The limiting concentration and corresponding settling velocity were found to be
2.84% mass concentration or 25.2274 kg m-3, and 0.2278 mm s-1, respectively.
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OBJECTIVES Sedimentation is the tendency for particles in a suspension to settle out of the fluid by their
reaction (motion) to the forces acting on them [1]. The main purpose of gravitational
sedimentation is to separate solids from a liquid for purpose of obtaining the liquid or solid that
may be of value, or separation before disposal [2]. Gravitational sedimentation is widely used in
many industries for treating wastewaters containing suspended material such as chromium from
wastewaters of tanning industries [3]. Gravitational sedimentation is also widely used in food
industries for separating debris from raw materials, crystals from their mother liquor and product
particles from air streams [4].
The main objectives of this experiment were:
To investigate the effect of initial suspension concentration on sedimentation
characteristics
To analyse the rate of settling versus concentration curve from a single batch test
To identify the concentration at which the mass settling rate of the solids is a minimum
at a mass concentration of 2.5%
To determine the settling velocity at 2.5% concentration
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APPARATUS/PROCEDURE
Figure 1 above shows a sketch of the W2 Sedimentation Study Apparatus used for the
experiment.
Other apparatus used for this experiment include water, the substance that was suspended in the
water, and a stopwatch.
The procedure followed in conducting the experiment:
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1. The diameter of the tubes was measured.
2. The black lighting of the apparatus was turned on.
3. The tube containing the 2% mass concentration was removed from the Armfield
apparatus and shaken until a uniform suspension was obtained. The tube was then
replaced and a stopwatch was simultaneously started.
4. The height of suspension was recorded every 30 seconds until the rate of change of
height suddenly decreases.
5. Steps 3 to 4 were repeated for 2.5%, 3% and 4% mass concentrations.
6. After 24 hours the final compaction heights for the four different mass concentrations
were recorded.
NOMENCLATURE
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CL – the limiting concentration
C0 – the original suspension concentration at the original height H0
d – equivalent sphere diameter
GS – mass settling rate
Hi*- the y-intercept of the tangent at the critical point, Hi
ms – mass of solids
S – slope of linear part of graph of height of suspension interface against time for a given mass concentration.
Uc – sedimentation velocity of particle in suspension
V – volume of occupied test vessel.
µ - liquid viscosity
ρ – liquid density
ρp – particle density
THEORY
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Sedimentation is the tendency for particles in a suspension to settle out of the fluid by their
reaction (motion) to the forces acting on them [1]. In high concentration suspensions, the
frictional force experienced by particles, at a given velocity, relative to the fluid, is increased by
the interactions between particles [5]. The sedimentation velocity tends to decrease steadily as
the concentration of suspension is increased [5].
The sedimentation velocity of a particle, uc, according to Steinuor’s studies is given by:
[5].
Figure 2 above shows the four zones of sedimentation of concentrated suspensions. [5]
At the beginning of sedimentation of a suspension, after a brief acceleration period, the interface
between the clear liquid and suspension moves down at a constant rate as particles settle at
bottom of tube [5]. When this interface approaches the sediment layer or the top of zone C, the
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rate of decrease, decreases until the critical settling point. Figure 3 below shows the variation of
the height of interface between zones A and B with time.
Figure 3 above shows the effect of concentration on the sedimentation of calcium carbonate
suspensions. [This figure was taken from [5] (Coulson and Richarson)]
Figure 3 illustrates that the higher the concentration, the smaller the rate of fall of the suspension
height as the upward velocity of the displaced fluid is greater [5].
The rate of sedimentation in the linear period of settling is given by:
The limiting concentration, CL can be determined by:
Where, C0 is the original suspension concentration at the original height H0
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Hi*is the y-intercept of the tangent at the critical point, Hi.
Hi* is determined from the graph of height of suspension interface against time for a given mass
concentration using the following procedure:
1. Draw tangents to the curve for the two linear regions (constant rate and compaction).
2. Draw a bisector at the point of intersection of the tangent lines so that the bisector cuts the sedimentation curve. This point of intersection of bisector with sedimentation curve gives the critical point.
3. The point of intersection of the tangent at critical point with the y-axis gives Hi*.
The settling velocity, ʋL at the limiting concentration is the gradient of the sedimentation curve at the critical point Hi. The gradient of the tangent at critical point therefore gives the settling velocity.
RESULTSTable 1 below shows suspension height at different times for different mass concentration suspensions.
Time (s) H (mm) at 2% Conc.H (mm) at 2.5% Conc.H (mm) at 3% Conc. H (mm) at 4% Conc.
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0 840 840 840 840
30 831 835 835 837
60 825 827 828 834
90 815 818 822 830
120 808 810 815 827
150 795 802 807 823
180 783 787 800 819
210 777 780 793 816
240 765 768 786 813
270 753 758 779 809
300 740 749 771 806
330 725 739 765 803
360 713 729 758 799
390 700 717 751 796
420 689 709 744 793
450 676 699 738 790
480 662 688 731 786
510 652 680 724 784
540 637 671 718 781
570 623 660 712 778
600 609 652 705 775
630 597 644 699 772
Time (s) H (mm) at 2% Conc.H (mm) at 2.5% Conc.H (mm) at 3% Conc. H (mm) at 4% Conc.
660 584 634 692 769
690 571 623 684 765
720 558 615 679 763
750 545 606 673 760
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780 532 597 668 758
810 520 589 662 755
840 508 580 656 753
870 495 570 650 750
900 480 563 644 747
930 469 555 638 744
960 457 546 633 742
990 442 537 627 739
1020 426 528 622 736
1050 416 520 617 733
1080 405 513 611 731
1110 389 504 605 728
1140 379 498 600 726
1170 364 488 595 723
1200 354 481 590 721
1230 342 474 585 718
1260 332 466 580 715
1290 322 459 575 713
1320 308 451 571 710
1350 299 444 566 708
1380 293 438 562 705
1410 288 430 558 702
Time (s) H (mm) at 2% Conc.H (mm) at 2.5% Conc.H (mm) at 3% Conc. H (mm) at 4% Conc.
1440 283 425 553 700
1470 279 418 549 697
1500 276 412 545 695
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1530 272 407 541 692
1560 269 401 537 690
1590 266 395 532 687
1620 262 390 528 684
1650 259 385 524 682
1680 256 380 521 679
1710 253 376 517 677
1740 250 372 513 675
1770 247 367 508 672
1800 243 363 505 669
1830 241 359 502 667
1860 238 355
1890 235 352
1920 232 347
1950 229 344
1980 226 341
2010 224 337
2040 221 333
2070 218 330
2100 215 326
2130 212 323
2160 209 319
2190 207 315
Time (s) H (mm) at 2% Conc.H (mm) at 2.5% Conc.H (mm) at 3% Conc. H (mm) at 4% Conc.
2220 311
2250 308
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Table 2 shows the final compaction height after 24 hours for 2%, 2.5%, 3%, and 4% mass concentration.
% Mass Concentration 2 2.5 3 4
Final Compaction Height after 24 hrs (mm) 73 98 124 160
The internal diameter of the tubes, D was measured to be 5.1cm.
Graph 1 above shows the variation of suspension height with time for 2%, 2.5%, 3%, and 4%
mass concentration suspensions.
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CALCULATIONSCalculating Mass Settling Rate
The rate of sedimentation in the linear period of settling is given by:
From graph 1 above it can be seen that the hindered settling linear portion of the sedimentation curves occurred in the approximate time interval 400s to 1000s.
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Graph 2 above shows the hindered settling linear portion of the sedimentation curves for different mass concentrations and relationships of linearity.
S (mm/s) = coefficient of x in the linear relationship for the hindered settling linear portion of a sedimentation curve, for a given mass concentration.
Finding V:
V= (internal cross-sectional area of the tube) × (suspension height at time: 0 seconds)
=
=
= 0.0017 m3.
Finding ms:
ms = % mass concentration × mass of water
Mass of water = density of water × volume of water
Volume of water
= × [(suspension height at time: 0 seconds) – (final compaction height after 24 hours)]
At 25°C the density of water is 997 kg m-3 [5].
For 2% mass concentration suspension:
ms = (2/100) × 997 × ( 0.840 – 0.073)
= 0.031243 kg
Therefore the mass settling rate, for 2% mass concentration suspension, is:
GS = - (S × ms) / V
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= - ((-0.4331 × 10-3) × 0.031243) / 0.0017
= 0.00796 kg m-2 s-1.
Table 3 shows calculated values for determining the mass settling rate for 2%, 2.5%, 3%, and 4% mass concentration suspensions.
% Mass Concentration 2% Conc. 2.5% Conc. 3% Conc. 4% Conc.
S (m/s) -0.00043 -0.0003 -0.0002 -0.000094
Height of Suspension at t = 0s (m) 0.84 0.84 0.84 0.84
V(m-3) 0.0017 0.0017 0.0017 0.0017
Final Compaction Height after 24hrs (m)
0.073 0.098 0.124 0.16
Volume Of Water (m-3) 0.001567 0.001516 0.001463 0.001389
mw (kg) 1.562142 1.511225 1.458271 1.38495
ms (kg) 0.031243 0.037781 0.043748 0.055398
G (kg m-2 s-1) 0.00796 0.006658 0.005263 0.003063
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Graph 3 shows mass settling rate against concentration.
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Calculating Concentration at which Mass Rate of Solids is a Minimum, CL
Graph 4 above shows the sedimentation curve for the 2.5% mass concentration.
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C0 = (ms / V)
= (0.037781 / 0.0017)
= 22.2241 kg m-3
H0 = 0.8400 m
On graph 4, Hi* was graphically found to be 0.7400 m.
Hence, the limiting concentration is:
CL = (C0 × H0) / Hi*
= (22.2241 × 0.84) / (0.74)
= 25.2274 kg m-3
Alternatively, in terms of % mass concentration:
CL = (C0 × H0) / Hi*
= (2.5% × 0.84) / (0.74)
= 2.84%
Calculating the settling velocity, ʋL for the limiting concentration
ʋL = gradient of tangent of critical point on sedimentation curve
=
= - 0.2278 mm s-1
= 0.2278 mm s-1
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DISCUSSION The sedimentation curves for different mass concentrations, illustrated in graph 1, are similar to
those in figure 3 (taken from Coulson and Richardson, 1991). Graph 1 shows that rate of fall of
suspension height decreases with increasing concentration. That is, the rate of mass settling
decreases with increasing concentration. According to the theory, this is due to an increased
upward velocity of displaced fluid. This means that gravitational sedimentation is of low cost to
industries as long as the suspension to be settled is not too concentrated such that the process
becomes too time consuming.
Graph 1 already shows that the rate of mass settling decreases with increasing concentration.
Graph 3 shows that this rate of decrease of mass settling with increasing concentration, is linear
in the linear hindered settling region. This linear relation can be used to determine the mass
settling rate for any concentration suspension of the same substance and liquid.
The limiting concentration is the concentration at which the mass rate of solids is a minimum.
For the 2.5% mass concentration suspension the limiting concentration was found to be 2.84%
mass concentration or 25.2274 kg m-3 and the corresponding settling velocity to be
0.2278 mm s-1. If a sedimentation tank or thickener were to be designed for this concentration
suspension the fastest rate of addition of solids that would be used depends on the limiting
concentration and its corresponding settling velocity.
The main error/problem that occurred for this experiment was determining the suspension
height, especially for the 2% and 2.5% mass concentration suspensions. For these lower mass
concentration suspensions the suspension height was not well defined - there was a ‘cloud’ of
particles above the suspension height. This was probably due to the rapid decrease in suspension
height as this was not an issue for 4% concentration suspension - in which suspension height
decreased slowly. As time progressed this ‘cloud’ disappeared and the suspension height became
more defined.
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The suspensions were made-up of coloured particles to make the determination of the
suspension height easy.
CONCLUSION The effects of initial suspension concentration on sedimentation characteristics were determined
from plots of suspension height with time (sedimentation curves) for different mass
concentrations, and mass settling rate in linear hindered settling against mass concentrations.
Plots showed that the rate of fall of suspension height decreased linearly, in the linear hindered
settling region, with increasing mass concentrations.
The concentration at which mass settling rate of solids is a minimum for the 2.5% mass
concentration, and the corresponding settling velocity was determined through graphical analysis
of the sedimentation curve for the 2.5% concentration suspension. The limiting concentration
and corresponding settling velocity were found to be 2.84% (or 25.2274 kg m-3) and
0.2278 mm s-1, respectively.
21
REFERENCES[1] Cited 24th November 2009. Available from the internet:
<http://en.wikipedia.org/wiki/Sedimentation>
[2] Svarosky, L. (2005). Solid Liquid Separation. Butterworth-Heinemann, Oxford.
[3] Cited 24th November 2009. Available from the internet:
<http://www.doiserbia.nb.rs/
(A(XLXjYBDsyQEkAAAANTk1YjJiODYtY2JkMy00NTQ5LWI1NjktM2ViYmMyYWQ0NjB
lgwKt8Ko37nFc1ehaA1U2lNYLHWY1))/img/doi/1450-7188/2008/1450-71880839121V.pdf>
[4] Cited 24th November 2009. Available from the internet:
< http://www.nzifst.org.nz/unitoperations/mechseparation3.htm>
[5] Coulson, J. M. And Richardson, J. F. (1991). Chemical Engineering Vol. 2 (4th ed.)
Butterworth-Heinemann, Oxford.