Consolidation dewatering and centrifugal sedimentation of #occulated
activatedsludge
S. J. Lee
a, C. P. Chu
a, R. B. H. Tan
b, C. H. Wang
a;b, D. J. Lee
a;∗aDepartment of Chemical Engineering, National Taiwan University, 1, Sec. 4 Roosevelt Road, Taipei 10617, Taiwan
bDepartment of Chemical and Environmental Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore 117576, Singapore
Received28 June 2002; receivedin revisedform 19 September 2002; accepted24 December 2002
Abstract
This study investigated experimentally the consolidation dewatering and centrifugal-settling processes for activated sludge subjected to cationic polyelectrolyte #occulation. The results were reported for the dynamic response of sediment cake thickness (an index for cake compaction) under various doses of polyelectrolyte conditioning, compression–permeability cell con8guration and mode of operation (batch and continuous) in a centrifugal-settling cell. The reduction in sediment thickness of sludge by consolidation and centrifugation was foundto correspondmostly well with the optimal dose of polyelectrolyte basedon the capillary suction time. The relaxation/rebound of cake thickness was observed in both consolidation dewatering and centrifugal dewatering with comparable compaction/relaxation time scale ratios. The equilibrium sediment consolidation ratio increases with the e:ective solid pressure characterized by Pm and Ps, for the
consolidation dewatering and centrifugal sedimentation, respectively. The experimentally determined time scales of the cake consolida-tion dewatering/centrifugal sedimentaconsolida-tion processes agree reasonably well with the theory by Landman and Russel (Phys. Fluids A 5 (1993) 550).
? 2003 Elsevier Science Ltd. All rights reserved.
Keywords: Cake; Consolidation; C–P cell; Centrifugal settling; Plastic deformation,
1. Introduction
Multistage consolidation/centrifugation dewatering is sometimes encounteredin wastewater treatment processes. In order to achieve smooth function in such devices, it is im-portant to have fundamental understanding of these individ-ual unit operations for solid/liquid separation applications.
Buscall andWhite (1987) investigatedthe consolida-tion of concentratedsuspensions andproposeda theory of sedimentation. Their analysis considered empirical yield stresses for the network of #occulatedsuspensions which needto be determinedby further studies. In calculating the initial sedimentation rate under uniform acceleration, a methodhadbeen proposedto estimate the compressive yieldstress from centrifuge experiments. Subsequently, the basic concept was further extended via a series of studies by Landman and workers (Landman & Russel, 1993; Landman, White, & Eberl, 1995; de Kretser et al.,
∗Corresponding author. Tel.: +886-223625632;
fax: +886-22362-3040.
E-mail address:[email protected](D. J. Lee).
2001) to investigate the pressure 8ltration of #occulatedsus-pensions.Landman and Russel (1993)useda power-law ex-pression (to relate the empirical yieldstress with local solid volume fraction) in a one-dimensional model for a pres-sure 8lter andexaminedthe relative magnitudes of the time scales for 8ltration andsedimentation. Later,Landman et al. (1995)consideredthe pressure 8ltration of #occulatedsus-pensions by various types of rheological power-law func-tions for the compressive yieldstresses. The resulting simi-larity solution for consolidation stage agreed reasonably well with conventional engineering analysis of the same problem which correlates consolidation ratio with consolidation date by an empirical formula.
Results about the consolidation dewatering in compres-sion–permeability (C–P) cells have been reportedin the lit-erature (Lu, Huang, & Hwang, 1998;Wu, Lee, Zhao, Wang, & Tan, 2000; Wu, Lee, Wang, Chen, & Tan, 2001). It is usually assumed that the dependence of compressive stress on the local volume fraction in the cake can be determined through such a device. In general, sidewall friction consti-tutes a signi8cant fraction of the total pressure transmit-ted throughout the 8lter cake. Under such conditions, the 0009-2509/03/$ - see front matter ? 2003 Elsevier Science Ltd. All rights reserved.
deviation of porosity distribution from a one-dimensional cake structure is expected.
Centrifugal dewatering/settling processes using polyelec-trolyte #occulents have commonly been seen in wastewater treatment plants. Chu andLee (2001) showedthat sludge #occulation wouldyielda signi8cant sedimentation e:ect at the 8rst stage. They observedthat an optimal rotational speedexists to which the dewatering rate reaches a maxi-mum. Yen andLee (2001)showedthat the plastic defor-mation is observedin the centrifugal-settling method. For instance, the irreversible yielding in activated sludge cake formedunder 200–500 rpm centrifugation (equivalent to 8– 50g acceleration) can result in higher than 25% error in the estimation of bound water content. The error is made due to the fact that subjectedto the removal of centrifugal force, the sediment rebounds corresponding to over 25% rebound ratio.
Most of the above analyses were focusedon one-step consolidation dewatering or centrifugal-settling processes. Multistage processes have not been the main topic of re-search until recently.Usher, de Kretser, and Scales (2001)
proposeda new technique for dewatering characterization basedon steppedpressure 8ltration compressibility andper-meability tests to determine Py(’) andhinderedsettling
function R(’). The results were analyzedwith a set of key 8ltration equations using the pressure 8ltration theories de-velopedby Landman andcolleagues (Landman & Russel, 1993;Landman et al., 1995).
In view of the progress of the previous studies mentioned above, the objectives of the present study are three-fold: (i) quantitative comparison of the dewaterability of a wet cake by consolidation and centrifugal settling; (ii) understanding the di:erence in eJciency between the dewaterability of continuous andbatch steppedoperations; (iii) determining the relaxation of the wet cake subject to the release of exter-nal driving forces (consolidation pressure, rotatioexter-nal torque) andits implication on the elastic/plastic deformations of the cake.
2. Material and methods 2.1. The sample
Sample-U: Activatedsludge samples (pH 6.8–7.1) were taken from the re#ux stream of Ulu Pandan Sewage Treat-ment Works, Singapore. The design of the Works is based on conventional activated sludge process using di:used air aeration system, having a total treatment capacity of 361000 m3=day. After thickening, the dry solid content of
sludge, determined by weighing and drying at 104◦C, was 1.33% w/w. The chemical oxygen demand for the super-natant (COD) andthat for the total sludge (TCOD) are 103 and8500 mg=l, respectively. After the mixing andprior to the settling, a small quantity of sludge–polymer aggre-gates in the vessel was transferredcarefully into the fresh
electrolyte at the same pH andelectrolyte concentration as the original Sample-U andT.
Sample-T: Activatedsludge was taken from the wastew-ater treatment plant in Presidential Bread Plant (Chung-Li, Taiwan) which treats approximately 250 ton of foodpro-cessing wastewater per day using conventional activated sludge process. The sample was taken from the recycled sludge stream, whose sediment was the testing sample with a solidweight percent of 0.7% w/w.
2.2. Capillary suction time (CST) and cationic polyelectrolyte conditioning
Capillary suction apparatus as described inLee andHsu (1992, 1993)was employedto estimate the sludge 8lterabil-ity. In brief, the inner cylinder radius was 0:535 cm. The time requiredfor the 8ltrate to migrate from 1.5 to 3:0 cm was de8ned as the CST. The sludge was subject to chemi-cal or physichemi-cal conditioning. For chemichemi-cal conditioning, the cationic polyelectrolyte indicated as polymer T-3052 was obtainedfrom Kai-Guan Inc., Taiwan. The polymer T-3052 is a polyacrylamide with an average molecular weight of 107, anda charge density of 20%.
2.3. Light scattering tests
Small-angle laser light scattering tests were conducted using a Malvern Mastersizer/E which consists of a 5 mW He–Ne laser ( = 632:8 nm) as the light source, andan optic lens andphoto-sensitive detectors. The scatteredlight was collectedat angles between 0:03◦ and6:52◦ using a 31-element solid-state detector array. The light obscuration level of samples hadto be maintainedbetween 10% and 30% for reliable measurements. The Malvern Mastersizer/E was also usedto measure the aggregate size between 1.2 and600 m. The Mastersizer measures the scatteredlight 20 times, each time for 20 s, over a total of 400 s. A small magnetic stirrer was installedin the scattering chamber to suspendthe sample particles. The inducedcurrent didnot markedly a:ect the scattered intensity from samples. Such a stirrer is essential for reliable measurement, especially for #occulated sludge #ocs whose sizes, which determine the sedimentation velocities, are generally large.
2.4. C–P cells
Figs. 1a and b depict the schematic diagrams of the C–P cells andother supportive apparatus proposedbyTeoh, Tan, He andTien (2001) (cell-S, locatedat the National University of Singapore) andbyLu et al. (1998) (cell-T, locatedat the National Taiwan University). The loadat the top andthe transmittedpressure to the bottom surface were measuredtogether with the cake height during each test. The cell-S had a cylinder made of stainless steel with inner diameter 75:3 mm. The cylinder of cell-T was made
Fig. 1. Schematic diagram of the (a) C–P cell (cell-S) and (b) C–P cell (cell-T).
Fig. 1. continued.
of acrylate which has an inner diameter of 50:1 mm. Based on the same cake height, the cake/cell wall contacting area was greater for cell-S than that for cell-T. The other details for these two apparatus couldbe foundinWu et al. (2000)
andLu et al. (1998), respectively.
Cell-S: The loadat the top andthe transmittedpressure to the bottom surface were measuredtogether with the cake
height during each test. A complete C–P cell test com-prisedtwo stages: the compression stage andthe permeation stage. The cell couldtrack both stages since all data from pressure transducers as well as from the displacement mea-surement were automatically sent to a computer for storage andprocessing. The pressure range under investigation was 25–200 kPa. The choice of such a pressure range for test was attributedthe following two reasons. Firstly, in prelimi-nary tests at the appliedpressure of 50 kPa the cake structure of activatedsludge revealeda signi8cant collapse, which hadnot occurredat the test of the less pressure. Hence the lower limit for appliedpressure under investigation was set at 25 kPa. Moreover, since the total testing time hadto be limitedwithin 7 days, the upper pressure limit was taken as 200 kPa. Although the practical range for sludge dewater-ing couldbe up to 500–700 kPa, however as the present ex-perimental data illustrate, the basic characteristics for cake properties wouldkeep unchangedat pressures exceeding 200 kPa.
Cell-T: For the sake of comparison, all experimental con-ditions were maintained to be closely similar to cell-S, in-cluding slurry preparation as well as the subsequent cali-bration anddata acquisition. After the compression having reachedequilibrium under the appliedload, the thickness of compressedcake was measuredandrecorded. The pressure range under investigation is 13–202 kPa.
2.5. Consolidation–relaxation experiments
Prior to the C–P cell test the septum was 8rst 8lledwith 8ltrate. The slurry was carefully pouredinto the cylinder anddrainedto form a saturated, wet cake. The piston was positionedat the top of formedcake, through which the mechanical force was applied. During the compression the valve-A (permeation valve) was close andvalve-B open,
Fig. 2. Schematic illustration of the centrifugal tests. Ps: local solid
compressive pressure of the centrifugal test (Pa); R: distance between center of centrifuge andbottom of sediment (m); r: radial coordinate of cylindrical coordinate system (m); ri: distance from center of centrifuge
to surface of sediment (m): angular velocity of the centrifuge (rpm or rad/s).
which allowedthe drainage of the 8ltrate. Before andaf-ter having reachedmechanical equilibrium with the applied load, the thickness of compressed cake was continuously measuredandrecorded. Then the permeation test was con-ducted by allowing the 8ltrate to #ow from a constant-head reservoir through the valve-A andthe cake. An electronic balance measuredthe 8ltrate weight. With the #ow rate and the pressure drop data, the speci8c resistance to 8ltration of cake could be determined. The temperatures during testing were usedto correct the viscosity of 8ltrate.
The transmittedpressure at the bottom of the cake, Pt,
was also recordedandcomparedwith P. Consolidation– relaxation curve for testing sample-T (with four di:erent doses of original, 80, 160, and 280 ppm, respectively) on the cell-T was constructed. Five panels of L=L0 vs. time curves
are shown in the consolidation plot with increasing axial loads (in the order of 13, 32, 49, 104, and 202 kPa). Each plot is followedby a relaxation curve during which the axial load was suddenly released to ambient pressure (P =0), and then the cake thickness was recorded as a function of time. Similarly, the consolidation–relaxation curve for testing sample-U on the S-cell was constructedfor four di:erent doses of original, 80, 280, and 480 ppm, respectively. Four panels of L=L0vs. time curves are shown in the consolidation
plot with increasing axial loads (in the increasing order of P = 25, 50, 100, and200 kPa).
2.6. Centrifugal-setting–relaxation experiments
The arm-suspendedcentrifuge proposedbyYen andLee (2001)was modi8edandusedin the present study. Fig. 2
shows a sediment of equilibrium thickness in a centrifugal tube. Transparent plastic chamber (with the inner diameter andlength being 4 and7 cm, respectively) was usedfor bet-ter visual observation. The setting cell was connectedto a rotating arm. The length from the center of rotation to the
8lter medium and the span angle from the center of rotation to the 8lter medium were measured as 26:5 cm and12◦, re-spectively. A total of 97:4 g of sludge was put into the set-ting cell. The initial height of sample was 6:0 cm (L0). A
rotational speedranging from 300 to 1050 rpm was regu-latedby a variable-speedmotor through driving the motor belt. The e:ective one-dimensional centrifugal 8eld, accel-erating at the bottom of the cell of 27.4–336:2g, was anal-ogous to the one-dimensional consolidation process men-tionedin the proceeding section. A stroboscope emitting light synchronizedwith the rotating cell that “froze” the im-age of the supernatant–sediment interface of the centrifuged slurry. The corresponding images at di:erent time steps were capturedby a video camera. The stepwise change of ro-tation speedcouldbe carriedout in two di:erent modes: batch mode and continuous mode. Centrifugal-settling ex-periments were carriedout for testing Sample-T with four di:erent doses of original, 80, 160, and 280 ppm. Three panels of L=L0 vs. time curves were shown in the
consoli-dation plot with increasing rotation speed (batch operation in the order of 300, 450, 550, 850 rpm). Each of these plots was followedby a relaxation curve in which the torque to the rotation speed was suddenly removed, and then the cake thickness was recorded as a function of time. Similar pro-cedures were applied for Sample-U for four di:erent doses: original, 80, 280, and480 ppm, respectively. Four panels of L=L0 vs. time curves were shown in the consolidation plot
with continuous increasing rotation speedin the order of 350, 560 and1050 rpm.
In the batch mode of operation, the preliminary tests showedthat most of the sediments from Sample-T could reach mechanical equilibrium within 1500 s. Hence the centrifugal settling was recorded for 2000 s. The ex-ceptional cases were for the original sludge and at low rotational speeds 300 and 450 rpm, under which condi-tions the mechanical equilibrium was establishedafter about 3000 and2000 s, respectively. In order to capture the complete dynamic behavior of the sediment cake, the corresponding record times were set as 4000 and 3000 s, respectively. The sludge height equilibrated with the centrifugal force was termedas Lc. Subsequently,
the centrifuge speedwas reducedin 10 s till a complete stop. The sediment height was monitored continuously for another 600 s for the relaxation (rebound) of the sediment height. The 8nal sediment height was termed as Ls. In the continuous mode of centrifugal-settling–
relaxation experiments (Sample-U), the procedures were largely the same as the batch mode operation except that the increase of rotational speedwas carriedout in a stepwise way (350, 560 and1050 rpm). As a re-sult, the sediment formation followed a particle depo-sition pattern di:erent from the batch mode operation. The time taken to reach equilibrium was in general more than 3000 s, much longer than the batch opera-tion. The rebound of the sediment was recorded for about 800 s.
2.7. Comparison between consolidation dewatering and centrifugal-settling tests
The centrifugal acceleration can be relatedto the e:ec-tive radial pressure gradient across the sediment/cake by the following formula (Lee, 1994;Chu & Lee, 2001):
9P 9r = 9PL 9r = lr2 at r0¡ r ¡ ri; (1) 9P 9r = 9PL 9r + 9Ps 9r = lr2+ (s− l)(1 − )r2 at ri¡ r ¡ R; (2)
where Ps is the local solidcompressive stress, the local
porosity of the sediment, s and l the density of the solid
andliquid, and the angular velocity of the centrifuge. For a given rotational speed , one can use Eq. (2) to calculate the equivalent radial pressure gradient.
Integration of the solidpressure in Eq. (3) with respect to r yields the compressive stress at the bottom of the tube, Ps(R)
(Murase, Iwata, Adachi, Gmachowski, & Shirato, 1989): Ps(R) = (s− l)2
R
ri
(1 − )r dr; (3)
where ri denotes the distance from center of centrifuge to
surface of sediment. The reading of riis basedon the
aver-age of triplicate sample measurements from three di:erent locations. The error introducedin such averaging wouldnot be signi8cant when the ratio (R−ri)=R is much smaller than
1. If R R − ri, Eq. (3) couldbe approximatedas follows:
Ps(R) = (s− l)2R + r2 i
R
ri
(1 − ) dr
= (s− l)2R + r2 i!0; (4)
where !0 refers to the total solidvolume in the mixture
per unit sectional area. Eq. (4) is then appliedto Eq. (2) to evaluate the average radial pressure gradient across the cake:
dP dr = dPL dr + dPs dr = Lr2+ Ps(R) (R − ri): (5)
In using Eq. (5) to calculate the radial pressure gradient, it is assumedthat the solidcompressive stress at the surface and bottom of the sediment is 0 (refer to Fig.2) and Ps(R),
re-spectively. Table1lists the pressure gradient yielded in the centrifuge according to Eq. (5). From the tabulatedvalues, it is seen that the predicated radial pressure gradient via Eq. (2) is about the same magnitude as with Eq. (5); the rota-tional speed300–850 rpm (Sample-T) and350–1050 rpm (Sample-U) correspondto the equivalent radial pressure of 0.239–1.940 and0.326–2:961 MPa=m, respectively.
The analogy between the rotational speedandconsolida-tion axial loads can be deduced by matching the radial pres-sure gradient. For a given axial load P, the e:ective axial
pressure gradient across the cake is given by 9P
9x = P − Pt
H ; (6)
where H is the equilibrium thickness of the cake. Table2
summarizes the values of axial pressure gradient (dP=dx) computedby Eq. (6). In one of the columns, the de8nition of log mean pressure di:erence (Pm) is given by the following:
Pm=ln(P=PP − Pt
t): (7)
The dependence of Pm on the porosity is foundto agree
reasonably well with a previous work (Wu et al., 2000). 2.8. Scanning electron microscopic photographs
The sludge #ocs were 8rst immersed in glutaraldehyde andfollowedin OsO4 to chemically 8x the components
like protein and lipids. The moisture in the #ocs was grad-ually replacedby raising-concentration alcohol (50%, 60%, 70%, 80%, 90%, 95%, and100%) andacetone (100%). After critical point drying (CPD) (LADD) and coating by gold(SPISUPPLIES ION SUPTTER), the #ocs were ready for SEM observation (JSM-5600, JEOL, Japan). The pre-treating procedure of sludge cakes was slightly di:erent from the #ocs. The dewatered cakes (from centrifuge or C–P cell) were 8rst embedded in high-melting-point agarose to keep the entire shape. Some clump near the surface was taken away carefully andthen immersedin the glutaralde-hyde and OsO4. The subsequent procedures were then
com-pletely the same as the sludge #ocs. Agarose sticking on the cake (white portion) shouldbe carefully removedto ensure the cake surface couldbe observedby electron beam. 3. Results and discussion
The relevant properties (CST, -potential, andmean-mass -diameter) for Sample-T andSample-U are summarizedin Fig.3. In general, the solution pH is within the range 6.7– 7.1 andthe speci8c gravity of the solution is around1.4. An optimal dosage of sludge conditioner can be de8ned as either the amount of added chemicals that yields a distinct optimal dewaterability or the lowest amount of added chem-icals that results in an acceptable dewatering performance (Christensen, Sorensen, Christensen, & Hansen, 1993). The optimal polyelectrolyte dose for the Sample-T and Sample-U was foundto be 160 and280 ppm, respectively (Fig.3). The CST for original sludge was measured as 159 s (Sample-T) and96 s (Sample-U). With the increasing doses of #occu-lent, the CST was reduced till the optimal dose point where the CST values read25 and22 s for the Sample-T and Sample-U, respectively.
Zeta (-) potentials of aggregates were then measured by the zeta-meter (Zeter-Meter System 3.0, Zeter-Meter
Table 1
Equilibrium pressure gradient andyieldstress on the sediment/cake in centrifugal-settling experiments
-value L=L0 b Ps(Pa) dP=dr dP=dr P ((0)) (0)
(rpm) (dimensionless) (Eq. (4)) (Pa/m) (Pa/m) (Pa)
(Eq. (2)) (Eq. (5)) (Eq. (9)) (Eq. (10)) Sample-T, original 300 26:9g 0.500 0.0125 36.6 270,000 240,000 38.5 0.0139 450 60:6g 0.421 0.0128 82.7 609,000 539,000 88.9 0.0182 550 90:5g 0.400 0.0154 123.8 910,000 807,000 133 0.0212 850 216:3g 0.301 0.0234 300.0 2,180,000 1,940,000 304 0.0922 Sample-T, 80 ppm 300 26:9g 0.523 0.0119 36.5 270,0000 240,000 38.4 0.0133 450 60:6g 0.417 0.0132 82.9 609,000 540,000 87.3 0.0187 550 90:5g 0.378 0.0163 124 911,000 807,000 131 0.0234 850 216:3g 0.289 0.0234 299 2,180,000 1,930,000 316 0.113 Sample-T, 160 ppm 300 26:9g 0.497 0.0125 36.6 270,000 240,000 38.5 0.0138 450 60:6g 0.417 0.0132 83.0 609,000 540,000 87.4 0.0178 550 90:5g 0.423 0.0146 124 910,000 807,000 130 0.0188 850 216:3g 0.329 0.0210 299 2,180,000 1,940,000 309 0.0436 Sample-T, 280 ppm 300 26:9g 0.473 0.0131 36.6 271,000 240,000 38.6 0.0144 450 60:6g 0.364 0.0154 83.1 610,000 542,000 86.2 0.0205 550 90:5g 0.296 0.0211 125.7 913,000 810,000 131 0.0283 850 216:3g 0.311 0.0225 298 2,180,000 1,940,000 303 0.0427 Sample-U, original 350 36:7g 0.941 0.0098 61.3 381,000 326,000 63.3 0.0105 560 93:9g 0.928 0.0100 157 975,000 836,000 162 0.0114 1050 330:0g 0.675 0.0137 567 3,480,000 2,940,000 585 0.0259 Sample-U, 80 ppm 350 36:7g 0.857 0.0108 61.8 382,000 327,000 63.8 0.0117 560 93:9g 0.617 0.0150 162 995,000 837,000 167 0.0183 1050 330:0g 0.498 0.0186 577 3,540,000 2,950,000 596 0.0549 Sample-U, 280 ppm 350 36:7g 0.927 0.0100 61.4 368,000 326,000 63.4 0.0109 560 93:9g 0.826 0.0112 159 941,000 836,000 164 0.0136 1050 330:0g 0.534 0.0173 575 3,320,000 2,950,000 594 0.0801 Sample-U, 480 ppm 350 36:7g 0.650 0.0145 63.3 368,000 328,000 64.0 0.0154 560 93:9g 0.543 0.0174 164 944,000 840,000 166 0.0203 1050 330:0g 0.400 0.0236 583 3,320,000 2,960,000 590 0.0642
Inc., USA). The results for original sludge #ocs read
−12:9 mV (Sample-U) and −19:5 mV (Sample-T). The
readings for the #occulated sludge were in the range of
−12:8 to −14:9 mV (Sample-T) and −8:43 to −15:3 mV
(Sample-U). The particle size distribution was determined by Malvern Mastersizer/E with a mean-mass-diameter of approximately 151:9 m and68:7 mm for the Sample-U andSample-T, respectively. The true soliddensity was mea-suredby Accupyc Pycometer 1330 (Micromeritics), giving a measure of 1396:7 kg=m3 (Sample-U) and1450 kg=m3 (Sample-T) with a relative deviation of less than 0.5%.
The consolidation tests on cell-T showed faster sludge dewatering for increasing doses of polyelectrolyte #occu-lation (Fig. 4). There was hardly any dewatering for all samples when the axial load P was kept below 13 kPa. When P = 32 kPa, the collapse of the sediment cake was observedfor the samples with doses higher than 80 ppm. This was accompaniedby the dewatering of about 50 –60% of the total moisture contents in the conditioned sludge. In contrast, under the same level of axial load P, the dewatering of the original sludge was limited to only 10% of the total moisture contents. It was notedthat the
Table 2
Equilibrium pressure gradient and yield stress on the sediment/cake in consolidation dewatering experiments
P (Pa) Pt (Pa) Pm (Pa) b(dimensionless) H (mm) dP=dx(Pa=m)
Sample-T, original 14,000 2000 6160 0.0350 49.8 240,000 31,300 6000 15,300 0.0373 46.8 540,000 49,500 17,500 30,800 0.0467 37.4 858,000 107,000 71,500 88,100 0.0601 29.0 1,230,000 207,000 179,000 193,000 0.0758 23.0 1,210,000 Sample-T, 80 ppm 15,300 2000 6540 0.0324 47.1 283,000 30,900 18,000 23,900 0.0670 22.8 569,000 47,600 27,000 36,300 0.0762 20.0 1,030,000 104,000 80,000 91,600 0.0990 15.4 1,580,000 207,000 175,000 191,000 0.123 12.4 2,590,000 Sample-T, 160 ppm 13,000 1000 4680 0.0292 48.2 24,900 31,600 25,000 28,200 0.0746 18.9 349,000 47,600 37,000 42,100 0.0829 17.0 625,000 107,000 90,000 98,300 0.110 12.8 1,340,000 205,000 191,000 198,000 0.132 10.6 1,350,000 Sample-T, 280 ppm 13,000 1000 4680 0.0403 42.9 280,000 30,900 20,000 25,100 0.102 17.0 646,000 49,500 40,500 44,800 0.116 15.0 604,000 105,000 72,500 87,800 0.156 11.1 2,950,000 205,000 186,000 195,000 0.196 8.85 2,180,000 Sample-U, original 23,600 1200 7510 0.0267 49.9 449,000 49,400 2400 15,500 0.0511 26.1 1,800,000 98,800 44,300 68,000 0.0992 13.4 4,060,000 199,000 144,000 170,000 0.152 8.76 6,280,000 Sample-U, 80 ppm 23,600 1200 7500 0.0366 36.4 616,000 49,400 4790 19,100 0.0755 17.6 2,530,000 98,800 45,500 68,800 0.122 11.0 4,870,000 199,000 141,000 168,000 0.216 6.17 9,300,000 Sample-U, 280 ppm 23,600 1200 7500 0.0354 38.0 588,000 49,400 2400 15,500 0.0478 28.1 1,670,000 98,800 43,100 67,200 0.186 7.24 7,690,000 199,000 139,000 167,000 0.266 5.06 11,800,000 Sample-U, 480 ppm 23,600 1200 7500 0.0360 37.5 597,000 49,400 7190 2190 0.115 11.7 3,610,000 98,800 5390 74,100 0.214 6.3 7,130,000 199,000 150,000 173,000 0.328 4.11 11,900,000
polyelectrolyte #occulation hadimprovedsigni8cantly the dewatering capability under the same mechanical load range and the fastest consolidation dewatering occurred at 180 ppm, exceeding that with the CST estimated optimal poly-electrolyte dose (160 ppm in Fig. 3). Even at higher axial loads (P = 49, 104, 202 kPa), the decrease in the sediment
thickness showeda monotonic decrease anddewatering was about 60–80% of the original moisture contents in the #occulated sludge. Within this range of axial load, the dewatering of the original sludge was much more signi8-cantly ranging from 30% to 50% of the original moisture contents.
Fig. 3. Characteristics of Sample-T (left) andSample-U (right) sludge before andafter #occulation. Sample-T: pH=6:8, solidweight %=0:947%, density = 1450 kg=m3. Sample-U: pH = 6:8–7.1, solidweight % = 1:33%,
density = 1397 kg=m3.
Fig. 4. Consolidation–relaxation curve for Testing Sample-T (with four di:erent doses of original, 80, 160, and 280 ppm, respectively) on the T-cell. Five panels of L=L0vs. time curves are shown in the consolidation plot with increasing axial loads (in the order of 13, 32, 49, 104, and 202 kPa). Each
plot is followed by a relaxation curve corresponding to the suddenly release of axial load, and then the cake thickness is recorded as a function of time. The capillary suction pressure in CST test is commonly estimatedaround15 kPa (Lee & Hsu, 1992; Lin & Lee, 2001). This low pressure appliedtogether with the distinct particle packing might interpret the discrepancy observed for the optimal doses determined using CST and the present mechanical dewatering tests.
At the endof the consolidation, the axial loadP was re-movedandthe reboundof the sediment cake was observed over a periodof 60; 000 s. It was notedthat the relaxation (rebound) of the sediment cake was restored with a time scale comparable with that of the consolidation processes, irrespective of the doses of the polyelectrolyte #occulation. However, the restoredsediment thickness Lswas much
thin-ner than the original thickness L0. Within about 30; 000 s,
the relaxation/reboundwas apparently relatedto the recov-erable (elastic) deformation of the sediment cake, which constitutedof about 20–30% of the total deformation. The remaining 70–80% was left as unrecoverable (plastic de-formation). It was notedthat the recoveredcake is partly causedby the permeation of air into the consolidatedcake andhence the saturation of water in the inter-particle pores was not unity after the reboundhadoccurred.
The dependence of transmitted pressure Pt on P for the
original and#occulatedsludge Sample-T is shown in Table
2. It is notedthat the value of Pt=P increases with increasing
axial load P from about 10% to 90% for all types of samples tested. This con8rms the results shown in an earlier study such that the sidewall friction plays a key role in determining the consolidation dewatering behavior of a wet cake in a C–P cell (Wu et al., 2000).
Fig. 5. Centrifugation-settling–relaxation curve for Testing Sample-T (with four di:erent doses of original, 80, 160, and 280 ppm, respectively). Four panels of L=L0 vs. time curves are shown in the consolidation plot with continuous increasing rotation speed (in the order of 300, 450, 550, 850 rpm).
Each plot is followed by a relaxation curve in which the torque to the rotation is suddenly removed, and then the cake thickness is recorded as a function of time.
Using the same Sample-T, a series of centrifugal-setting-relaxation experiments were carriedout andthe results are shown in Fig. 5. It was notedthat under an acceleration equivalent to the consolidation process, the sediment forma-tion occurredwithin a much shorter time scale ranging from 1000 to 3000 s for the polyelectrolyte #occulatedsludge and original sludge, respectively. It was interesting to observe that, similar to the case of consolidation dewatering, #oc-culatedsludge reducedthe time requiredfor the sediment thickness L=L0to reach the value 0.3–0.5 as comparedto the
original sludge. The four rotational speeds had been calcu-lated(Table1) to correspondto the equivalent axial loads in the consolidation dewatering processes.
However, the resulting L=L0 vs. time curves showed
at least the following di:erences: (i) The 8nal equilib-rium sediment thickness was more dependent upon the
polyelectrolyte doses in the consolidation dewatering pro-cesses. In contrast, its dependence was much weaker in the centrifugal setting experiments. This couldbe observedby noting nearly all samples achieveda similar equilibrium thickness L=L0, irrespective of the polyelectrolyte doses.
(ii) The reboundof the sediment thickness was achieved within a much shorter time scale, 200–600 s. This was in direct contrast with an extremely long relaxation time 30,000–60; 000 s in consolidation dewatering experiments. The latter observation suggests that the structures of the packedcake after consolidation andcentrifugal settling were very di:erent. The last section provides some visual observations on the cake structure.
In order to understand the drastic di:erence in the dy-namic pattern developed in consolidation dewatering/batch centrifugal-setting experiments, similar sets of experiments
Fig. 6. Consolidation–relaxation curve for Testing Sample-U (with four di:erent doses of original, 80, 280, and 480 ppm, respectively) on the S-cell. Four panels of L=L0 vs. time curves are shown in the consolidation plot with increasing axial loads (in the order of 25, 50, 100, and 200 kPa).
were carriedout on Sample-U, using CP cell-S, andcon-tinuous centrifugal setting experiments andthe results for Sample-U were comparable. When P = 25 kPa, there was hardly any dewatering from the sediment cake (Fig. 6). When P exceeded 50 kPa, there was a signi8cant collapse for the sludge sediment conditioned with a polyelectrolyte dose of 480 ppm. For lower doses of polyelectrolyte (orig-inal sludge, 80 and 280 ppm), the dewatering data contra-dicted with the CST estimated optimal dose 280 ppm as shown in Fig. 3. There was a reversal of dewatering capa-bility for the lower dosed sludge samples at P = 50 kPa: the dewatering percentage for the three samples run in the decreasing order of the following sequence: 80 ppm, orig-inal sludge and 280 ppm with the sediment thickness L=L0
(under the equilibrium stage) of 0.5, 0.54, and 0.74, respec-tively. The order for the dewatering percentage at equilib-rium was changedat an even higher axial loadP. At P=100 and 200 kPa, the dewaterability of the original sludge and 80 ppm samples follows a similar trendas notedat 50 kPa. To explain for the mismatch of CST-estimatedoptimal dose and consolidation dewatering tests, the Sample-U was subjectedto another set of continuous centrifugal-settling/ relaxation (rebound) experiments and the results are shown in Fig. 7. These sets of experiments di:ered from the Sample-T in the followings: (i) In order to compare data with consolidation dewatering tests, the same polyelec-trolyte doses were used: original sludge, 80, 280, and 480 ppm. These turnedout to be di:erent from Sample-T. (ii) The centrifugal-settling experiments were carriedout in a continuous mode with stepwise increases of rotational speed. This was in direct contrast with the Sample-T whose tests were done in a batch mode. At the rotational speed of
350 rpm (equivalent to acceleration = 33:4g), the sediment thickness for the sludge conditioned with polyelectrolyte at the doses 80 and 480 ppm was signi8cantly reduced. The equilibrium thickness L=L0 for 80 and480 ppm samples
was measuredas 0.85 and0.65, respectively. In contrast, the equilibrium L=L0 values of the original sludge and
280 ppm samples were close to 0.95, not too far away from the original sediment height.
3.1. Yield stress
Theoretical estimation of the null-stress solids fraction g
(gelling point) andthe yieldstress Py() were conducted by
the following procedures. The relationship between normal stress and average solids fraction in the sediment controls the dewatering rate of the sediment. The normal stress on the supernatant/sediment interface in the centrifuge could be approximatedas follows: P = R−H R−H0 9pL 9r dr = R−H R−H0 (L2r) dr =22L[(R − H)2− (R − H 0)2]: (8)
Fig.8depicts the curves of normal stress P vs. average solids fraction in the sediment for Sample-U andSample-T sludge, respectively, with #occulent doses as the parameter. The dashedline in the 8gures representedthe original solids fraction of sludge 0. Slopes of the S–PS curves couldbe
taken as an index to characterize the sediment compactibil-ity. The intercept on the x-axis (P=0) was the corresponding gof the sludge. For Sample-U, g for sludges #occulated
Fig. 7. Centrifugation-settling–relaxation curve for Testing Sample-U (with four di:erent doses of original, 80, 280, and 480 ppm, respectively). Three panels of L=L0vs. time curves are shown in the consolidation plot with continuous increasing rotation speed (in the order of 350, 560, 1050 rpm). This
is followed by a relaxation plot in which the torque to the rotation is suddenly removed, and then the cake thickness is recorded as a function of time.
Fig. 8. g evaluation from P vs. curve: (a) for Sample-U sludge,
circle: 0 ppm; square: 80 ppm; triangle: 280 ppm; andinverse triangle: 480 ppm and(b) for Sample-T sludge, circle: 0 ppm; square: 80 ppm; triangle: 160 ppm; andinverse triangle: 280 ppm.
at all doses converged at 0.009, which almost coincided with 0. All #ocs in the initial suspension are in physical contact
with each other andform a network matrix. While being
subject to the subsequent centrifugal compaction, the sedi-ment readily yielded from 0.009 to 0.025, corresponding to the elevation of pressure to around25; 000 Pa. In compar-ison with the Sample-U, Sample-T sludge exhibited sti:er sediment with a higher g (nearly 0.013 for sludge
con-ditioned at all doses) and less compactible behavior. To achieve the same solids fraction, the required pressure (up to 63; 000 Pa) is two times higher than Sample-U sludge. While considering the e:ects of #occulation, though no ap-parent e:ects occurredon the g, the compatibility and
achievable 8nal solids fraction increased with the #occulent doses. Overdosing caused no deterioration on the dewater-ability.
Many 8ltration-relatedworks hadproposeddi:erent ways to estimate the yieldstress Py, which is essential to reveal
the deformation behavior of sediment or cake. To evaluate the yieldstress, herein we followedBuscall andWhite’s method(Buscall & White, 1987) to calculate the estimated yieldstress andsolids fraction at the centrifugal 8lter cell bottom (z = 0 de8nedin this reference). They assumeda relationship P ˙ ( − g)mfor initial guess to obtain the
Pyvs. correlation according to the following equations:
Py∼= P(0) ∼= U g0H0 1 −H2Req ; (9) (0) = 0H0 1 − 1 2R(Heq+ gdHdgeq) (Heq+ gdHdgeq)(1 − HReq) +H 2 eq 2R ; (10)
where Heq is the equilibrium sediment height, R is the
ra-dius of rotation for the centrifugal process. From Fig. 9, the range of m for Sample-T and-U is between 1 and2.
Fig. 9. The relation between the yieldstress andvolume fraction based on centrifugal-settling test: (a) Sample-T and(b) Sample-U. Py vs.
curves according to Eqs. (9) and(10).
The error involvedin using Eqs. (9) and(10) between m=1 and2 is below ca. 10%. Except for some data points at high Py, all the regression lines hadthe same intercepts on
the X -axis, which were 0.006 for Sample-U and0.01 for Sample-T. These two solids fractions, denoted as g;y, could
be viewedas a thresholdvalue for yielding. Noticeably, g;y
of Sample-U is lower than its 0, andin contrast, the one
of Sample-T is higher. A sti:er sediment matrix formed in the Sample-T sludge might be resulted from this. Similar to the situation described in Fig.8, #occulation wouldenhance the yielding under the same stress, at which the enhancement is more signi8cant in the case of Sample-T sludge.
However, such an observation deviates signi8cantly from the results of C–P cell, as the sludge required a much higher stress for signi8cant yield(50,000 Pa for Sample-U and 30; 000 Pa for Sample-T). Py may be an operational
de8-nition and vary according to the measuring methods. The comparison of Pyfrom di:erent methods is hardly possible.
3.2. Structure and dewatering dynamics for the wet cake formed by consolidation and centrifugal setting
Observations have been made from the surface pictures taken from the equilibrium cakes formedvia consolidation dewatering and centrifugal sedimentation, respectively, un-der di:erent pressure gradients. The calculated values of dP=dx are in general in the same order of magnitude with dP=dr (Tables1and2). This seems to be in direct contrast
with the observation such that the dewatering time scale re-quired by centrifugal sedimentation is about one order of magnitude smaller than the consolidation dewatering. It is seen that the cake formedby consolidation has a more com-pact structure (Fig.10).
To further elucidate this problem, we took the scanning electron microscopic photos of the sludge surface morphol-ogy prior to dewatering andafter centrifugation andcon-solidation (Fig.10). The observing position was at the pis-ton/cake interface for consolidated sludge and sediment/air interface for centrifugal settledcake. The magni8cation was set as 1000. In the case of original sludge, the single #oc is highly porous andlots of the 8lament couldbe noticed. The cake obtainedfrom dewatering hadmore compact ap-pearance. After centrifugal settling, the #ocs lookedshrunk andwere stackedclosely with each other (Fig. 10c). Fur-ther consolidation deteriorated the intrinsic porous struc-ture and#atten appearance was observed(Fig.10e). In the case of #occulated sludge, in contrast to the original sludge #ocs, a compact andlayer-by-layer structure was noticed. After the centrifugation, however, this structure seemedto be disrupted 8rst and then re-stacked. Consolidation also causedto #atten andcompress cake surfaces, but with a relatively porous morphology (comparing with the origi-nal sludge cake). To qualitatively describe the term “poros-ity”, we processedthe image analysis tests on these SEM pictures by the function “blob analysis” in the commercial software Inspector (Matrox), to obtain the two-dimensional projectedporosity andequivalent pore size dp(=4Ap=&,
of those dark and concave portions, where Ap is the
pro-jectedarea of the pore). The porosity is de8nedas the por-tion of projectedarea of inter-aggregate space, which might not include the moisture contained in the #oc/aggregates (surface water or chemically boundwater). The results are listedin Table3. In considering the e:ects of pressure on the cake structure, the porosity decreased from 0.369 for a single #oc to 0.349 for centrifugal settledcake andto 0.258 for the compressedcake of original sludge. Similar trends were also noticedin the case of #occulatedsludge, from 0.469 for a single #oc to 0.434 for centrifugal cake andto 0.414 for compressedcake. This couldbe realized by the fact that in general the equilibrium solidpressure in the consolidation dewatering (Pm: 4–200 and7–173 kPa
for the Sample-T andSample-S, respectively) is 1–2 orders of magnitude higher than the centrifugal sedimentation (Ps:
36–300 and60–600 Pa for the cell-T andcell-S, respec-tively). While considering the e:ects of #occulation, the #occulatedones were always with a higher porosity than those of original sludges. In contrast to the common ex-periences, the porosity of consolidated#occulatedsludge cake (0.414) was even higher than the original sludge #oc (0.369). The pore sizes of the sludge before and after de-watering were pretty similar (around2 m), but signi8cant changes were foundin the standarddeviation of pore sizes, where the deviation was generally decreased with increas-ing pressure.
(a) (b)
(c) (d)
(e) (f)
Fig. 10. Sediment/cake surface structure formed under centrifugal settling and consolidation dewatering: (a) Original sludge #oc; (b) #occulated sludge #oc; (c) centrifugal sludge cake (original); (d) centrifugal sludge cake (#occulated); (e) consolidated sludge cake (original); and (f) consolidatedsludge cake (#occulated).
Table 3
Surface structure of the sediment/cake formed in consolidation dewatering and centrifugal-settling experiments
Fig. 10a Fig. 10b Fig. 10c Fig. 10dFig. 10e Fig. 10f
Porosity 0.369 0.469 0.349 0.433 0.258 0.414
Pore size (m) 0.956 1.25 1.06 0.914 0.901 0.899
Standard deviation 2.00 2.80 2.08 1.81 1.16 1.70
Referring to Figs. 4 and5, the consolidation time scale is much longer than the centrifugal sedimentation. This couldbe explainedby the higher resistance o:eredto water #ow throughout the cake due to the more compact structure achievedby consolidation.
Using scale analysis,Landman and Russel (1993) com-paredthe 8ltration andsedimentation time scales for
concentratedsuspensions. They foundthat the ratio of the time scale is given by
TFiltration TSedimentation ≈ U g0l0 ' V (0) V (b); (11)
where V (’) and ' refer to the sedimentation velocity and constant pressure drop, respectively. ’0 and ’b refer to
the volume fraction of solids at the supernatant and sedi-ment/cake, respectively.
One of the underlying assumptions used here is that 8ltration properties couldbe determinedby compression– permeation tests in a C–P cell andhence the 8ltration time scale is comparable with the consolidation dewatering pro-cess. Furthermore, the sedimentation process is governed by the magnitude of gravitational acceleration. Looking at the following two limiting cases considered by Landman and Russel (1993): (i) When the solidfraction is close to the random close packing volume fraction, the 8ltration time scale is comparable to or larger than the sedimentation time scale. (ii) When low to moderate pressure di:erence and ’b is of the order of 0.2, the 8ltration time is three orders
of magnitude smaller than the gravitation settling time. From Table 1, the centrifugal acceleration (=r2=g)
andsolidosity sare in the range =26–330 and0.01–0.02,
respectively. Taking the 8ltration time scale to be compara-ble to the consolidation dewatering time scale, TFiltration ∼
TConsolidation. Suppose the time scales of centrifugal settling
is relatedto the gravity sedimentation by the following: T
TSedimentation ≈
1
: (12)
By Eqs. (11) and(12), the following time scale ratio is readily available: TConsolidation T ≈ U g0l0 ' V (0) V (b): (13)
Following Landman and Russel (1993), the parame-ter ' is scaledwith the yieldstress Py. The data of the
centrifuge experiments are processedwith the methodre-portedbyBuscall andWhite (1987)andChu, Ju, Lee, and Mohanty (2002). The results show that the yieldstress of the activated sludge Sample-T is of the order of 10 –100 Pa. For instance, in Sample-T, the parameter values for U, ’0, l0are 450 kg=m3, 0.00655, and0:05 m,
respec-tively. Since ’b (=0:01 − 0:02) ∼ ’0 (0:0065), the ratio
V (’b)=V (’0) ∼ O(1). Taking these all into account it is
seen from Eq. (13) that TConsolidation T ≈ U g0l0 ' V (0) V (b) ≈ 0:144 ≈ 4 − 18: (14)
From Eq. (14), it is estimatedthat the consolidation (8l-tration) time scale is one order of magnitude higher than the sedimentation time scale. Hence, the experimentally deter-mineddynamic time scale agrees reasonably well with the theory byLandman and Russel (1993).
4. Conclusions
This work has reviewedthe similarity anddi:erence between the consolidation dewatering and centrifugal
sedimentation processes. Both processes showed qualita-tively similar features for the optimal dose of #occulation. The dewatering rate of the consolidation processes was one order of magnitude lower than the centrifugal sedimentation although both processes reach roughly the same equilibrium cake thickness andmoisture contents. The di:erence in the moisture removal rate is discussedandthe results matched reasonably well with the theory of Landman and Russel (1993). The continuous andbatch operation of centrifugal sedimentation did not introduce signi8cant di:erence in the moisture removal rate andequilibrium sediment/cake thick-ness. The reboundof cake was observedfor both processes when the external driving forces (axial loadandrotation torque) were removedalthough the mechanism for such be-havior was di:erent for the two processes.
Acknowledgements
We wouldlike to acknowledge the National Science Council (Taiwan) for the support under the Grant Num-ber NSC 89-2214-E-002-058. CHW thanks the National Taiwan University for the visiting appointment during January–May 2002.
References
Buscall, R., & White, L. R. (1987). On the consolidation of concentrated suspension. I: The theory of sedimentation. Journal of Chemical Society, Faraday Transaction I, 83, 873–891.
Christensen, J. R., Sorensen, P. B., Christensen, G. L., & Hansen, J. A. (1993). Mechanisms for overdosing in sludge conditioning. Journal of Environmental Engineering, 119, 159–171.
Chu, C. P., Ju, S. P., Lee, D. J., & Mohanty, K. K. (2002). Batch gravitational sedimentation of slurries. Journal of Colloid and Interface Science, 245, 178–186.
Chu, C. P., & Lee, D. J. (2001). Experimental analysis of centrifugal dewatering process of polyelectrolyte #occulated waste activated sludge. Water Research, 35, 2377–2384.
de Kretser, G., Shane, S. P., Scales, P. J., Boger, D. V., & Landman, K. A. (2001). Rapid 8ltration measurement of dewatering design and optimization parameters. AIChE Journal, 47, 1758–1769.
Landman, K. A., & Russel, W. B. (1993). Filtration at large pressure for strongly #occulatedsuspensions. Physics of Fluids A, 5, 550–560. Landman, K. A., White, L. R., & Eberl, M. (1995). Pressure 8ltration of
#occulatedsuspensions. AIChE Journal, 41, 1687–1700.
Lee, D. J. (1994). Measurement of boundwater in waste activatedsludge: Use of the centrifugal setting method. Journal of Chemical Technology and Biotechnology, 61, 139–144.
Lee, D. J., & Hsu, Y. H. (1992). Fluid#ow in capillary suction apparatus. Industrial & Engineering Chemistry Research, 31, 2379–2384. Lee, D. J., & Hsu, Y. H. (1993). Cake formation in capillary
suction apparatus. Industrial & Engineering Chemistry Research, 32, 1180–1185.
Lin, W. W., & Lee, D. J. (2001). Liquidsaturation pro8le in capillary suction time 8lter paper #uid#ow in capillary suction apparatus. Industrial & Engineering Chemistry Research, 40, 808–813. Lu, W. M., Huang, Y. P., & Hwang, K. J. (1998). Stress distribution
in a con8nedwet cake in the compression–permeability cell andits application. Powder Technology, 97, 16–25.
Murase, T., Iwata, M., Adachi, T., Gmachowski, L., & Shirato, M. (1989). An evaluation of compression–permeability characteristic in the intermediate concentration range by use of centrifugal and constant-rate compression techniques. Journal of Chemical Engineering of Japan, 22, 378–381.
Teoh, S. K., Tan, R. B. H., He, D., & Tien, C. (2001). A multifunction test cell for cake 8ltration studies. Transaction of Filtration Society, 1, 81–90.
Usher, S. P., de Kretser, R. G., & Scales, P. J. (2001). Validation of a new 8ltration technique for dewatering characterization. AIChE Journal, 47, 1561–1570.
Wu, R. M., Lee, D. J., Wang, C. H., Chen, J. P., & Tan, R. B. H. (2001). Novel cake characteristics of waste-activatedsludge. Water Research, 35, 1358–1362.
Wu, R. M., Lee, D. J., Zhao, J., Wang, C. H., & Tan, R. B. H. (2000). Discrepancy in cake characteristic measurement: Compression– permeability cell. Journal of Chemical Engineering of Japan, 33, 869–878.
Yen, P. S., & Lee, D. J. (2001). Errors in boundwater meas-urements using centrifugal setting method. Water Research, 35, 4004–4009.
