yuan2010

Powder Technology 199 (2010) 111–119
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Powder Technology
j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / p o w t e c
Strength and breakage of activated sludge flocs
Yuan Yuan, Ramin R. Farnood ⁎
Department of Chemical Engineering and Applied Chemistry, University of Toronto, 200 College St., Toronto, Ontario, Canada M5S 3E5
a r t i c l e
i n f o
Article history:
Received 18 November 2008
Received in revised form 11 October 2009
Accepted 27 November 2009
Available online 3 December 2009
Keywords:
Floc breakage
Floc strength
Binding force
Taylor–Couette flow
Activated sludge
a b s t r a c t
The breakage of activated sludge flocs under turbulent shear conditions was investigated as a function of floc
size. Municipal activated sludge flocs were fractionated by sieving to narrow size fractions. Shear stress
distribution functions for the breakage of activated sludge floc samples were obtained. It was found that by
increasing the floc size, this distribution was skewed towards smaller shear stress values and became
broader. Results of experiments showed that the median shear stress, τ50, required for floc breakage reduced
by about 23% from 3.9 Pa for 45–63 μm sieve fraction to 3 Pa for the 150–180 μm sieve fraction. Under steady
conditions, the median shear stress for the breakage of fragments that formed due to the breakage of larger
flocs was as much as three times larger than that of the original flocs.
© 2009 Elsevier B.V. All rights reserved.
1. Introduction
Better understanding of the breakage of activated sludge flocs under
hydrodynamic stress could help improve the performance of solid/
liquid separation and disinfection processes in wastewater treatment
systems. Floc breakage depends on its strength in tension, compression,
and shear. To quantify floc strength, various methods have been
developed such as hydrodynamic stress, sonication methods, and
micromechanical and micromanipulation techniques. A comprehensive
comparison of these methods could be found in a recent review paper
[1]. In particular, techniques that are based on hydrodynamic stress
utilize a variety of different flow conditions to break up the flocs [2–
19,43]. The change in the floc size is then monitored either directly using
particle size analyzers [10], microscopy [8], or high speed imaging
[4,20]; or indirectly by measuring changes in the turbidity of the sample
[9,21].
Experimental and theoretical studies suggest that larger flocs break
more readily than the smaller ones under shear stress [22,23]. Tambo
and Hozumi [15] investigated the breakage of kaolin–aluminum sulfate
flocs and concluded that the maximum diameter of such a floc in
turbulent flow is a function of the mean effective dissipation energy.
Parker et al. [24] found that the relationship between maximum stable
floc diameter, dmax, and the mean velocity gradient, G, can be expressed
by dmax =cG− n. Similar results reported by other investigators indicate
that the power n varies between 0.4 and 4 for turbulent flow and various
aggregate types [25]. It has been proposed that as floc size increases the
floc density is reduced, and reduction in the mass concentration within
⁎ Corresponding author. Tel.: + 1 416 946 7525; fax: + 1 416 978 8605.
E-mail address: [email protected] (R.R. Farnood).
0032-5910/$ – see front matter © 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.powtec.2009.11.021
flocs will decrease the number of bonds per unit volume of floc and
therefore decrease the floc strength [3,23].
The breakage of flocs may occur due to three different mechanisms: 1— large-scale fragmentation where a floc is broken into two or
more smaller flocs, 2— surface erosion where single primary particles
or their small aggregates are eroded off the floc [21], and 3— chipping
due to impact upon solid surfaces. For example, in studying wood
fiber flocs, Lee and Brodkey [26] reported that a shear stress of 2 Pa
would result in floc breakage through massive fragmentation and
small-scale erosion. Fragmentation will cause a shift in the particle
size distribution towards smaller particles without any change in the
number of primary particles while erosion will create a large number
of primary particles. Based on the floc breakage mechanisms, several
theoretical models have been reported to rationalize the floc strength
and breakage process under hydrodynamic shear [7,8,13,15,17,20].
The available data on floc breakage deals with suspensions of polydispersed flocs with a wide size distribution. This, at best, provides
only average strength value and masks critical information regarding
floc breakage process. Furthermore, the majority of previous research
is focused on the synthetic flocs that differ significantly from activated
sludge flocs encountered in the wastewater treatment processes.
Therefore the objectives of this study were: (1) to quantify the
strength of activated sludge flocs as a function of the floc size, and (2) to
investigate the activated sludge floc breakage process. In particular, the
focus of this work was the large particle fractions that survive exposure
to hydrodynamic shear. This is particularly important for the performance of downstream treatment processes such as disinfection systems.
To achieve these objectives, activated sludge flocs were sieved to a
narrow size fraction and were subjected to hydrodynamic shear stress
using a Taylor–Couette flow cell. Changes in the particle size distribution
were analyzed to estimate the shear sensitivity of activated sludge flocs.
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Y. Yuan, R.R. Farnood / Powder Technology 199 (2010) 111–119
2. Theory
Flocs exposed to hydrodynamic stress break up if stresses acting
on them exceed the floc strength over a sufficiently long period of
time. However, the floc strength is commonly considered to be a
deterministic function of its size. This is an oversimplification since
similar size flocs exhibit a large spectrum of shapes and structures and
therefore respond differently under similar shear stress levels.
The strength distribution of flocs can be monitored by subjecting
them to rising levels of hydrodynamic stress and monitoring the
number of broken flocs. By increasing the level of stress, a growing
number of flocs that are weaker than the applied hydrodynamic force
would break up. At steady state, the floc size distribution reaches a
stable level. For a sufficiently dilute suspension, the kinetics of this
process is dominated by floc breakage and the net change in the
number of flocs within a specific size range is equal to the difference
between “death” caused by the breakage of aggregates within this
size range and “birth” due to the breakage of larger flocs [10]. However, if flocs are mono-dispersed with characteristic length within [d,
d + δ] where δ ≪ d, the birth rate can be neglected and the change in
the number of flocs can be exclusively attributed to the floc death
due to breakage. After breakage, the number of surviving flocs within
[d, d + δ] represents the “cumulative” number of flocs that are
“stronger” than the hydrodynamic stress exerted on them. Therefore,
the fractional reduction in the concentration of large flocs at various
shear stress levels will represent the cumulative distribution of shear
stress required for floc breakage.
Fractionation can be used to narrow the size distribution of suspended
aggregates, but fractionated aggregates have a polydispersed size
distribution, schematically shown by curve 1 in Fig. 1. Upon the
application of shear, weaker flocs break to give birth to a large number
of smaller particles. The result is a bimodal size distribution similar to
curve 2 in Fig. 1. However, in order to calculate the number of broken flocs
based on the change in the particle size distribution, the effect of birth on
the floc count should be minimized if not eliminated. This can be achieved
by monitoring change in the total number of flocs that are larger than a
threshold size: the larger the threshold floc size, the smaller the
contribution of “birth” to the total number of flocs that are larger than
this threshold value.
To examine this idea, activated sludge flocs were subjected to
hydrodynamic shear stress in a Taylor–Couette flow cell. Under such
conditions, suspended flocs will be exposed to a mixture of shear flow
with high vorticity, irrotational strains; rotational flow within eddies,
and streams with no distortion or rotation [4]. Because of the complex
nature of such systems, the root mean square of velocity gradient is
commonly used to characterize the turbulent shear rate [1]:
G=
ð1Þ
where ɛ is the energy dissipation rate and ν is the kinematic viscosity.
In turbulent Taylor–Couette flow, the total energy dissipation can
be expressed in terms of torque [27]:
ε=
TΩ
2πρLða2o −a2i Þ:
ð2Þ
Here T is the torque, Ω is the rotational speed, ρ is the fluid density,
L is the length of annulus, and ai and ao are the radii of inner and outer
cylinder, respectively.
To determine the total dissipation rate, the value of torque is
required. Here, we use Wendt's expressions to estimate the torque [28]:
θ = 1:45
η3 = 2
1:5
Re
ð1−ηÞ7 = 4
for 4 × 102 b Re b 104
= 0:23
η3 = 2
1:7
Re
ð1−ηÞ7 = 4
for 104 b Re b 105
ð3Þ
where θ(=T/ρν2L) is the dimensionless torque, η is the ratio of the
radius of inner cylinder to the radius of the outer cylinder, and Re is
the Reynolds number defined by:
Re =
Ωai ðao −ai Þ
:
ν
ð4Þ
Using Eqs. (1) to (3), an estimation of the turbulent shear rate, G, can
be obtained, and then used to calculate the turbulent shear stress
according to [7]:
τ = μG:
ð5Þ
Turbulent shear stress given by Eq. (5) has reportedly been used to
approximate the hydrodynamic shear stress acting on a floc [4].
However, it is important to recognize that in reality the shear stress
exerted on a floc under turbulent conditions is a complex function of
turbulent flow field and the floc–fluid interactions.
In this study, we adopt the maximum shear stress criteria, i.e. it is
assumed that flocs will break if the turbulent shear stress exceeds a
critical value that is considered to be the floc strength [29]. Therefore,
the cumulative number of broken flocs as a function of the turbulent
shear stress is related to the floc strength distribution. However, it
should be noted that due to the spatial distribution of turbulent
stresses within the fluid, various flocs will have a different shear stress
history depending on their trajectory in the flow cell. Here, we use the
average “global” r.m.s velocity gradient given by G = (ε/ν)1/2 to obtain
an estimation of the average shear stress exerted on flocs.
It has been suggested that the breakage mechanism of flocs is
controlled by the Kolmogorov microscale, λ [30]:
λ=
Fig. 1. Schematic diagram showing the size distribution of fractionated activated sludge
flocs before (curve 1) and after (curve 2) exposure to hydrodynamic shear stress.
rffiffiffi
ε
ν
ν3
ε
!1 = 4
ð6Þ
where ν is the kinematic viscosity of fluid. It is proposed that under
inertial subrange conditions (d NN λ), flocs are more likely to break by
large-scale fragmentation, while surface erosion is proposed to
dominate the break up in viscous subrange (d bb λ).
Y. Yuan, R.R. Farnood / Powder Technology 199 (2010) 111–119
3. Experimental
3.1. Samples
Activated sludge samples were obtained from the Ashbridge Bay
Municipal Wastewater Treatment Plant, Toronto, Canada. These
samples were collected from the effluent channel of the aeration
tank and carried using a sealed 20 L plastic tank. During stationary
operation, the aeration tank VSS was 1500–2000 mg/L with a sludge
age of 6.5 days and an average effluent BOD5 of 10 mg/L. Samples
were fractionated in the laboratory immediately after receiving based
on the procedure described below. All experiments were started
immediately after fractionation and were completed within 48 h.
3.2. Size fractionation and particle sizing
Activated sludge flocs were separated into narrow size fractions
using a set of eight sieve trays with mesh sizes of 45 μm, 63 μm, 75 μm,
90 μm, 106 μm, 125 μm, 150 μm, and 180 μm (VWR, stainless steel).
These sieves were vertically assembled with smaller sieve trays at the
bottom and wastewater sample was gently added to the top sieve. To
achieve better particle separation and to minimize floc breakage
during fractionation, each fraction was washed carefully using a
gentle flow of water for at least 20 min. Six sieve size fractions, namely
45–63, 63–75, 75–90, 90–106, 106–125, and 150–180 μm, were
collected and a stock suspension of each size fraction was prepared
by dispersing the collected flocs in deionized water.
The floc size distribution for each fraction was determined using a
Coulter particle size analyzer (Multisizer 3, Beckman Coulter, Miami,
US) with a 280 μm aperture was used for measuring the size
distribution of flocs. To achieve the desired particle concentration
for the size analysis, 10 mL of the activated sludge floc suspension was
added to 60–80 mL of the electrolyte. A measurement time of 60 s was
used to ensure a constant volume of sample is analyzed in all tests.
113
Table 1
The turbulent shear rate and shear stress as a function of the rotational speed,
calculated based on Eq. (5).
N (rpm)
Shear rate (s− 1)
Turbulent shear stress (Pa)
1000
2000
3000
4000
5000
6000
2120
5040
8560
12,600
17,100
21,800
2.1
5.0
8.6
12.6
17.1
21.9
3.3. Shear experiments
The experimental apparatus for shear breakage is depicted in
Fig. 2. The flow cell was a custom-made device consisted of a stainless
steel spindle (4.0 cm in diameter and 4.0 cm in length) and a
transparent acrylic cup (4.4 cm diameter and 6.5 cm long). The gap
between the spindle and the cup was 0.2 cm. The spindle was driven
by a variable speed motor (Servodyne 50003-04, Cole-Parmer
Instruments Co.) and its rotational speed was adjusted between 500
and 6000 rpm using a digital controller. The turbulent shear rate and
shear stress as a function of the rotational speed, calculated based on
Eq. (5), are given in Table 1.
For each experiment, the flow cell was filled with 10 mL of
fractionated activated sludge floc suspension with a volume concentration between 10− 4 and 10− 3 mL/mL. The floc suspension was
exposed to the target rotational speed and was allowed to reach
steady breaking conditions. The suspension was then removed for
particle size analysis. This procedure was repeated at various speeds
from 500 to 6000 rpm for each of the six size fractions.
4. Results and discussion
4.1. Initial floc size distribution
The Coulter size distributions of 45–63 μm, 75–90 μm, 106–
125 μm, and 150–180 μm sieve fractions prior to breakage experiments are shown in Fig. 3, for clarity 63–75 μm fraction is not shown
in this figure. The mode sizes for these fractions were 29, 43, 61, and
78 μm; respectively, that were less than the corresponding sieve size
ranges. This is expected since Coulter particle size analyzer is based on
the electrozone sensing that measures the solid volume of particles.
Hence, the high porosity of activated sludge flocs leads to the
undersizing of these flocs by a factor of about 2 [31]. In this study,
Coulter particle sizing was used to determine the relative changes in
the floc size distribution, therefore the underestimation of the
absolute floc size does not affect the quantitative analysis of data.
Fig. 2. Schematic diagram of the Taylor–Couette flow cell used in this study.
Fig. 3. Coulter size distributions of fractionated activated sludge samples.
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Y. Yuan, R.R. Farnood / Powder Technology 199 (2010) 111–119
Fig. 5. Effect of shear rate on floc size.
Fig. 4. Effect of shear time on the median floc size, d50.
4.2. Shear time
A set of experiments was conducted to study the time needed to
reach the steady state floc size distribution in the Taylor–Couette flow
cell. A suspension of 106–125 μm activated sludge floc size fraction
was exposed to 1500 rpm for 5, 10, 15, 20, 25 and 30 min. The results
summarized in Fig. 4 showed that the median floc size, d50, decreased
steadily with time and reached a plateau level after about 15 min.
Therefore, to ensure steady state floc size distribution, all the shear
experiments in this study were performed for 20 min.
4.3. Floc binding force
As discussed earlier, floc breakage data is commonly represented
in terms of a power law relationship, d = cG− n, where G is the average
shear rate and d is the floc size. The exponent, n, provides information
about the sensitivity of floc to increase in the shear rate. This
parameter is related to the floc strength [1,22].
Table 2 provides a list of several earlier studies reported in the
literature for various types of flocs. The G–d diagrams from these
studies are plotted in Fig. 5. The value of exponent n in Table 2 varies
between 0.16 and 0.81, depending on the floc type and hydrodynamic
shearing conditions. In the present study, the value of n for 45–63, 63–
75, and 75–90 µm fractionated activated sludge samples were found
to be 0.47 (0.37–0.55), 0.60 (0.38–0.82), and 0.54 (0.29–0.79),
respectively, where numbers in parenthesis represent the confidence
intervals. However, differences among these values were not
statistically significant, suggesting that the dominant breakage
mechanism is likely the same for the above fractionated samples.
Several theoretical models have been proposed for the stable floc
diameter as a function of shear rate. These theoretical models are
based on either force balance or energy balance; i.e. floc breakage
occurs when the external forces (or energy) acting on a floc exceed
the floc binding force (or binding energy). Furthermore, these models
are typically classified into viscous subrange and inertial subrange
depending on the relative size of flocs with respect to the turbulence
microscale.
Fig. 5 shows that in the present study, the average size of activated
sludge flocs remained larger than the turbulence microscale. A list of
theoretical models that are suitable for such conditions is given in
Table 3. Models 1 and 3, proposed by Parker et al. [24] and Kobayashi
et al. [7], predicted that floc size was proportional to G− 1/2. On the
other hand, Bache et al. [3] and Tambo and Hozumi [15] used a floc
size–density function and found that exponent n was a function of the
floc-size density exponent, Kp, that is related to the fractal dimension
of the floc according to Kp = 3 − DF. Considering the fractal dimension
of activated sludge flocs is of the order of 2, both model 2 and model 4
predict that stable floc diameter is approximately proportional to G− 1.
Based on the above discussion, the values of exponent n for the
fractionated activated sludge samples were close to the theoretical
predictions of Parker et al. [24] and Kobayashi et al. [7] (models 1 and
3 in Table 3). In fact, using regression analysis, the G–d data for the
fractionated floc samples could be expressed by:
−1 = 2
dw;avg = C1 G
:
ð7Þ
The values of coefficient C1 were 2.6 × 10− 3, 3.9 × 10− 3, and
3.5 × 10− 3 m/s1//2 for the 45–63 µm, 63–75 µm, and 75–90 µm
fractions, respectively. The average relative error of Eq. (7) for the
experimental data in the present study is 13%.
Table 2
Value of exponent n for various types of flocs reported in the literature.
Floc type
Activated sludge
Clay + Al2(SO4)3
Clay + Al2(SO4)3
Latex + NaCl
Humic acid + Al2(SO4)3
Latex + KCl
Sonicated activated sludge
Latex + KCl
Clay + PAM/Al2(SO4)3
Sediment + alum/cPAM/chitosan
Activated sludge
1
Strain rate1 (s− 1)
1
2
10 –10
102–103
102–103
101–102
102–103
101–103
101–102
101–103
101–102
102–103
103–104
Estimated shear stress, 2Approximate floc size range.
Floc size2 (μm)
Exponent, n
Technique
Source
1000–5000
150–1500
100–500
10–50
120–240
10–100
150–300
10–100
60–500
30–90
45–180
0.17–0.37
0.16–0.19
0.43–0.61
0.19–0.26
0.44
0.54
0.27
0.37–0.41
0.37–0.60
0.33–0.81
0.47–0.60
Mixer
Paddle mixer
Paddle mixer
Couette flow
Multi-grid mixer
Paddle mixer
Paddle mixer
Orifice flow
Paddle mixer
Paddle mixer
Couette flow
[24]
[15]
[22]
[41]
[3]
[7]
[36]
[16]
[42]
[2]
This study
Y. Yuan, R.R. Farnood / Powder Technology 199 (2010) 111–119
Table 3
Theoretical models for stable floc size under inertial subrange.
Model
Stable floc size1
Reference
1
1
3
dmax ∝ðAf σÞ =8 G− =2
[24]
2
3
4
dmax ∝σ =8 G
1
3
dmax ∝ðfNc Þ =8 G− =2
−1=Kp
1
dmax ∝ðβφÞ =K G
[15]
[7]
[3]
3
−2=ð1þKp Þ
p
1
σ: tensile strength of floc, Af: cross sectional area of fragments, Kp: exponent of floc
density function, f: cohesive force between primary particles, Nc: number of contacts
between clusters, β: proportion of broken bonds, φ: bond energy.
According to Parker et al. [24], the breakage of activated sludge
flocs by filament fracture may be idealized as the breakage of two
identical spherical primary particle clusters separated by a filamentous strand. The forces accelerating these clusters act in opposite
directions and are resisted by the tensile strength of the floc as
determined by the floc binding forces. Furthermore, in the inertial
subrange, the hydrodynamic forces accelerating these clusters may be
approximated by the acceleration of eddies that are in the order of the
cluster size. Based on these assumptions and using force balance,
authors showed that the value of coefficient C1 could be estimated as:
8=3
C1 =
3Bg
πρp βν2 = 3
!3 = 8
ð8Þ
where B is the floc binding force at the plane of rupture (=σAf), g is
the ratio of cluster diameter to floc diameter, ρp is the floc density, ν is
the dynamic viscosity of fluid, and β is the mean-square velocity
constant in the inertial subrange that experimentally is found to be 1.5
[32].
Using Eq. (8) it is possible to estimate an average value for floc
binding force. Assuming that g ∼ 0.5, ν ∼ 10− 6 m2/s, ρp ∼ 103 kg/m3,
and using the values of exponent n given in Table 2, the binding force
of the fractionated activated sludge flocs are estimated to be about 130
to 380 nN. In general, B depends on the floc characteristics; however,
the value of B has been reported to be in the order of 10− 1–103 nN for
various floc types (Table 4).
It is worth noting that; with the exception of the micromechanical
measurements of Yeung and Pelton [44], the binding force of activated
sludge flocs is generally 1–3 orders of magnitude larger than the
reported values for similar size synthetic flocs listed in Table 4. Higher
binding force of activated sludge flocs compared to these weaker
synthetic flocs may be explained based on the differences in the
dominant type of intra-floc binding forces. In the case of weak
synthetic flocs, primary particles are held together by electrostatic,
Table 4
Estimated floc binding force for various types of flocs as reported in the literature.
Floc type
Floc binding
force, nN
Technique
Source
Humic acid + Al2(SO4)3
Latex + KCl
Silica + FeCl3
Latex + KCl
CaCO3 + dual component
polymeric flocculant
Clay + PAM/Al2(SO4)3
Polymeric particles +
alum/PAM
Clay + Al2(SO4)3
Activated sludge
Activated sludge
45–63 µm
63–75 µm
75–90 µm
3–5
0.5–5
4–70
0.5–20
15–270
Multi-grid mixer
Converging flow
Straining flow
Converging flow
Micromanipulations
[3]
[17]
[38]
[16]
[44]
2–4
1–20
Paddle mixer
Orifice flow
[42]
[39]
200a
2000–3000a
Paddle mixer
Mixer
[22]
[24]
120a
380a
280a
Couette flow
This study
a
Estimated using Eq. (6).
115
van der Waals and DLVO [33] type forces. However, entanglement by
EPS (extracellular polymeric substances) plays a key role in the
cohesion forces within activated sludge flocs [34]. Using correlative
microscopy, Droppo et al. [35] found that fibrilar EPS formed a
framework within the activated sludge floc that provided structural
stability. Further evidence regarding the role of polymer entanglement was provided by Biggs and Lant [36] who studied the strength of
flocs formed from the primary particles obtained by the sonication of
activated sludge aggregates. Flocs formed in this manner lacked the
EPS entanglement and therefore their strength was of the same
magnitude of mineral flocs listed in Table 4. Although the relatively
higher binding force in Young and Pelton's experiments could be due
to biased sampling of large strong flocs, in principle it is possible to
prepare synthetic flocs with higher binding forces by proper selection
of floc type and floccuant system.
4.4. Floc strength distribution
Under turbulent flow conditions, floc size depends on the floc
binding forces and turbulence dissipation rate [37]. The binding force
of floc in turn is a function of floc characteristics and internal structure.
However, as pointed out by Blaser [38], “because of the internal
inhomogeneity, the binding force cannot be taken simply as a function,
for example of the floc size”, but he added that floc binding force “has
to be treated as a random variable; i.e. given a floc of a definite size,
there is a certain probability that the floc breaks or not.” A similar
argument has been made by Kramer and Clark [29] who stated that
aggregates within the same size class have a distribution of bonding
strength. In other words, the shear stress required for the breakage of
activated sludge flocs is a stochastic variable.
Despite the significant role of floc binding force and floc strength in
floc breakage process, there is limited experimental data in the
literature regarding the statistical distribution of these parameters. In
studying the breakage of flocculated polymeric particles under
straining flow conditions, Higashitani et al. [39] found that binding
force of two-fold particles varied from about 1 nN to 20 nN and the
probability of breakage of these particles exhibited a power law
distribution. Similarly, using a multi-grid mixer, Bache et al. [40]
determined the distribution of pressure forces for the breakage of
latex and rice starch flocs.
In the present study, changes in the floc size distribution after
breakage were used to quantify the probability of breakage of
activated sludge flocs at various hydrodynamic shear conditions.
The number distribution curves for activated sludge samples prior to
and after breakage at 1000, 2000, 3000, and 4000 rpm are shown in
Fig. 6. Since the volume concentration of flocs in the Couette flow cell
was low (10− 4–10− 3 mL/mL), changes in the floc size distribution
were dominated by the floc breakage process. Furthermore, to
minimize the effect of floc birth, a lower threshold size of dmode was
used such that only flocs larger than dmode were considered in the
analysis. Therefore, the fraction of broken flocs could be directly
calculated from the floc size distribution data and the floc breakage
ratio could be defined as:
b=
N0 −Nτ
N0
ð9Þ
where N0 and Nτ are the number of flocs larger than the mode floc size
(d N dmode) under the steady state conditions before and after
exposure to shear stress, τ, respectively.
At a given level of turbulent shear stress, breakage ratio is the total
(cumulative) fraction of flocs that are broken under the applied shear
stress. Therefore, plot of τ versus b represents the cumulative
distribution function (CDF) of the shear stress required for floc
breakage, or equivalently the probability of breakage of a floc at a
given shear stress.
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Y. Yuan, R.R. Farnood / Powder Technology 199 (2010) 111–119
Fig. 7. Cumulative fraction of breakage of activated sludge flocs. (a) 45–63, 63–75 and
75–90 µm, and (b) 90–106, 106–125 and 150–180 µm. Data from Bache et al. [3] for
latex and starch aggregates are also included.
Fig. 7 shows the breakage ratio of activated sludge floc fractions as
a function of the applied shear stress for rotational speed between 500
and 6000 rpm. The Reynolds number was in the range of 2600–31,000
that corresponds to turbulent flow regime. In general, the breakage
ratio increased and asymptotically approached unity with increasing
the shear stress.
The median shear stress (τ50); i.e. the shear stress at which the
number of flocs reduced by 50%, for various activated sludge floc size
fractions are given in Table 5. According to this table, by increasing the
floc size from 45–63 μm fraction to 150–180 μm fraction, τ50
decreased by 23% from 3.9 Pa to 3.0 Pa. For comparison, results for
rice starch flocs (∼ 2200 µm) and latex flocs (∼ 600 µm) by Bache et al.
[40] were 0.72 Pa and 1.4 Pa, respectively. Based on Fig. 7, synthetic
flocs containing latex particles and rice starch granules were
significantly “weaker” than the activated sludge flocs analyzed in
the present work. This difference is likely due to differences in the floc
Table 5
Median, 10%ile and 90%ile shear stress values for floc breakage, and coefficients of shear
stress distribution function; Eq. (8), for various activated sludge floc samples.
Fig. 6. Coulter particle size distributions for the activated sludge flocs before and after
breakage at various rotational speeds given in rpm: (a) 75–90 μm; (b) 63–75 μm; and
(c) 45–63 μm.
Sieve size fraction (µm) τ50 (Pa) τ10 (Pa) τ90 (Pa) k (Pa− 1/2) a (Pa−1) θ
m
45–63
63–75
75–90
90–106
106–125
150–180
Resieved 45–63
Resieved 75–90
1
1
1
1
1
1
2
2
3.9
3.9
3.4
3.6
3.2
3.0
9.8
7.8
2.4
2.2
1.4
1.0
1.0
0.7
6.6
5.3
13.3
7.8
9.5
8.2
8.4
8.3
22.6
17.4
0.63
0.83
0.74
0.83
0.77
0.72
0.62
0.71
0.86
0.67
0.54
0.33
0.45
0.29
0.38
0.46
2.90
2.34
1.52
0.95
1.08
0.53
3.34
3.29
Y. Yuan, R.R. Farnood / Powder Technology 199 (2010) 111–119
structure and composition. Similar results have been reported by
Bache et al. [3] who found that synthetic alumino-humic flocs were
significantly weaker than natural flocs found in turbid waters.
Fig. 7 also shows a wide variation in the shear stress required for
the breakage of activated sludge flocs: depending on the flocs size
fraction, 10th percentile and 90th percentile shear stress values were
0.7–2.4 Pa and 8.2–13.3 Pa, respectively (Table 5). This wide variation
is due to the variability in the internal floc structure and strength. To
better quantify this variability, the G–b data provided in Fig. 7 was
used to estimate the probability density function (PDF) of the shear
stress for the breakage of activated sludge size samples. In order to do
this, the experimental breakage data were first fitted to the following
distribution function:
117
figure, by increasing the floc size from 45–63 μm to 150–180 μm, the
distribution of shear stress was increasingly skewed towards smaller
shear stress values and the distribution became broader. This means
that by increasing the floc size, it is more likely to encounter weaker
flocs while a small fraction of relatively stronger flocs remains in the
population. In particular, the PDF for the largest floc size range, i.e.
150–180 μm, shows a more rapid initial increase compared to the
smaller flocs, indicating that a larger number of bigger flocs break at a
relatively lower levels of shear stress values. This difference is
expected since larger flocs are significantly weaker than smaller ones.
4.5. Floc breakage process
Using the above equation, the probability density of shear stress
for floc breakage was obtained and plotted in Fig. 8. Based on this
According to Fig. 5, the activated sludge flocs in the present study
remained larger than the turbulent microscale. Therefore, shearing
experiments were conducted under inertial subrange conditions and
floc breakage process was likely dominated by large-scale fragmentation [30]. However, erosion and fragmentation likely occurred
simultaneously [22], i.e. flocs that were of the order of or larger than
the turbulent microscale broke into large fragments, and those
fragments that were smaller than the turbulent microscale were
further eroded into smaller flocs and primary particles. In addition,
turbulent eddies have a wide size range. Hence, for a given size floc,
eddies that are bigger than the floc size could cause surface erosion
while small eddies may result in the fragmentation of floc. This
concept is supported by the floc size distribution after exposure to
hydrodynamic shear in Fig. 6. This figure shows that upon exposure to
shear, larger flocs were broken to form a large number of
intermediate-size fragments and as well as small flocs. Furthermore,
the presence of these fragments under steady state conditions
indicates that they resisted the hydrodynamic shear stress. In other
words, fragments that were generated due to the floc breakage were
“stronger” than the original flocs. Therefore, under steady state shear
conditions, the breakage of larger flocs resulted in the formation of
smaller flocs that could either further decrease in size by erosion or
fragmentation, or resist the breakage all together. To further examine
this concept, the intermediate-size fragments were isolated and
tested for their shear sensitivity. A 90–106 µm sieve fraction sample
was exposed to hydrodynamic shear stress at 5.0 Pa (i.e. 2000 rpm)
for 20 min. The sheared sample was then removed and resieved to
recover 45–63 µm and 75–90 µm fragment fractions. These samples
were then examined using the procedure described earlier. The
breakage ratios of the resieved fractions are given in Fig. 9. This
figure shows that the breakage process was delayed until shear
stress reached to about 5 Pa, i.e. the same shear level that the initial
90–106 µm sample was exposed to. Compared to the breakage ratio
for fresh fractions given in Fig. 7a, the resieved fragments clearly
Fig. 8. Probability density of shear stress for the breakage of various activated sludge
floc size fractions.
Fig. 9. Cumulative fraction of breakage of resieved activated sludge floc samples. Data
for 106–125 µm is included for comparison.
pffiffi
−k τ m
bðτÞ = f ðτÞð1−e
Þ
ð10:aÞ
where f (τ) is given by:
f ðτÞ =
1
τ + 1 = tanhðθÞ
1+
tanhðaτ−θÞ :
2
τ+1
ð10:bÞ
The above PDF is merely a mathematical function that can
accurately describe various features of experimental data shown in
Fig. 7.
Constants k, a, θ, and m were determined by non-linear
optimization using Mathematica™ (version 6.0), and their values for
various activated sludge samples are given in Table 5. Eq. (8) fitted the
experimental data with r2 = 0.99.
As discussed earlier, by definition, the above equation represents
the cumulative distribution function of shear stress for the floc
breakage. Therefore, the probability density function, PDF(τ), can be
determined from:
PDFðτÞ =
d
½bðτÞ
dτ
ð11Þ
that gives:
pffiffi
−k τ m
PDFðτÞ = gðτÞð1−e
Þ
ð12:aÞ
2
gðτÞ =
aðx + 1Þðx + cothθÞ sech ðax−θÞ−ðcothθ−1Þ tanhðax−θÞ
2ðx + 1Þ2
ð12:bÞ
mk
ðx + cothθÞ tanhðax−θÞ
pffiffi
+
1
:
+ pffiffiffi
x+1
4 xð1−e−k τ Þ
118
Y. Yuan, R.R. Farnood / Powder Technology 199 (2010) 111–119
g
m
n
Af
B
C1
G
N0
Nτ
Re
T
L
β
ε
Fig. 10. Probability density of shear stress for the breakage of re-sieved activated sludge
floc samples. For comparison, results for the 106–125 um size fraction are also included.
exhibited a higher resistance to breakage. The median shear stress
values for resieved fractions were more than twice larger than those
for freshly sieved activated sludge floc samples of the same size
fraction (Table 5).
The shear stress distribution for the breakage of reseived 45–63 µm
and 75–90 µm samples is given in Fig. 10. For comparison, the shear
stress distribution of the original flocs; i.e. 90–106 µm size fraction, is
also plotted on the same figure. This figure shows that smaller
fragments (i.e. 45–63 µm and 75–90 µm resieved fractions) generated
by the hydrodynamic breakage of larger flocs (i.e. 90–106 µm fraction)
are significantly stronger. The shear stress distribution of the resieved
fragments shifted to higher values such that the median shear stress
was 2–3 times higher than that of the original 90–106 µm fraction. This
result further emphasized on the heterogeneous nature of the floc
internal structure and binding forces. In addition, compared to the
original 45–63 µm and 75–90 µm (see Fig. 8), the strength distribution
of the resieved fractions is significantly shifted towards larger values.
5. Conclusions
The binding forces of fractionated activated sludge flocs with a
narrow size distribution were estimated to be in the order of 102 nN.
The hydrodynamic shear stress required for the breakage of activated
sludge flocs within the same narrow size fraction exhibited a large
variation. This emphasizes the variability in the internal floc structure
and strength. Furthermore, by increasing the activated sludge floc size,
the distribution of hydrodynamic shear stress required for the
breakage of activated sludge flocs became broader and shifted towards
smaller shear stress values. The median hydrodynamic shear stress for
the breakage of activated sludge flocs was found to decrease with the
floc size according to a power law relationship, τ50 ∼ d− 0.26, while τ10
was a stronger function of the floc size such that τ10 ∼ d− 1.2.
Under steady shear conditions, the breakage of larger flocs
resulted in the formation of smaller fragments that could resist the
breakage all together. The median shear stress for the breakage of 45–
63 µm fragments formed by exposing a 90–106 µm sieve fraction to a
hydrodynamic shear stress value of 5 Pa was three times larger than
that of the initial sample.
Nomenclature
a
Parameter in Eq. (10.b)
ai
Radius of spindle (m)
ao
Radius of the cup (m)
b
Breakage ratio defined by Eq. (9)
d
Floc diameter (m)
f
Auxiliary function defined by Eq. (10.b)
η
λ
μ
ν
θ
ρ
ρp
σ
τ
τ50
τ10
τ90
Ω
Ratio of cluster diameter to floc diameter (–)
Exponent in the breakage ratio function (Eq. (10))
Exponent of in G–d power law relationship
Cross sectional area of filament (m2)
Floc binding force (N)
Constant
Turbulent shear rate (s− 1)
Initial number of flocs
Number of flocs after exposure to shear stress τ
Reynolds number
Torque (N m)
Length of annulus in Couette flow cell (m)
Mean-square velocity constant in the inertial subrange (–)
Turbulent energy dissipation rate per unit of mass
(N m s− 1 kg− 1)
=a/b
Kolmogorov microscale (m)
Viscosity (kg m− 1 s− 1)
Kinematic viscosity (m2 s− 1)
Dimensionless torque number (=T/ρν2L)
Fluid density (kg/m3)
Floc density (kg/m3)
Floc tensile stress (N m− 2)
turbulent shear stress (N m− 2)
Median shear stress (N m− 2)
10th percentile shear stress (N m− 2)
90th percentile shear stress (N m− 2)
Rotational speed of spindle (rad s− 1)
Acknowledgements
The support from Natural Science and Engineering Research
Council of Canada (NSERC), Canada Foundation for Innovation (CFI),
the government of Ontario, and University of Toronto is gratefully
acknowledged.
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