American Journal of Analytical Chemistry, 2013, 4, 732-738
Published Online December 2013 (http://www.scirp.org/journal/ajac)
http://dx.doi.org/10.4236/ajac.2013.412088
Open Access AJAC
Coag-Flocculation Kinetics of Mucuna sloanei Seed for
Phosphorus Removal from Waste Water
Kamoru Akinpelu Babayemi1*, Okechukwu Dominic Onukwuli2, Matthew Chukwudi Menkiti2,
Akindele Oyetunde Okewale3
1Department of Chemical Engineering, Anambra State University, Uli, Nigeria
2Department of Chemical Engineering, Nnamdi Azikiwe University, Awka, Nigeria
3Department of Chemical Engineering, Landmark University, Omuaran, Nigeria
Email: *akinbabs40@yahoo.com
Received October 2, 2013; revised November 15, 2013; accepted November 25, 2013
Copyright © 2013 Kamoru Akinpelu Babayemi et al. This is an open access article distributed under the Creative Commons Attribu-
tion License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
cited.
ABSTRACT
Mucuna sloanei (MS) an environmentally friendly biomass was used as a coagulant for treatment of phosphorus con-
taining waste water. The study evaluates the coag-flocculation efficiency of MS and its functional kinetic parameter
response to varying pH and dosage of the waste water effluent. Coag-flocculation reaction order α, coag-flocculation
rate constant K, and coagulation period τ1/2 were determined. The maximum coag-flocculation performance (97.4%) is
recorded at rate constant, K of 1.24 × 104 l/mg·min, dosage of 400 mg/l, pH of 8 and coagulation period τ1/2 of 0.100
min while the minimum (61%) is recorded at K of 3 × 105 l/gm·min, dosage 100 mg/l, pH of 2 and τ1/2 of 8.900 mins.
The results confirm that MS coagulant is an effective coagulant obeying the theory of fast coagulation in the conditions
of the experiments.
Keywords: Coag-Flocculation; Mucuna slonaei; Phosphorus
1. Introduction
Coagulation is an established process for transforming
small particles into larger aggregates (flocs) and for ad-
sorbing dissolved organic matter onto particulate aggre-
gates so that these impurities can be removed in subse-
quent sedimentation and filtration stages [1].
Coag-flocculation of waste water may be accomplished
with any of the common water coagulants including lime,
iron and aluminum salts and synthetic polymers.
However, the search for a better alternative to conven-
tional coagulants has become an important challenge in
the water treatment process with the aim of minimizing
the detrimental effects associated with the use of such
coagulants. The use of coagulants of biological origin has
become imperative. Some of the coagulants and floccu-
lants of biological origin that have been used include
Chitosan [2], tannins [3], aqueous extract of the seed of
Moringa Oleifera [4], extract of Okra, nirmali seed [5]
and Mucuna sloanei which is the subject of the study.
Mucuna sloanei are wild plants found in some parts of
the semi and sub-Saharan and tropical zones of Africa.
The seeds are edible and are used for the thickening of
soups in some parts of Nigeria. They possess unique
characteristic behavior in hot water displaying different
degrees of the viscoelastic properties [6]. The seeds are
toasted for easy removal of the hull or par-boiled and
then ground to obtain a fine powder or paste, when wet
milled. The powder may be used as recipes of some food
items and in beverages [7]. Consumption of Mucuna as
food has also been reported from Mozambique and Ma-
lawi [8].
Mucuna gum is a galactomannan consisting of D-ga-
lactose and D-mannose as the main sugars [9]. The en-
dosperm was found to constitute 67.15% of the whole
seed with about 32.6% as gum. It may also be a rich
source of crude protein [10].
The chemical and nutritional evaluation of the raw
seed of M. sloanei suggested that this could be a rich
source of crude protein after cooking. The galactoxy-
loglucan isolated from the cotyledon consists of Glc:Xyl:
Gal in a molar ratio of 1:8:1.7:1.0 and a molar mass of
1.6 × 106 g·mol1 [11]. This work, however, attempts to
*Corresponding author.
K. A. BABAYEMI ET AL. 733
explore and generate interest in the utilization of Mucuna
sloanei (MS) seed as a coagulant. Coag-flocculation per-
formance and kinetic of MS under various pH of the in-
dustrial waste effluent are also investigated.
2. Materials and Methods
The sample of Mucuna sloanei seed was sourced from a
village market, in Ihiala, Anambra State. The seeds were
dried, dehulled and ground into fine power after which it
was sieved through 0.2 mm sieve. The fraction with par-
ticle size less than 0.2 mm was then processed into a co-
agulant using standard method [12].
The jar test was conducted based on standard Bench
Schale Nehelometric method (single angle procedure) for
the examination of water and waste water [13,14] using
model WZS-185MC Turbidimeter, Gulenhamp magnetic
stirrer and Delta 320 pH meter.
The percentage of turbidity removal was calculated
using Equation (1)
Removal efficiency

0
0
%
CC
EC
100 (1)
where C0 and C are the initial and residual concentration
of the waste water effluent respectively.
Theoretical Principle
The rate of flocculation is a function of the particles
(count) concentration C, and the intensity of Brownian
motion characterized by the diffusivity D. Consideration
of the particle diffusion flux in a mono dispersed system
toward a particle of radius “a” (chosen as the central one)
on the basis of Fick’s equation yields an expression for
the rate of decrease in the particle number.
d
d
cKC
t
 (2)
Integrating Equation (1) gives
d
lnln ln
d
c
K
C
t

 

 (3)
From which
K
and
can be determined from a
plot of d
ln d
c
t



against .
ln C
In Equation (1), K is coagulation rate constant/colli-
sion frequency
α: is the order of coagulation reaction
C: is the concentration of the particles (TSS)
It has been shown by some researchers that for the
conditions described above [15].
8πKR
D
(4)
where
2Ra
From Einstein’s equation [16]
B
D
KTB (5)
where B is the friction factor, T is the absolute tempera-
ture (0K) and KB is the Boltzman constant (Molar gas
constant per particle).
For the simplest case of a smooth spherical particle of
radius “a” immersed in a fluid of viscosity µ, B is given
by Stoke’s relation.
6π
B
a
(6)
Putting Equation (6) into Equation (5) gives
6π
B
K
T
Da
(7)
But 2Ra
Therefore 2
6π3π
BB
K
TKT
DRR



(8)
Putting Equation (8) into Equation (4) gives
8
8π
3π3
B
KT KT
KR
R





B
(9)
Putting Equation (9) into Equation (2) when 2
yields
2
d8
d3
B
KT
cC
t



(10)
Applying the method of separable variable and inte-
grating Equation (2) within the following limits:
At t = 0, C = c0 at t = t, C = C, yields
2
dd
d
cKt
c
 (11)
Integrating Equation (11) above yields
0
11
K
t
cc
 (12)
Multiply both sides of Equation (12) by C0 to give
0
0
1
CCKt
C (13)
Making “C” the subject of the formular, yields

00
0
0
111
CC
CCKt t
CK

(14)
Let
0
1CK
(15)
Therefore Equation (14) becomes
0
1
C
Ct
(16)
When t
then Equation (16) becomes
Open Access AJAC
K. A. BABAYEMI ET AL.
734
0
11 2
CC
C
0
(17)
Thus at 0
,2
C
tC
. This quantity is called the co-
agulation period, which is the time during which the ini-
tial concentration of particles is halved. For Brownian
coagulation of mono dispersed particles at early stage (t
30 minutes), the time evolution of the cluster-size dis-
tribution for colloidal particle is usually described thus:
 
11
d1,,
d2
n
ij in
jn i
Cijcc incc
t

 


(18)
where d
d
n
C
t is the rate of change of concentration of
particle of size n (concentration/time).
β is a function of the coag-flocculation transport mecha-
nism. The appropriate value of β for Brownian transport
is given by [15].
8
3
B
BR P
K
T

(19)
where KB is Boltzman’s constant (J/K)
T is Absolute temperature (K)
For Brownian aggregation at early stages (t 30 min-
utes) Equation (18) can be solved exactly, resulting in the
expression [16].

1
0
1
0
0
1
2
11
2
n
nt
n
t
CKC
C
t
KC
















(20)
Recall from Equation (15)
0
1
CK



, Putting Equa-
tion (15) in Equation (20)
We have

1
1
0
2
12
n
nt
n
t
C
Ct






(21)
Let 2
and put in Equation (21)



1
1
01
n
nt
n
Ct
Ct
(22)
Equation (22) gives general expression for particle of
n-th order. Hence for primary particles (n = 1)

10 2
1
1
CC
t



(23)
For twins (n = 2)


20 3
1
t
CC
t
(24)
For triplets (n = 3)


2
30 4
1
t
CC
t



(25)
The process of aggregation is a complicated phe-
nomenon. Analysis shows that Equation (16) holds for
the overall concentration of all particles, which mono-
tonically decreases in time like the number of primary
particles:
0
1
i
C
Ct
(26)
Linearising Equation (26) gives
00
111
i
t
CC C

(27)
where a plot of 1
i
C
versus t gives
Slope =
0
1
C
, Intercept =
0
1
C
Now that
can be obtained from slope of Equation
(27) while the theoretical quantities
is found with the
aid of Equation (15) [16].
00
13
8B
CK KTC
 (28)
As 0
01
,
2
C
Ct

2
Therefore,

12
00
33
80.5 4
BB
tKT CKTC


(29)
where 12
t is coagulation period/half life.
In the work of [16] it was shown that the coagulation
rate constant could be determined by monitoring the chan-
ges in the turbidity of the coagulation liquid with time.
The particle concentration during early stages of co-
agulation can be determined directly, by visual particle
counting or indirectly from turbidity measurement [17].
3. Results and Discussion
Figures 1-5 show the effect of coagulant dosage on the
turbidity removal at various pH. It can be seen from the
figure that turbidity removal increases with increase in
coagulant dosage. Figures 1-4 show the removal effi-
ciency as function of time for various MS coagulant
dosages at pH of 2, 4, 6 and 8 respectively. It can be seen
from the figure that the removal efficiency increases very
fast within the first ten minutes for a particular dosage
after which a decrease in efficiency began to set in. The
figures also show that the removal efficiency of MS co-
Open Access AJAC
K. A. BABAYEMI ET AL. 735
0
10
20
30
40
50
60
70
0 20406080100
E%
t, mi n
100mg/l
200mg/l
300mg/l
400mg/l
500mg/l
Figure 1. Coagulation efficiency profile for varying MS
dosage at pH = 2.
0
10
20
30
40
50
60
70
80
90
100
0 20406080100
E%
t, m in
100mg/l
200mg/l
300mg/l
400mg/l
500mg/l
Figure 2. Coagulation efficiency profile for varying MS
dosage at pH = 4.
0
20
40
60
80
100
120
0 20406080100
E%
t, m in
100mg/l
200mg/l
300mg/l
400mg/l
500mg/l
Figure 3. Coagulation efficiency profile for varying MS
agulant increases with dosage. However, in Figure 5, it
dosage at pH = 6.
was observed that as pH was increased further to 10, the
0
20
40
60
80
100
120
0 20406080100
E%
t, m in
100mg/l
200mg/l
300mg/l
400mg/l
500mg/l
Figure 4. Coagulation efficiency profile for varying MS
dosage at pH = 8.
0
10
20
30
40
50
60
70
80
90
100
0 20406080100
E%
t, m in
100mg/l
200mg/l
300mg/l
400mg/l
500mg/l
Figure 5. Coagulation efficiency profile for varying varyin
rate of removal began to decrease. It could be deduced
occulation parameters at various
do
9000 with the
ex
g
MS dosage at pH = 10.
from the above observation that the optimum turbidity
removal of MS coagulant occurred at the optimum pH of
8 and 400 mg/l dosage.
The values of coag-fl
sages and pH are presented in Tables 1 to 5 above.
The R2 and coag-flocculation rate constant K contained
in the various tables were determined from plots 1/ct
versus time as shown in Figures 6 to 10.
The values of, R2, being greater than 0.
ception of the results at pH of 2, are satisfactory and
this confirms the theory of perikinetic as the controlling
mechanism of coag-flocculation under study [18]. The-
highest value of K is recorded for 400 mg/l at pH of 8
while the least value is recorded for K at pH of 2 as pre-
sented in Table 4. The corresponding value of τ1/2 is
0.100 min at pH of 8 and 400 mg/l dosage. For pH of 2,
and 400 mg/l dosage, τ1/2 is 8.900 mins. This indicates
that the best coagulation performance could be achieved
Open Access AJAC
K. A. BABAYEMI ET AL.
Open Access AJAC
736
MS at varying pH and 100 mg/l dosage.
Parameters pH = 10
Table 1. Coagulation kinetic parameters of
pH = 2 pH = 4 pH = 6 pH = 8
γ
α
R2
K (l/
1
5.
8.60 × 1025
1.
1.
4.45 × 1025
1
1.
3.31 × 1025
1
2.
2.89 × 1025 5.18 × 10
mg·min)
βBR (l/mg·min)
εp (l/mg)
τ1/2 (min)
C0 (mg/l)
(Np)0
.0 × 103
2.0000
0.5870
3 × 105
6 × 105
40 × 1012
8.900
373
0 × 103
2.0000
0.9540
2 × 104
2.4 × 104
2.18 × 1013
2.200
373
.0 × 103
2.0000
0.9794
8 × 104
3.6 × 104
3.30 × 1013
1.400
373
.0 × 103
2.0000
0.9840
0 × 104
4.0 × 104
3.60 × 1013
1.300
373
1.0 × 103
2.0000
0.9713
6 × 105
1.2 × 106
1.10 × 1013
4.400
373
25
Table 2. Coagulation kinetic parameters MS at varying pH and 200 mg/l dosage.
Parameters pH = 10
of
pH = 2 pH = 4 pH = 6 pH = 8
γ
α
R2
K (l/
1
8.37 × 10
1
1
3.37 × 10
1.
2.
2.59 × 1025
1.
2.
2.47 × 1025
1.
3.79 × 1025
mg·min)
βBR (l/mg·min)
εp (l/mg)
τ1/2 (min)
C0 (mg/l)
(Np)0
.0 × 103
2.0000
0.7070
3 × 105
6 × 105
5.4 × 1012
8.900
373
25
.0 × 103
2.0000
0.9836
.8 × 104
3.6 × 104
3.30 × 1013
1.400
373
25
0 × 103
2.0000
0.9749
4 × 104
4.8 × 104
4.40 × 1013
1.100
373
0 × 103
2.0000
0.9854
6 × 104
5.2 × 104
4.70 × 1013
1.000
373
1.0 × 103
2.0000
0.9742
2 × 104
2.4 × 104
2.20 × 1013
2.200
373
Table 3. Coagulation kinetic parameters MS at varying pH and 300 mg/l dosage.
Parameters pH = 10
of
pH = 2 pH = 4 pH = 6 pH = 8
γ
α
R2
K (l/
1
8.06 × 1025
1.
1.
3.25 × 1025
1
4.
1.68 × 1025
1
5.
1.44 × 1025
1.
3.49 × 10
mg·min)
βBR (l/mg·min)
εp (l/mg)
τ1/2 (min)
C0 (mg/l)
(Np)0
.0 × 103
2.0000
0.7420
3 × 105
6 × 105
5.4 × 1012
8.900
373
0 × 103
2.0000
0.9738
8 × 104
3.6 × 104
3.30 × 1013
1.400
373
.0 × 103
2.0000
0.9616
7 × 104
9.4 × 104
8.54 × 1013
0.500
373
.0 × 103
2.0000
0.9610
6 × 104
1.1 × 105
1.01 × 1014
0.400
373
1.0 × 103
2.0000
0.9696
2 × 104
2.4 × 104
2.18 × 1013
2.200
373
25
Table 4. Coagulation kinetic parameters MS at varying pH and 400 mg/l dosage.
Parameters pH = 10
of
pH = 2 pH = 4 pH = 6 pH = 8
γ
α
R2
K (l/
1.
8.00 × 1025
1.
1.
3.07 × 1025
1.
7.
1.08 × 1025
1
1. 4
7.22 × 1024 3.37 × 1025
mg·min)
βBR (l/mg·min)
εp (l/mg)
τ1/2 (min)
C0 (mg/l)
(Np)0
0 × 103
2.0000
0.6830
3 × 105
6 × 105
5.4 × 1012
8.900
373
0 × 103
2.0000
0.9844
9 × 104
3.8 × 104
3.45 × 1013
1.400
373
0 × 103
2.0000
0.9703
9 × 104
1.58 × 105
1.44 × 1014
0.300
373
.0 × 103
2.0000
0.9576
24 × 10
2.48 × 105
2.25 × 1014
0.100
373
1.0 × 103
2.0000
0.9850
1 × 104
2.0 × 104
1.81 × 1013
2.600
373
Table 5. Coagulation kinetic parameters MS at varying pH and 500 mg/l dosage.
Parameters pH = 10
of
pH = 2 pH = 4 pH = 6 pH = 8
γ
α
R2
K (l/mg·min)
βBR (l/mg·min)
εp (l/mg)
τ1/2 (min)
C0 (mg/l)
(Np)0
1.
2.0000
0.6830
3 × 105
6 × 105
5.4 × 1012
8.900
373
7.76 × 1025
1.
2.0000
0.9840
2.3 × 104
4.6 × 104
4.18 × 1013
1.100
373
2.59 × 1025
1
2.0000
0.9749
8.9 × 104
17.8 × 104
1.61 × 1014
0.300
373
1.02 × 1025
1
2.0000
0.2764
4.1 × 104
8.2 × 104
7.45 × 1013
0.600
373
7.22 × 1024
2.0000
0.9882
1.5 × 104
3.0 × 104
2.72 × 1013
1.700
373
2.83 × 1025
0 × 103 0 × 103 .0 × 103 .0 × 103 1.0 × 103
K. A. BABAYEMI ET AL. 737
y = 3E-05x + 0.005
0.587R² =
y = 3E-05x + 0.
R² =
y = 3E-05x + 0.005
R² = 0.742
y = 3E-05x + 0.006
R² = 0.683
y = 3E-05x + 0.006
R² = 0.656
0.00E+00
1.00E-03
2.00E-03
3.00E-03
4.00E-
5.00
6.00
7.
8.00E-03
9.00E-03
020406080
C
t
, l/mg
t, mi n
005
0.707
03
E-03
E-03
00E-03
1/
100mg/l
200mg/l
300mg/l
400mg/l
500mg/l
Figure 6. Kinetic plot of 1/Ct versus time for MS dosage at
pH = 2.
y = 0.00012x + 0.00663
R² = 0.95395
y = 0.00018x + 0.00661
1.50E-02
1/C
t
, l/mg
R² = 0.98357
y = 0.00018x + 0.00750
R² = 0.97381
y = 0.00019x + 0.00787
R² = 0.98441
y = 0.00023x + 0.00903
R² = 0.99126
0.00E+00
5.00E-03
1.00E-02
2.00E-02
2.50E-02
0 20406080
t, m in
100mg/l
200mg/l
300mg/l
400mg/l
500mg/l
Figure 7. Kinetic plot of 1/Ct versus time for varying MS
dosage at pH = 4.
y = 0.00018x + 0.00706
R² = 0.97935
y = 0.00024x + 0.00767
4.00E-02
1/C
t
, l/mg
y = 0.00020x
R² = 0.974 94
y = 0.00047x + 0.00721
R² = 0.96167
y = 0.00079x + 0.00542
R² = 0.97028
y = 0.00089x + 0.00574
R² = 0.97486
0.00E+00
1.00E-02
2.00E-02
3.00E-02
5.00E-02
6.00E-02
7.00E-02
0 20406080
t, mi n
100mg/l
200mg/l
300mg/l
400mg/l
500mg/l
Figure 8. Kinetic plot of 1/Ct versus time for varying MS
dosage at pH = 6.
of MS coagulant at K = 1.24 × 103 (mg·min)1 and τ1/2 =
0.100 mins.
+ 0.00808
8397R² = 0.9
y = 0.00026x
R² =
y = 0.00056x + 0.00725
R² = 0.96106
y = 0.00041x + 0.01534
R² = 0.27636
y = 0.00124x + 0.00228
R² = 0.95768
0.00E+00
1.00E-02
2.00E-02
3.00E-02
5.0
8.
0 20406080
1/C
t
, l/mg
t, m in
+
0.98535
0.00826
4.00E-02
0E-02
6.00E-02
7.00E-02
00E-02
9.00E-02
100mg/l
200mg/l
300mg/l
400mg/l
500mg/l
Figure 9. Kinetic plot of 1 C
t versus time for varying MS
dosage at pH = 8.
y = 0.00006x + 0.00801
R² = 0.97133
1.50E-02
t
, l/mg
y = 0.00012x + 0.00848
R² = 0.97417
y = 0.00010x + 0.01125
R² = 0.98499
y = 0.00015x + 0.01238
R² = 0.98821
0.00E+00
5.00E-03
2.00E-02
2.50E-02
0 20406080
C
t, mi n
y = 0.00012x + 0.00963
R² = 0.96961
1.00E-02
1/
200mg/l
300 g/lm
400mg/l
500mg/l
Figure 10. Kinetic plot of 1/Ct versus time for varying MS
dosage at pH = 10.
At nearly invariant values of K, εp relates directly to
2K = βBR. The consequence is that high εp results in high
kinetic energy to overcome the zeta potential. The impli-
cation is that the double layer is either reduced or the
colloids destabilized to actualize low τ1/2 in favour of
high rate of coagulation [18].
re obtai previous researches
[19].
4. Conclusion
The removal efficiency E > 80% recorded at the opti-
mum pH of 8 and dosage of 400 mg/l supported by the
value of τ1/2 = 0.100 minute presents the potential of
Mucuna sloanei as a source of organic derived coagulant
applicable in large scale water treatment. The obtained
results are in agreement with previous works [19].
The results show that high values of τ1/2 correspond to
low εp and K, an indication of repulsion in the system.
Similar results wened by
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738
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Nomenclatures
βBR: Collision
εp: Collision efficiency
τ1/2: Coagulation period/Half life
R2: Coefficient of Determination
α: Coag-flocculation reaction order
MS: Mucuna sloanei
K: Coagulation rate constant
C: Concentration of particles
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