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GENERAL RESEARCH Adsorption Characteristics and Optimal Dosage of Flocculants in the Solid Separation of Suspensions Akira Suzuki,† Hideo Maruyama,*,† Hideshi Seki,† Isamu Kashiki,‡ and Norio Inoue† DiVisions of Marine Bioresources and Marine EnVironment and Resources, Graduate School of Fisheries Sciences, Hokkaido UniVersity, Minato-cho 3-1-1, Hakodate 041-8611, Japan
A new, simple model for flocculation of suspended particles was proposed taking into account the bridging between a flocculant-adsorbed surface on a particle and a bare surface on another particle. Experimental data on the adsorption of flocculants onto particles were fitted to a Langmuir-type adsorption isotherm, and two adsorption parameters were obtained by the fitting. Flocculation experiments were conducted for quartz suspensions with two types of polymer flocculants that had been developed in our previous studies. The flocculation efficiency of the flocculant was evaluated by turbidimetry. An attempt was made to apply the proposed model to the experimental flocculation efficiency, and it was shown that the model can well explain the experimental results. As a result, it was revealed that one of the model parameters, R, plays the most important role in flocculation phenomena, and it gives the fraction of particles surface covered by flocculant at an optimum flocculation. Introduction The separation of suspended solids from aqueous environments has been an important operation in the fields of water treatment, mineral processing, and so on. Flocculation is an effective and widely used technique for these purposes. Most currently accepted flocculants are polyvalent polymers or alum. These flocculants are known to bridge between particles by chemical binding forces and to form large flocs having high settling velocities. Therefore, many discussions on bridging flocculation have appeared in the literature. Ruehrwein and Ward1 first proposed the basic principle of bridging flocculation in 1952, presenting a model in which a single polymer chain was bridging between two or more particles. Since then, some more vigorous studies about bridging flocculation have been developed.2-9 In these previous studies, the influence of flocculant characteristics such as electrical charge density and chemical structure on the optimum flocculant dosage or flocculation efficiency has been the main focus. In the current study, we propose a flocculation model that takes into account the bridging reaction between adsorbed polymer flocculant surface on a particle and the bare surface on another particle. To verify the validity of the model, adsorption and flocculation experiments were conducted for quartz suspensions with two types of polymer flocculants that were developed in our previous studies.10-17 Flocculation Model 1. Adsorption of Flocculant on Particles. In the flocculation process of suspended particles, two successive steps are required. * To whom correspondence should be addressed. E-mail: maruyama@ elsie.fish.hokudai.ac.jp. † Division of Marine Bioresources. ‡ Division of Marine Environment and Resources.
The first step involves the adsorption of flocculant molecules onto the bare particle surface, and the second is the bridging between the adsorbed flocculant and the bare surface of another particle. The adsorption step can be generally expressed as
S + F T FS
(1)
where F and S denote the flocculant molecule and the surface of a particle, respectively, and FS represents the flocculantoccupied surface of a particle. The equilibrium constant, Ka (dm3/g), of eq 1 can be written as
Ka )
θa [FS] ) [S][F] θsC
(2)
where C (g/dm3) represents the equilibrium concentration of flocculant in water phase and θa and θs represent the fraction of particles surfaces occupied by flocculants and the fraction of bare surfaces of particles, respectively. Because θa + θs ) 1, we obtain θa as
θa )
KaC 1 + K aC
(3)
As a result, the amount of flocculant adsorbed on the particles, X (g/g of particles), is
X ) γθa )
γKaC 1 + K aC
(4)
where γ (g/g of particles) represents the saturated amount of adsorbed flocculant on the particles. As seen in eq 4, the adsorption equilibrium can be expressed by a Langmuir isotherm.16-17
10.1021/ie0506769 CCC: $33.50 © 2006 American Chemical Society Published on Web 01/06/2006
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On the other hand, the material balance of the flocculant gives
wX ) (C0 - C)V
(5)
where w (g) and V (dm3) denote the mass of particles in the suspension and the volume of the suspension, respectively, and C0 (g/dm3) represents the initial concentration of flocculant in the suspension. From eqs 4 and 5, one obtains
(
)
C0 1 w C2 - C0 - γ C)0 V Ka Ka
(6)
From the solution of this equation, we can determine the residual concentration of flocculant, C, in the water phase at the adsorption equilibrium as
1 C ) (P + xP2 + 4C0/Ka) 2
(7)
1 w P ≡ C0 - γ V Ka
(8)
where
Provided that the two adsorption parameters, γ and Ka, are known, we can evaluate the relationship between the initial concentration of flocculant, C0, and the surface fraction of particles covered by flocculant, θa, using eqs 3 and 7. 2. Bridging between a Covered Surface and a Bare Surface. Simply, flocculation process can be considered to be a binding reaction between the surface covered with flocculant on one particle and the bare surface of another particle. Therefore, we can write this bridging reaction as
mFS + nS T FmSm+n
(9)
where FS and S express the surface covered by flocculant and the bare surface, respectively, and m and n denote the stoichiometric coefficients with respect to FS and S, respectively. The equilibrium constant of the reaction expressed by eq 9 can be written as
Kb )
f θa (1 - θa)n m
(10)
where f represents the surface density of the number of flocculant molecules used to form the new particle (or floc) bridged by flocculant (i.e., the above FmSn). Because a more strongly bound floc will be formed for larger values of f, we can reasonably assume that the flocculation efficiency, η, will be proportional to f, that is
η ) AKbθam(1 - θa)n ) Kfθam(1 - θa)n
(11)
where A is a proportionality constant and Kf )AKb. Replacing n/m by R, eq 11 can be rewritten as
η ) Kf[θa(1 - θa)R]m
η can experimentally be determined as
(12)
In this study, the relative turbidity, T/T0, was used as an experimental measure of the degree of flocculation. T and T0 represent the turbidities of a solid suspension in the presence and in the absence, respectively, of flocculant in the supernatant water after a certain settling time. Because the ratio of the solid particles removed from suspensions by flocculation and sinking during the settling is considered to be the flocculation efficiency,
η≡1-
T T0
(13)
Hereafter, we attempt to compare the theoretical value of η with the experimental value and to verify the validity of the flocculation model presented above. Materials and Methods 1. Chemicals. Albumin (from egg), methyl glycol chitosan (MGCh), potassium polyvinyl sulfate (PVSK), methyl alcohol, sodium hydroxide, and hydrochloric acid were purchased from Wako Pure Chemical Industries (Osaka, Japan). Albumin was of practical-grade quality, and other chemicals were of reagentgrade quality. According to the manufacturer, the degrees of polymerization for MGCh and PVSK were above 400 and 1500, respectively. The molecular weight of the albumin used was ∼40 000-45 000 g/mol. All chemicals were used without further purification. 2. Suspended Particles. Quartz sand was purchased from Wako Pure Chemical Industries (Osaka, Japan), and it was used for making suspensions to be flocculated. Quartz powder was prepared by the following procedure: The quartz sand was washed with distilled water and dried at 60 °C. Then, it was pulverized for 48 h using a ball mill. The powder was washed with distilled water repeatedly and dried at 60 °C for 48 h. The particle size was measured by a Coulter counter (type ZM), which gave a number-average diameter of 1.5 µm. Suspensions of quartz powder were prepared as follows: To soak the surface of particles thoroughly with water, 12 g of quartz powder was boiled with 1000 mL of distilled water in a flask. A dilute HCl or NaOH solution was added to adjust the final pH in the suspension to 6.5-7.0. In this study, this suspension was used as the stock suspension for all experiments. 3. Preparation of MeOA. Egg ovalbumin (OA) was methylated according to the method reported by Fraenkel-Conrat and Olcott.18 The procedure was almost the same as in our previous study.16 An aqueous solution of OA (ca. 10 g/dm3) was prepared, and a 0.1 M HCl solution was added. At pH 4.6 (isoelectronic point of OA), OA precipitated, and the mixture was centrifuged at 3000 rpm for 20 min. The precipitated OA was washed with methyl alcohol and dispersed in a 100-fold volume of methyl alcohol containing 0.05 M HCl. This solution was stirred for 24 h at room temperature. The methylated OA (MeOA) was collected in a centrifuge at 3000 rpm for 20 min and then washed with distilled water. The MeOA was dialyzed for 24 h to remove methyl alcohol and HCl. The degree of methylation was determined from the change in the number of carboxylic groups before and after methylation by a potentiometric titration.16 By varying the methylation time and the concentration of methyl alcohol, MeOA samples having different degrees of methylation were prepared. In this study, two types of MeOA with methylation degrees of 62% and 79% were used. 4. Preparation of MP-ACF. An associated colloidal flocculant10-15 formed by the combination of methyl glycol chitosan (MGCh) and potassium polyvinyl sulfate (PVSK) was prepared in the following manner. MGCh and PVSK solutions were mixed at an adequate ratio, and the resultant solution was agitated well at room temperature with a magnetic stirrer. The pH of the solution was adjusted to 5.5 by adding 1 M NaOH solution. The solution was centrifuged at 3300 rpm for 30 min to remove ineffective sediment. Then, the supernatant was used as a flocculant. Hereafter, this flocculant is abbreviated as MP-
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ACF. The mixing ratio, r, was defined as nc/na, where nc and na denote the equivalent numbers of moles based on the numbers of aminonium functional groups in MGCh and of sulfonic functional groups in PVSK, respectively. In this study, MPACFs having r ) 1.05 or 1.14 were used for experiments. 5. Adsorption of Flocculants on Quartz. For each flocculant adsorption experiment, 11 mL of flocculant (MeOA or MPACF) solution with an adequate concentration was prepared and poured into a cylindrical plastic vessel (2.4 cm in diameter, 5.7 cm in height). After thermal equilibrium at 30 °C, 4 mL of 12 g/dm3 quartz stock suspension was added to the solution. The suspension was stirred for the necessary time to attain adsorption equilibrium, and then the quartz was separated from the liquid phase by centrifugation at 4000 rpm for 20 min. Preliminary experiments showed that 2 h is sufficient time to attain adsorption equilibrium in the present study. The concentrations of MeOA and MP-ACF were determined by a general UV spectrophotometric method (Hitachi U-1500 or JASCO Ubest30 spectrometer) at 210 and 265 nm, respectively. The amount of flocculant adsorbed onto quartz was determined from the difference between the flocculant concentrations in the initial and final states. 6. Clarification Experiments. Clarification experiments were carried out similarly to the adsorption experiments. The mixture of the quartz suspension and the flocculant solution was gently agitated for 2 h (adsorption step). Subsequently, the suspension was agitated violently (deflocculation step). Both agitations were carried out using a turn-over-type rotating machine with the rotating speeds of ca. 100 min-1 (the same speed as in the adsorption experiments) and ca. 400 min-1, respectively. The latter violent agitation was carried out to temporarily completely destroy some flocs that might be formed in the preceding gentle step into the initial primary quartz particles and to set all the suspensions in the same flocculation state (i.e., no flocculation) before the next flocculation step started. Then, the suspension was left to stand without agitation for 1 min (flocculation step). A 2-mL sample was taken from the supernatant layer at a position 1 cm below the surface. The turbidity of the sample was measured spectrophotometrically at 700 nm (Hitachi U-1500 or JASCO Ubest-30 spectrometer). The experimental flocculation efficiency, η, was calculated according to eq 13 using the relative turbidity values, T/T0, obtained experimentally Results and Discussion 1. Adsorption of MeOA and MP-ACF onto the Quartz Surface. The adsorption isotherms of MeOA and MP-ACF onto quartz surface are shown in Figures 1 and 2, respectively. The solid lines were calculated according to eqs 4, 7, and 8 using the adsorption parameters listed in Table 1. The experimental data for each flocculant well fitted a theoretical solid line calculated using the same set of parameters (Table 1). A comparison between the two sets of obtained adsorption parameters listed in Table 1 shows that MeOA has a smaller saturated density, γ, and a larger equilibrium constant, Ka, than MP-ACF. 2. Application of Model to Experimental Flocculation Efficiency. The experimental results of clarification tests for quartz suspensions with MeOA and MP-ACF are presented in Figures 3 and 4, respectively. The ordinate, η, represents the flocculation efficiency, and the abscissa, C0, indicates the flocculant dosage (initial flocculant concentration). In each set of experiments, there occurs a clear maximum in η with increasing C0. The solid line in this figure represents the theoretically calculated η for each flocculant based on the above-
Figure 1. Adsorption isotherm of MeOA onto quartz surface at 30 °C. The concentration of the quartz particles is 4 g/dm3. The solid line represents the theoretical curve calculated using eq 4 with the parameters listed in Table 1.
Figure 2. Adsorption isotherm of MP-ACF onto quartz surface at 30 °C. The concentration of the quartz particles is 4 g/dm3. The solid line represents the theoretical curve calculated using eq 4 with the parameters listed in Table 1. Table 1. Adsorption Parameters for MeOA and MP-ACF on Quartz Particles
MeOA MP-ACF
γ (g/g of particles)
Ka (dm3/g)
2.51 × 10-2 2.14 × 10-3
1.65 × 102 9.34 × 101
described model (eq 12). The model parameters, Kf, m, and R, used for the calculation were determined by a least-squares method using the data on the flocculation experiments presented in this figure. MP-ACF showed almost the same flocculation curve irrespective of the mixing radio, r, of cationic (MGCh) to anionic (PVSK) polymer, as can be seen in Figure 4. On the other hand, MeOA, which has a higher methylation degree, clearly exhibited a higher flocculation efficiency than MeOA, which has a lower methylation degree. The flocculation parameters, Kf, m, and R, that were determined by the leastsquares method and used for the calculation are summarized in Table 2. 3. Influence of Flocculant Properties on Optimum Flocculation. Differentiation of eq 12 gives θopt (the θa value at maximum flocculation efficiency) as
θopt )
1 1+R
(14)
Therefore, a flocculant having a large value of R gives its optimum flocculation efficiency at a small coverage fraction,
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Figure 3. Flocculation efficiencies of MeOA at 30 °C as a function of initial flocculant concentration. The concentration of the quartz particles is 4 g/dm3. The methylation degrees of MeOA are indicated in the figure. The dotted and solid lines represent the theoretical curves calculated using eqs 3, 7, 8, and 12 for MeOA with methylation degrees of 62% and 79%, respectively. The parameters used for calculation are listed in Tables 1 and 2.
Figure 4. Flocculation efficiencies of MP-ACF at 30 °C as a function of initial flocculant concentration. The concentration of the quartz particles is 4 g/dm3. The mixing equivalent mole ratios of MGCh to PVSK are indicated in the figure. The solid line represents the theoretical curve calculated using eqs 3, 7, 8, and 12 with the parameters listed in Tables 1 and 2. Table 2. Model Parameters for Flocculation of Quartz Suspensions by MeOA and MP-ACF MeOA (MD ) 64%) MeOA (MD ) 79%) MP-ACF
A
m
R
Kf
θopt
2.10 1.41 1.45
0.36 0.13 0.15
2.80 5.41 4.00
3.46 × 102 2.32 × 102 1.35 × 102
0.26 0.15 0.20
θopt. The amount of flocculant adsorbed on the surface of particles at the optimum flocculation can be easily estimated as
Xopt ) γθopt )
γ 1+R
(15)
From eqs 3 and 14, the residual flocculant concentration left in the water phase after flocculation can also be determined as
Copt )
1 RKa
(16)
Using eqs 15 and 16, the flocculant dosage for the optimum flocculation is predicted as
Dopt ) wXopt + VCopt )
wγ V + 1 + R RKa
(17)
Figure 5. Flocculation efficiencies of MeOA at 30 °C as a function of the fractional coverage of the quartz surface by flocculant. The concentration of the quartz particles is 4 g/dm3. The methylation degrees of MeOA are indicated in the figure. The dotted and solid lines represent the theoretical curves calculated using eq 12 for MeOA with methylation degrees of 62% and 79%, respectively. The parameters used in the calculations are listed in Table 2. The abscissas of the experimental data in Figure 3 were converted to the fractional coverage of the quartz surface by flocculant using eqs 3, 7, and 8.
Figure 6. Flocculation efficiencies of MP-ACF at 30 °C as a function of the fractional coverage of the quartz surface by flocculant. The concentration of the quartz particles is 4 g/dm3. The mixing equivalent mole ratios of MGCh to PVSK are indicated in the figure. The solid line represents the theoretical curve calculated using eq 12 with the parameters listed in Table 2, and the abscissas of the experimental data in Figure 4 were converted to the fractional coverage of the quartz surface by flocculant using eqs 3, 7, and 8.
Figures 5 and 6 are replots of Figures 3 and 4, respectively, in which the abscissa has been converted from C0 to θa. The values of the optimum coverage fraction, θopt, obtained using eq 14 are also listed in Table 2. The predicted θopt values well agree with the experimental results. The smallest θopt value, that is, the largest R value, was found for the use of MeOA with the methylation degree of 79%. On the basis of the above discussion, the following conclusions can be summarized: An excellent flocculant should have large values of R and Ka and a small value of γ. Such a flocculant provides a small flocculant dosage (see eq 17) and a low residual concentration of flocculant in water phase. Conclusion In this work, we proposed a new, simple flocculation model that takes into account the bridging between a flocculantadsorbed surface on one particle and a bare surface on another particle. To verify the validity of the model, adsorption and flocculation experiments were carried out using quartz particles as the adsorbent or the particles to be flocculated and two kinds
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of polymer substances (MeOA and MP-ACF) as the adsorbates or flocculants. The adsorption of each flocculant onto that quartz surfaces well fitted to a Langmuir-type adsorption isotherm. The experimental flocculation efficiency was successfully explained by the present model. As a result, it was revealed that one of the model parameters, R, has the most important role in flocculation phenomena and determines the optimum fraction of particle surfaces covered by a flocculant. Acknowledgment The authors express their thanks to Mr. Y. Yamaguchi, former student of the graduate school at Hokkaido University, for his help with the experimental work. Literature Cited (1) Ruehrwein, R. A.; Ward, D. W. Mechanism of Clay Aggregation by Polyelectrolytes. Soil Sci. 1952, 73, 485. (2) Smellie, R. H.; La Mer, V. K. Flocculation, Subsidence and Filtration of Phosphate Slimes: VI. A Quantitative Theory of Filtration of Flocculated Suspensions. J. Colloid Sci. 1958, 13 (6), 589. (3) Healy, T. W.; La Mer, V. K. The Energetics of Flocculation and Redispersion by Polymers. J. Colloid Sci. 1964, 19 (4), 323. (4) La Mer, V. K. Filtration of Colloidal Dispersions Flocculated by Anionic and Cationic Polyelectrolytes. Discuss. Faraday 1966, 42, 248. (5) Fleer, G. J.; Lyklema, J. Polymer Adsorption and Its Effect on the Stability of Hydrophobic Colloids. II. The Flocculation Process as Studied with the Silver Iodide-Polyvinyl Alcohol System. J. Colloid Interface Sci. 1974, 46, 1. (6) Sakohara, S. Removal of Turbidity by the Use of an Organic, Polymeric Flocculant. Analysis Using a Simple Bridging Model. Int. Chem. Eng. 1981, 21, 652.
(7) Gregory, J. Polymer Adsorption and Flocculation in Sheared Suspensions. Colloids Surf. 1988, 31, 231. (8) Nystro¨m, R. S.; Rosenholm, J. B.; Nurmi, K. Flocculation of Semidilute Calcite Dispersions Induced by Anionic Sodium PolyacrylateCationic Starch Complexes. Langmuir 2003, 19, 3981. (9) Biggs, S.; Habgood, M.; Jameson, G. J.; Yan, Y. Aggregate Structures Formed via a Bridging Flocculation Mechanism. Chem. Eng. J. 2000, 80, 13. (10) Kashiki, I.; Suzuki, A.; Gotoh, K. Clarifiability of a New Associated Colloidal Flocculant. Kagaku Kogaku Ronbunshu 1982, 8 (1), 73. (11) Kashiki, I.; Suzuki, A. Solubility Tendency of the Associated Colloidal Flocculant and Its Flocculation Ability. Kagaku Kogaku Ronbunshu 1982, 8 (6), 722. (12) Kashiki, I.; Suzuki, A. On a New Type of Flocculant. Ind. Eng. Chem. Fundam. 1986, 25 (1), 120. (13) Kashiki, I.; Suzuki, A. Flocculation System as a Particulate Assemblage: A Necessary Condition for Flocculants to be Effective. Ind. Eng. Chem. Fundam. 1986, 25 (3), 444. (14) Suzuki, A.; Kashiki, I. Flocculation of Suspension by Binary (Polycation-Polyanion) Flocculant. Ind. Eng. Chem. Res. 1987, 26 (7), 1464. (15) Kashiki, I.; Suzuki, A. Associated Colloidal Flocculants under Wide pH Variation. J. Chem. Eng. Jpn. 1988, 21 (4), 352. (16) Seki, H.; Suzuki, A. Flocculation of Diatomite by Methylated Egg Albumin. J. Colloid Interface Sci. 2003, 263 (1), 42. (17) Seki, H.; Suzuki, A.; Maruyama, H. Adsorption of Egg Albumin onto Methylated Yeast Biomass. J. Colloid Interface Sci. 2004, 270 (2), 304. (18) Fraenkel-Conrat, H.; Olcott, H. S. Esterification of Proteins with Alcohols of Low Molecular Weight. J. Biol. Chem. 1945, 161 (1), 259.
ReceiVed for reView June 9, 2005 ReVised manuscript receiVed November 7, 2005 Accepted November 28, 2005 IE0506769
