Adsorption Neutralization Model and Floc Growth Kinetics Properties

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Adsorption Neutralization Model and Floc Growth Kinetics Properties of Aluminum Coagulants Based on Sips and Boltzmann Equations Zhen Wu,†,‡ Xian Zhang,*,†,‡ Chunjiao Zhou,§ Jing-lin Pang,† and Panyue Zhang*,⊥ †

Department of Chemical Engineering, Ordos Institute of Technology, Ordos 017000, China Department of Chemical Engineering, Redbud Innovation Institute of Ordos, Ordos 017000, China § College of Science, Hunan Agriculture University, Changsha 410128, China ⊥ College of Environmental Science and Engineering, Beijing Forestry University, Beijing 100083, China ‡

ABSTRACT: Single-molecule aluminum salt AlCl3, medium polymerized polyaluminum chloride (PAC), and high polymerized polyaluminum chloride (HPAC) were prepared in a laboratory. The characteristics and coagulation properties of these prepared aluminum salts were investigated. The Langmuir, Freundlich, and Sips adsorption isotherms were first used to describe the adsorption neutralization process in coagulation, and the Boltzmann equation was used to fit the reaction kinetics of floc growth in flocculation. It was novel to find that the experimental data fitted well with the Sips and Boltzmann equation, and the significance of parameters in the equations was discussed simultaneously. Through the Sips equation, the adsorption neutralization reaction was proved to be spontaneous and the adsorption neutralization capacity was HPAC > PAC > AlCl3. Sips equation also indicated that the zeta potential of water samples would reach a limit with the increase of coagulant dosage, and the equilibrium zeta potential values were 30.25, 30.23, and 27.25 mV for AlCl3, PAC, and HPAC, respectively. The lower equilibrium zeta potential value of HPAC might be the reason why the water sample was not easy to achieve restabilization at a high coagulant dosage. Through the Boltzmann equation modeling, the maximum average floc size formed by AlCl3, PAC, and HPAC were 196.0, 188.0, and 203.6 μm, respectively, and the halfway time of reactions were 31.23, 17.08, and 9.55 min, respectively. The HPAC showed the strongest floc formation ability and the fastest floc growth rate in the flocculation process, which might be caused by the stronger adsorption and bridging functions of Alb and Alc contained in HPAC. KEYWORDS: PAC, HPAC, aluminum species, Sips equation, Boltzmann equation

1. INTRODUCTION Aluminum coagulants, a kind of widely used inorganic coagulants in water and wastewater treatment, can be divided into single-molecule aluminum like AlCl3·6H2O, Al2(SO4)3· 18H2O, and AlK(SO4)2·12H2O and polymer aluminum like polymeric aluminum chloride (PAC), polymeric aluminum ferric sulfate (PAFS), and polymeric aluminum chloride sulfate (PACS) et al.1−4 The polymeric aluminum is usually obtained by forced prehydrolysis of single-molecule aluminum, and the main difference between single-molecule aluminum and polymeric aluminum is their different dominant hydrolyzed species in water solution.5−7 There are many hydrolyzed species in aluminum solution that have been identified by scientists, such as Al(OH)2+, Al(OH)2+, [A16(OH)15]3+, [A17(OH)17]4+, [AlO4Al12(OH)24(H2O)12]7+, [Al16(OH)38]10+, [A130O8(OH)56(H2O)24]18+, and [A19(OH)n](27−n)+.8−10 It is usually believed that the single-molecule aluminum solution possesses a large amount of mononuclear and oligomer polymer species Ala, while the medium polymeric species Alb and high polymeric species Alc are the main ingredients in © XXXX American Chemical Society

polymeric aluminum solution. In addition, it is generally considered that the coagulation mechanism of single-molecule aluminum and polymeric aluminum has a fundamental difference; otherwise, it is difficult to explain the fact that the coagulation effect of polymeric aluminum doubled that of single-molecule aluminum. Tang et al. believed that both the traditional single-molecule aluminum and the prehydrolyzed polymeric aluminum had a hydrolysis and adsorption process when they were added into water.11,12 However, because the hydrolysis and adsorption occurred microsecond rapidly, they could not be directly measured currently. Humic acid (HA) is a group of natural organic macromolecules which is normally derived from decomposition of animal or plant remains by microorganisms. HA is a kind of typical natural organics found in source water and usually dissolved in water to form a stable colloidal system. HA is also Received: November 8, 2016 Accepted: January 13, 2017 Published: January 18, 2017 A

DOI: 10.1021/acsami.6b14273 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX

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ACS Applied Materials & Interfaces

U.K.) and Laser Particle Size Analyzer (CIS100, Ankersmid Co., The Netherlands), respectively. All coagulation experiments were carried out at a room temperature of 20 °C using the beaker test with a six-paddle gang stirrer (MY30006B, Meiyu Co., Wuhan, China). The 500 mL working HA solution was added into a 1000 mL beaker. A measured amount of coagulant was added into the working HA solution. After a rapid mixing, the sample was taken using a syringe immediately to measure zeta potential by Zetasizer Nano ZS (3000HS, Malvern Co., U.K.). The residual mixture was stirred continually at 200 rpm for 2 min, followed by being slowly stirred at 30 rpm for 20 min and settled for 30 min. The supernatant sample after coagulation and settlement was withdrawn and filtered through common qualitative filter paper for UV254 measurement with UV−vis spectrometer (2550, Shimadzu Co., Kyoto, Japan) at the wavelength of 254 nm. There was a good correlation between UV254 and HA concentration in water, so the HA concentration of supernatant was calculated by the standard curve between UV254 and HA concentration. HA removal rate was calculated by eq 1

usually used as a representative removal target in coagulation studies of natural organic matters (NOM) in water.13−15 The surface charge absorption on colloidal particles is an important factor to make colloidal pollutants keep a stable dispersion in water.16 Thus, the coagulation process is actually aimed at breaking the original surface charge equilibrium and making the colloidal particles destabilize and settle. Zeta potential, known as the surface electric potential of colloidal particle, is one of the basic parameters affecting the colloidal stability of the system.17,18 In this study, single-molecule aluminum salt AlCl3, medium polymerized polyaluminum chloride (PAC), and high polymerized polyaluminum chloride (HPAC) were prepared in a laboratory. The particle size distribution, density, and hygroscopicity of prepared coagulants were characterized. The beaker tests were used to investigate the coagulation properties of prepared coagulants for the removal of HA in water. The Langmuir, Freundlich, and Sips adsorption isotherms were used to describe the relationship between coagulant dosage and increased zeta potential of water samples for the first time. The floc growth kinetics of these three coagulants were fitted with the Boltzmann equation and the significance of each parameter in the model was discussed simultaneously.

HA removal rate =

Co − Ce × 100% Co

(1)

where Co (mg/L) represents the HA concentration of raw water sample and Ce (mg/L) represents the HA concentration of water sample after coagulation. The floc growth kinetics was measured by Laser Particle Size Analyzer (CIS100, Ankersmid Co., The Netherlands). After a dosage of 0.02 mmol/L coagulant was added into the working HA solution, the sample was mixed rapidly and taken into the detector using a syringe immediately. The sample in the detector was slowly stirred under magnetic force, and the mean diameter and size distribution of flocs were measured every 1 or 2 min until the floc growth reached an equilibrium. All the experiments were carried out in duplicate, and the mean and standard deviation values were calculated using the Microsoft Excel program.

2. MATERIALS AND METHODS 2.1. Synthesis of Aluminum Coagulants. All reagents used in the research were of analytical grade. All solutions were prepared with deionized water except for those pointed out specifically. AlCl3 solution was prepared by dissolving a certain amount of AlCl3·6H2O in deionized water. Liquid PAC was prepared by slowly neutralizing AlCl3 solution (1.0 mol/L) with NaOH solution (0.6 mol/L) at room temperature under vigorous stirring until the B value reached 2.4. Liquid HPAC was prepared by heating the PAC solution at 95 °C for 12 h under stirring and refluxing.19,20 Total aluminum concentration (Alt) of AlCl3, PAC, and HPAC solutions were 0.2 mol/L and all solutions were aged at room temperature for 5 d before characterization and coagulation test. 2.2. Characterization of Aluminum Coagulants. Aluminum hydrolytic species distribution was determined with time-developed Al−Ferron complex colorimetry with a UV−vis spectrometer (2550, Shimadzu Co., Japan).21,22 Based on the reaction kinetics difference between Al species and Ferron reagent (8-hydroxy-7-iodoquinoline-5sulfonic acid), Al species can be divided into mononuclear and oligomer polymer species Ala, medium polymeric species Alb, and high polymeric species Alc, which reacts with the Ferron reagent within 1 min, in 1−120 min, and over 120 min, respectively. The particle size of aluminum hydrolytic species was measured with a Zetasizer Nano ZS (3000HS; Malvern Co.). The density of coagulant solutions was detected with a MEIPO densimeter. The liquid coagulant samples were dried in an oven at 60 °C to form a solid sample for the hygroscopicity test, namely, “Dust property test method” (GB/T 16913.6-1997). The solid samples were placed in a certain humidity environment, and the weight increase rate after 24 and 48 h were both calculated as the hygroscopic rate of coagulants samples. 2.3. HA Sample and Coagulation Test. HA was purchased as powder from C.P., Institute of Fine Chemicals Division, Tianjin, China. The apparent molecular weight of HA is mainly distributed in the range of 1000−5000 Da. A stock HA solution was prepared by dissolving a measured amount of HA powder in 0.1 mol/L NaOH solution. With strong shear mixing for 2 h, the HA powder dissolved completely and the HA concentration of stock solution was 1 g/L. The working HA solution was prepared by diluting the stock HA solution to a HA concentration of 10 mg/L. Alkalinity of the working HA solutions was adjusted to 10 mg/L with a NaHCO3 solution of 0.12 mol/L. Zeta potential and particle size distribution of the working HA solution were detected by Zetasizer Nano ZS (3000HS, Malvern Co.,

3. RESULTS AND DISCUSSION 3.1. Characterization of Aluminum Coagulants. Aluminum hydrolytic species distribution and some other characteristics of prepared coagulants are listed in Table 1. It Table 1. Aluminum Species Distribution and Some Other Characteristics of Different Coagulants aluminum species distribution (%)

hygroscopic rate (%)

coagulants (Alt = 0.2 mol/L)

Ala

Alb

Alc

density (g/cm3)

24 h

48 h

AlCl3 PAC HPAC

93.4 32.1 27.3

6.6 62.5 32.1

0.0 5.4 40.6

1.027 1.031 1.033

12.73 4.46 4.55

26.14 5.40 5.40

can be seen that the AlCl3 contained a majority of Ala, a small amount of Alb, and no Alc, while the PAC possessed most of Alb, a portion of Ala, and a small amount of Alc. It was different from AlCl3 and PAC in that the aluminum species in HPAC were more dispersed and Alc occupied the main ingredient. The density of AlCl3, PAC, and HPAC solution was slightly larger than that of pure water, and exhibited the order of AlCl3 < PAC < HPAC. The density difference of AlCl3, PAC, and HPAC might be caused by the different aluminum species contained in them, and the increase of density might be caused by the formation of a colloidal system by higher polymerized species. It also can be seen from the hygroscopicity of coagulants (Table 1) that the AlCl3 had a strong affinity for water, which B


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Figure 1. Particle size distribution of coagulants.

may make it more inclined to immediate hydrolyze when added into the water samples. The PAC and HPAC coagulants obtained through forced prehydrolysis might have a hydrolytic stability in water. The particle size distribution of AlCl3, PAC, and HPAC are shown in Figure 1. Maybe due to the aggregation of aluminum hydrolytic species, the particle size of these three coagulants all reached a nanometer scale, and the mean size of AlCl3, PAC, and HPAC were calculated to be 1.27, 2.26, and 4.15 nm, respectively. The HPAC coagulant showed the biggest mean particle size and its particle size distribution was more dispersed than that of AlCl3 and PAC. 3.2. HA Sample and HA Coagulation Properties. Figure 2 shows the zeta potential and particle size distribution of prepared HA working solution. It can be seen that the prepared

HA working solution exhibited a significant characteristic as charged sol, and the zeta potential of the sol system was −18 mV. HA is a kind of natural organic molecules with a large number of hydroxyl, carboxyl, and aromatic ring groups on the molecular skeleton. The functional groups of HA may hydrolyze or adsorb the charged particles in water to exhibit a negatively charged characteristic. In addition, as shown in Figure 2, the particle size of HA in working solution varied from 3.0 to 14.0 μm, and the average size was 8.1 μm. It should be noted that the particle size obtained with the laser light scattering detector did not fully represent the true size of a single HA molecule. The HA molecules in water may interconnect or adsorb the water molecules, exhibiting a larger size. The effect of coagulant dosage on the zeta potential and HA removal rate are shown in Figure 3. It can be seen that, with the increase of coagulants dosage, zeta potential of water samples increased rapidly at a low dosage range and then rose slowly at a higher dosage range. The isoelectric point (the dosage when the zeta potential value reached zero) was about 0.12, 0.08, and 0.08 mmol/L for AlCl3, PAC, and HPAC, respectively; and when the dosage of coagulant increased to 0.8 mmol/L zeta potential of HA water system increased to 30.9, 25.6, and 24.9 mV for AlCl3, PAC, and HPAC, respectively. It also can be seen from Figure 3 that HA removal rate increased rapidly with a small dosage of coagulant. When the coagulant dosage increased to 0.06 mmol/L, HA removal rate reached 90.78%, 93.06%, and 94.26% for AlCl3, PAC, and HPAC, respectively; then the removal rate of HA increased slowly along with the increase of coagulants dosage. The maximum HA removal rates were 98.01%, 97.51%, and 98.50% when the coagulants dosage were 0.48, 0.16, and 0.16 mmol/L for AlCl3, PAC, and HPAC, respectively. When the coagulant dosage was higher than 0.48 mmol/L, HA removal rates dropped rapidly for AlCl3 and PAC, while decreasing slightly for HPAC. When the coagulants dosage was 0.80 mmol/L, HA removal rate was only 0.25% and 20.20% for AlCl3 and PAC but 95.26% for HPAC. Compared with AlCl3 and PAC, HPAC coagulant reached the highest HA removal rate at a dosage of 0.16 mmol/L, and was less prone to restabilization when the coagulant dosage was higher. The coagulation behavior differences of AlCl3, PAC, and HPAC might be caused by the different aluminum species in different coagulants, and the dominated hydrolytic species Alc contained in HPAC might enhance the adsorption, bridging, and sweeping actions in the coagulation process.

Figure 2. Zeta potential and particle size distribution of HA working solution. C


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the molar volume of the solvent; zeψd is the electric interaction energy, Φ is the van der Waals interaction energy, KB is the Boltzmann constant, and T is the thermodynamic temperature; the sum of zeψd and Φ is also recognized as the adsorption energy Ea. Vm If the letter K is used to represent , and the zeψ + φ

(

NA exp

d KBT

)

numerator and denominator of eq 1 are multiplied by Kn0 simultaneously, eq 2) is changed to eq 3: σm =

σnKn0 1 + Kn0

(3)

where K is a constant under a certain temperature for a given colloidal system. The adsorption isotherm model is a mathematical formula that can be used to express the relationship between adsorbent and adsorbate at a certain temperature, which provides basic data to evaluate the adsorption process on whether it is practical. The Langmuir adsorption isotherm is the most commonly used adsorption isotherm and can be presented as eq 4,25 qe =

3.3. Adsorption Neutralization Modeling. Zeta potential change of colloidal system after coagulant dosing is usually caused by the adsorption of coagulant species onto colloidal particles so that the adsorption isotherm may be used to quantitatively describe the adsorption neutralization of aluminum species onto HA particles. Actually, the adsorption model of colloidal charge and concentration of opposite ions can be theoretically deduced according to the charged colloidal theory proposed by Stern.23,24 Stern believed that if only the adsorption of oppositely charged ions were considered, the relationship between surface charge density of the Stern layer (σm) and concentration of oppositely charged ions outside the electric double layer (n0) corresponded to eq 2, σn σm = zeψ + φ NA 1 + n V exp Kd T

(

B

)

1 + KLCe

(4)

where Ce is defined as the equilibrium concentration of adsorbate, qe is the adsorption amount of the unit mass of adsorbent, qm is the maximum adsorption amount when the adsorption process reaches equilibrium, and KL is the Langmuir adsorption constant. Comparing eq 3 with eq 4, it can be seen that the relationship between σm and n0 is almost the same as that between qe and Ce, which means that the balance established by adsorbed ions in Stern layer and unabsorbed ions in diffusion layer may be described with the Langmuir adsorption isotherm. It is well-known that the Langmuir isotherm equation is established under certain assumptions, such as the adsorption is a monolayer, the adsorption sites are homogeneous, and the particle is absorbed completely independently. Actually, it is difficult to fully meet these assumptions proposed by Langmuir in an actual adsorption process. So Freundlich offered a nonhomogeneous surface adsorption isotherm, whose mathematical expression is shown as eq 5,26

Figure 3. Effect of coagulant dosage on zeta potential and HA removal rate.

0 m

qmKLCe

qe = KFCe1/ n

(5)

where Ce and qe have the same means as in Langmuir isotherm, KF is the Freundlich adsorption constant, and n (dimensionless) is the Freundlich exponential coefficient. The Freundlich empirical formula can be well used for monolayer adsorption; however, the constants in the formula have no physical meaning and cannot be used to explain the mechanisms of adsorption. Sips presented a Sips adsorption isotherm in 1948 which is similar to the Freundlich equation; the difference is that the Sips isotherm has a saturation adsorption under certain conditions. The Sips adsorption isotherm also can be considered as the result of introducing a nonuniform parameter in the Langmuir isotherm, so it also can be called as the extended Langmuir isotherm (LangmuirEXT). The mathematical function of Sips adsorption isotherm is expressed as eq 6,27

(2)

where σn is defined as the surface charge density that adsorbs monolayer opposite ions, NA is the Avogadro constant, Vm is D


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ACS Applied Materials & Interfaces qe =

qmKSCeγ 1 + KSCeγ

(6)

where Ce, qe, and qm have the same means as in the Langmuir isotherm, KS is the Sips adsorption constant, γ is a parameter that is introduced to represent the heterogeneity of adsorbent surface, and the γ value being closer to 1 indicates that the adsorbent surface is more homogeneous. In the coagulation process, with the increase of aluminum dosage, the positively charged aluminum species increased and the surface charge density of the Stern layer (σm) changed accordingly. As the zeta potential is usually used to represent the surface charge situation of Stern layer, the relationship between aluminum dosage and zeta potential change should fit well with the adsorption isotherms. To quantitatively describe the adsorption of aluminum species onto HA particles, the Langmuir, Freundlich, and Sips models were used to fit the experimental data. The fitted results are shown in Figure 4. It can be seen from Figure 4 that the experimental data fitted much better with the Sips isotherm rather than the Langmuir isotherm for the three coagulants. There are various functional groups on the HA particles surface and the adsorption sites of HA are not homogeneous, so the coagulation process may be inconsistent with the Langmuir assumptions. The experimental data also do not fit well with the Freundlich isotherm because the adsorption of aluminum species on to HA particles may reach a limit for the repulsion of homosexual ions; however, the adsorption capacity increases unlimitedly when the adsorbate is enough according to the Freundlich isotherm. The Sips isotherm combines the limited adsorption and nonhomogeneous surface adsorption of the Langmuir isotherm and the Freundlich isotherm together, so it is more suitable for describing the relationship between coagulant dosage and zeta potential variation. The fitted parameters of the Sips equation are listed in Table 2. From Figure 4 and Table 2, it can be seen that with the increase of coagulants dosage, the zeta potential of the water system reaches a limited value. The equilibrium value of the zeta potential can be obtained by adding the qm value together with −18.0 mV (the zeta potential value of raw HA sample), and they are 30.25, 30.23, and 27.25 mV for AlCl3, PAC, and HPAC, respectively. The lower zeta potential value of HPAC at reaction equilibrium is the reason why the water sample is not easy to restabilize at high HPAC dosage. According to the relationship between the Gibbs free energy and the reaction equilibrium constant Ks expressed in Table 2, the Gibbs free energy of adsorption neutralization can be calculated as eq 7: ΔG = −RT ln K s

(7)

Figure 4. Relationship between coagulant dosage and increased zeta potential modified with adsorption isotherms.

where ΔG is the Gibbs free energy of reaction, KS is the Sips reaction constant, T is the thermodynamic temperature of reaction, and R is the molar gas constant. The ΔG is calculated to be −7177.7, −8064.9, and −10275.4 J/mol for AlCl3, PAC, and HPAC, respectively. The negative Gibbs free energy indicates that the coagulant adsorption neutralization reaction is a spontaneous process. Moreover, the Sips reaction constant KS has the same meaning as the KL in the Langmuir equation, so the larger the KS, the stronger adsorption neutralization capacity the coagulant possesses. The KS values listed in Table 2 show that the adsorption neutralization capacity of these coagulants

Table 2. Fitted Parameters of Sips Equation Sips isotherm: qe =

E

qmKSCeγ 1 + KSCeγ

coagulant

Qm (mV)

KS

γ

R2

AlCl3 PAC HPAC

48.25 48.23 45.25

19.02 27.35 67.73

1.51 1.57 1.99

0.997 0.997 0.990


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direction of particles, and the mathematical function of Boltzmann equation can be expressed as eq 830,31 A1 − A 2 y = A2 + x−x 1 + exp d 0

are HPAC > PAC > AlCl3, and the simulation result is in good agreement with the experimental data. The γ in the Sips equation represents the heterogeneity of adsorbent surface, and the γ value being closer to 1 indicates that the adsorbent surface is more homogeneous. Although all AlCl3, PAC, and HPAC coagulants are aluminum salts, the hydrolysis species of them are different, which may result in different γ values. It can be seen from Table 2 that the γ value is 1 < AlCl3 < PAC < HPAC, so the surface heterogeneity of these coagulants are AlCl3 < PAC < HPAC. The more dispersed aluminum species and particle size in HPAC may lead to larger surface heterogeneity than that in AlCl3 and PAC. 3.4. Flocculation Kinetics Modeling. Flocculation kinetics discusses the speed of floc growth, and the flocculation process should reach a certain speed to meet the water treatment requirement. So, the discussion of flocculation kinetics is an important aspect of water treatment flocculation research.28,29 The floc growth with AlCl3, PAC, and HPAC is shown in Figure 5. After the addition of coagulant, the floc

( )

(8)

x

where y represents the average particle size of flocs, x is the reaction time, and A1, A2, x0, and dx are the reaction parameters. The experimental data are fitted by the Boltzmann equation with the relationship between reaction time and the average particles size. The fitting curves are shown in Figure 6 and the

Figure 6. Floc growth kinetics with different coagulants modified by Boltzmann equation.

Table 3. Fitted Parameters of Boltzmann Equation Boltzmann equation: y = A 2 +

A1 − A 2 1 + exp

Figure 5. Floc growth with different coagulants. coagulants AlCl3 PAC HPAC

growth could be divided into three distinct phases. At the first stage, the floc size changed slowly with the increase of coagulant dosage, and this process lasted about 20, 14, and 7 min for AlCl3, PAC, and HPAC, respectively. At the second stage, the average diameter of flocs grew rapidly, and the growth process reached equilibrium after about 36, 24, and 12 min for AlCl3, PAC, and HPAC, respectively. The flat sections at the second stage might be caused by the randomness of floc growth and particle size detection. And then, at the last stage the floc growth reached an equilibrium period; the average floc size of AlCl3, PAC, and HPAC were about 164, 190, and 194 μm, respectively. The floc formation is a complex process, and some floc growth kinetics models have been proposed to simulate this process, such as diffusion-limited aggregation (DLA) model, ballistic aggregation (BA) model, and reaction-limited aggregation (RLA) model. However, the DLA, BA, and RLA models are all based on certain assumptions without consideration about the electrostatic interactions between particles, so there are some limitations for their use in flocculation process modeling. The Boltzmann transport equation describes the particle distribution function evolution with time considering the velocity distribution and scattering

( ) x − x0 dx

A1

A2

x0

dx

R2

5.879 3.212 8.417

196.0 188.0 203.6

31.23 17.08 9.550

4.814 2.633 1.115

0.980 0.969 0.995

fitting parameters are listed in Table 3. As shown in Figure 6 and Table 3, there are good correlations between reaction time and floc growth size, and the correlation coefficients (R2) were 0.981, 0.971, and 0.994 for AlCl3, PAC, and HPAC coagulants, respectively.

( )

It can be seen from eq 8 that when x → ∞ and exp

x − x0 dx

→ ∞, y = A2. With completion of the flocculation, the floc size reaches a limit value, and the A2 represents the maximum size of flocs at equilibrium. For AlCl3, PAC, and HPAC coagulants, the A2 is 196.0, 188.0, and 203.6 μm, respectively. The fitted floc size with PAC and HPAC is basically consistent with the experimental data in Figure 5, while the fitted floc size of AlCl3 is quite different from the experimental data; the reason may be that the flocculation of AlCl3 is too slow to reach a full equilibrium in the testing period.

( ) of AlCl , PAC, and HPAC is

When x = 0, exp

−x 0 dx

3

approximately equal to zero, y ≈ A1. So the A1 in eq 8 can be used to express the average particle size in the initial stage of F



■

flocculation. For AlCl3, PAC, and HPAC coagulants, the A1 value is 5.879, 3.212, and 8.417 μm, respectively, and there is a certain deviation between the simulated and experimental data.

( ) = 1, y =

Furthermore, when x = x0 and exp

x − x0 dx

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A1 + A 2 . 2

The x0 can be used to represent the halfway reaction time until the floc grows to the limit at equilibrium, and the 1/dx may be a parameter that is associated with the reaction rate. The x0 is important in reaction kinetics, and the smaller the x0, the faster the floc growth rate is. It can be seen from Table 3 that the x0 of AlCl3, PAC, and HPAC is 31.23, 17.08, and 9.55 min, respectively. Compared with AlCl3 and PAC, HPAC showed the strongest floc formation ability in the flocculation process. The medium polymeric species Alb and high polymeric species Alc in HPAC may play an active role in the floc growth process. The strong adsorption and bridging function of Alb and Alc may make the floc growth more rapid, and the flocculation equilibrium can be reached in a shorter period. The high polymeric species Alc and large hydrolysis species size in HPAC could improve the bridge-aggregation and sweepflocculation actions in the coagulation process. Some studies indicated that the multidispersion of the coagulation system has a significant effect on the kinetics of coagulation and flocculation.32 If the system is a multidispersion system and contains large particles, the small colloidal particles in water can be coagulated effectively by the effect of fluid shearing force.

4. CONCLUSIONS The characterization of coagulants showed that Alc was the main ingredient in HPAC and the aluminum species were more dispersed in HPAC than that in AlCl3 and PAC. The maximum HA removal rate was 98.01%, 97.51%, and 98.50% for AlCl3, PAC, and HPAC, respectively; and AlCl3 and PAC were more likely to result in restabilization at a coagulant dosage more than 0.48 mmol/L. The Sips model fitted well with the experimental data. With the increase of coagulants dosage, the zeta potential of the water system reached a maximum value, and the equilibrium zeta potential values were 30.25, 30.23, and 27.25 mV for AlCl3, PAC, and HPAC, respectively. Through the Boltzmann equation fitting, the maximum average floc size formed by AlCl3, PAC, and HPAC was 196.0, 188.0, and 203.6 μm, and the half reaction times were 31.23, 17.08, and 9.55 min, respectively.

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Research Article

AUTHOR INFORMATION

Corresponding Authors

*Telephone: +86-477-8591197. E-mail: [email protected] (X.Z.). *Telephone: 86-10-62336900. E-mail: panyue_zhang@bjfu. edu.cn (P.Y.Z.). ORCID

Xian Zhang: 0000-0002-3740-9585 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the Colleges and Universities’ Scientific Research Project of Inner Mongolia Autonomous Region (NJZZ16370, NJZZ13017), National Natural Science Foundation of China (51578068, 51521006), and financial supports from the Furong Scholar of Hunan Province. G


Research Article

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Adsorption Neutralization Model and Floc Growth Kinetics Properties

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