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Abstract

Adsorption of methylene blue from synthetic wastewater using Fe₃O₄ nanoparticles encapsulated with alginate beads is carried out. The adsorption experiments were conducted in a continuous column equipped with an external magnetic field. The effects of important factors such as initial dye concentration, dose of Fe₃O₄ in beads, adsorption time, and intensity of magnetic field on the Methylene blue (MB) adsorption have been studied experimentally. The Taguchi method is applied for optimization of operating conditions in dye adsorption onto the magnetic alginate beads. The variance analysis showed that the adsorption time is most effective factors by higher contribution percent in dye adsorption. The optimum conditions are achieved as 20 mg l⁻¹ dye concentration, 1 Gy dose of Fe₃O₄ in beads, 60 min of adsorption time, and 440 G of magnetic field intensity. The equilibrium adsorption data were analyzed using isotherm models and results revealed that the experimental data are in agreement with Freundlich isotherm model and the kinetic analyses showed that the adsorption kinetics was described accurately by pseudo-first-order model.

Keywords

Adsorption nanoparticles Taguchi method isotherm models kinetic models

Introduction

Wastewater that is discharged by textile industries and dye manufacturing has become an environmental problem and often poses severe environmental and health hazards. There are more than 10,000 different commercial dyes used in the textile processes, which is almost 15% of total production and is lost as effluent during dye production and dyeing process. The environmental damage caused by dyeing wastewater is increasing and research also is piling up (Bhatnagar and Jain, 2005; Noroozi and Sorial, 2013; Volmajer Valh et al., 2011).

Physical and chemical processes such as membrane processes, electrochemical techniques, coagulation/ flocculation, ion exchange, and biosorption methods can be used for dye removal. Adsorption of pollutant and dyes from wastewater is considered to be superior to other techniques because of low cost, simplicity of design, and producing no contaminants such as flocculants (Fersi and Dhahbi, 2008; Forgacsa et al., 2004; Kannan et al., 2013; Mahmoodi et al., 2011; Nguyen and Juang, 2013; Robinson et al., 2001).

Sodium alginate is one of the most extensively investigated biopolymer composed from guluronic and mannuronic acid, which can be used as a sorbent due to good hydrophilicity, low cost, nontoxicity, and biocompatibility (Lakouraj et al., 2014; Veglio et al., 2002). The removal efficiency of alginate can be improved using the magnetic nanoparticles augmented into the alginate beads 9(Idris et al., 2012).

The use of magnetic materials is one of the promising ways for removal of pollutants from aqueous solution. In environmental applications, the magnetite particles are usually dispersed in a polymer matrix such as alginate beads. One of the effective magnetic materials to remove a wide range of organic and inorganic pollutants is ferro-fluids. Ferro-fluids are colloidal liquids made of nanoscale ferromagnetic, or ferrimagnetic, particles suspended in a carrier fluid such as water (Idris et al., 2012).

Removal of methylene blue and methyl orange by magnetic alginate bead in a batch system is conducted by Rocher et al. (2008). They studied the effects of initial dye concentration, pH, and calcium content of the beads on the adsorption. The results showed that the Langmuir model fits the adsorption data and adsorption kinetics experiments well fitted by pseudo-second-order equation.

Shokohi et al. (2011) have used magnetic sodium alginate beads for removal of reactive black dyes from aquatic solution. Their results showed that by increasing adsorbent dose and adsorption time, the removal efficiency was increased. Also the isotherm and kinetic analyses showed that their data are compatible with the Langmuir isotherms and pseudo-second-order kinetics models.

Soni et al. (2012) investigate adsorption behavior of o-nitrophenol from aqueous medium, using nano iron oxide loaded calcium alginate beads and the effects of pH, adsorbent dose, adsorption time, and temperature on adsorption capacity were investigated. The isotherm analyses indicate adsorption data were better described by Freundlich isotherm model.

Dye removal ability of magnetic ferrite nanoparticles encapsulated with alginate was investigated by Mahmoodi (2013). The kinetics analysis and dye adsorption isotherms were carried out and results showed that the intraparticle diffusion model is dominant in the dye adsorption.

Based on the above described work, it appears that the application of magnetic nanoparticles has been extensively studied and these materials are very effective to remove pollutants from aqueous solutions. To our knowledge, removal of pollutants using magnetic alginate beads under external magnetic field has not been reported.

A well planned set of experiments, in which all parameters of interest are varied over a specified range, is a reasonable approach to obtain systematic data. The Taguchi method is one such approach for conducting experiments using a statistical approach to understand the significance of independent factors and levels. In this work, the Taguchi method has been used because by using this method the number of experiments conducted in most of the cases is lesser than that of any other experiments using a statistical approach.

In this study, Fe₃O₄ nanoparticles encapsulated with alginate beads were used as a sorbent for removal of MB from synthetic wastewater in a continuous column equipped with external magnetic field. Taguchi method was applied to determine the optimum conditions for process factors of initial dye concentration, dose of Fe₃O₄ in beads, adsorption time, and intensity of magnetic field in four levels. The dye adsorption isotherms and kinetic analysis were carried out.

Materials and methods

Chemicals and reagents

Fe₃O₄ magnetic nanoparticles supplied by Nano Amor Company (New Mexico, USA) with particle size of 30 nm and purity of 99% are shown in Figure 1(a). Sodium alginate powder was purchased from Acros Organic Company, and Methylene blue (C₁₆H₁₈ClN₃S.3H₂O, molecular weight = 373.88) was obtained from UNI-Chem Reagents Company. All MB solutions used in this study were prepared by dilution from stock solution (1 g l⁻¹). All other chemicals purchased from Merck (Germany).

Figure 1.

(a) Fe₃O₄ magnetic nanoparticles and (b) synthesized magnetic alginate beads.

Synthesis and characteristics of the beads

In the first step, Fe₃O₄ nanoparticles were dispersed in deionized water by ultrasonic vibrator for 30 min. Fe₃O₄ nanoparticles are coated using citric acid for better dispersion. The mixture was stirred with a magnetic stirrer for 18 h at 30℃. Then, 1 g of sodium alginate was dissolved in 200 ml of ferro-fluid. The suspension mixed for 60 min was then added drop wise by syringe into a CaCl₂ solution (300 ml, 0.5 mol l⁻¹) to form the magnetic alginate beads. The produced beads were kept in the calcium bath during 24 h, and then washed several times with distilled water and kept in a distilled water bath. The compositions of the magnetic beads (calcium, sodium, and iron amount) were determined using atomic absorption spectrometer. Figure 1(b) shows the synthesized magnetic alginate beads.

Adsorption experiments

Continuous adsorption experiments are carried out in a fixed-bed adsorption unit consisting of a glass column (2.5 cm ID and 50 cm height), equipped with external magnetic field (coil with 6000 rotate wire) and a cooling system, which avoids from heating of coil. The column is packed with the generated beads (10 g of wet basis) for 100 ml of synthetic wastewater at ambient temperature (293.15 K). Synthetic wastewater passed from the container into the column flows through the packed bed. The volume flow rate of synthetic wastewater was fixed at 0.92 l min⁻¹.

NaOH and HCl (0.1 M) were used to adjust the pH value. Dye concentration was measured using a UV/Visible spectrophotometer (λ_max = 665 nm). The amount of dye adsorbed per unit mass of adsorbent (q) and color removal rate (%R) were calculated as follows (Runping et al., 2008)

q_{e} = \frac{V (C_{0} - C_{e})}{M}

(1)

% R = \frac{(C_{0} - C_{e})}{C_{0}} \times 100 %

(2) where V (l) is the solution volume, C₀ (mg l⁻¹) is the initial MB concentration, C_e (mg l⁻¹) is the MB concentration at equilibrium, and M (g) is the weight of magnetic alginate beads.

Design of experiments by Taguchi method

The design of experiments by Taguchi method is an efficient approach for optimization of process conditions. Taguchi method involves the following steps (Oguza et al., 2006; Santra et al., 2014): (a) selecting the process factors, (b) selecting the number of level for factors, (c) selecting the appropriate orthogonal array, (d) conducting the experiments based on orthogonal array arrangement, (e) analyzing the experimental result by analysis of variance (ANOVA), (f) selecting the optimum level of factors and predicting the response at the optimum condition, and (g) verifying the predicted response by conformational experiment.

In this study, four orthogonal factors are applied including initial dye concentration, dose of Fe₃O₄ nanoparticles in beads, adsorption time, and intensity of magnetic field with four levels as shown in Table 1. Orthogonal array of L₁₆ (4⁴) from the Taguchi method is applied in the experiments design. In the Taguchi method, the S/N ratio can be used to measure the standard deviation and higher S/N ratio values are favorable for dye removal. The S/N ratio used for dye adsorption is defined as follows (Engin et al., 2008)

S / N = - 10 Log \frac{1}{n} (\sum \frac{1}{y 2})

(3) where n is the number of replication and y is response (dye removal percentage).

Table 1.

Orthogonal factors and their levels.

Factors	Level 1	Level 2	Level 3	Level 4
Initial dye concentration(mg l⁻¹)	20	30	50	100
Dose of Fe₃O₄ in beads (g)	0	0.25	0.5	1
Adsorption time (min)	10	20	40	60
Intensity of magnetic field (G)	0	146	293	440

Results and discussion

Effect of pH

The pH of the dye solution is an important parameter in the removal efficiency and the adsorption capacity. The pH of solution influences the dye chemistry, surface charge, and the degree of ionization of the functional groups of the adsorbent. The functional groups such as hydroxyl and carboxyl groups in alginate structure are affected by the pH of solutions, and under various pH values, electrostatic attraction, ionic properties, and structure of adsorbent and dye molecules could play very important roles on removal efficiency.

Although the effect of pH on adsorption of dye has been studied extensively, no consistent results have been provided (Lata et al., 2007; Mahmoodi, 2013; Navarro et al., 2013; Salisu et al., 2015). Two reasons for the discrepancies observed in the results are the different methods for preparation of magnetic beads and different operating conditions of the adsorption process. For instance, the variety of the initial dye concentration in solution and dye properties can be influenced by the initial pH of the dye solution. According to the results reported by Lata et al. (2007), Mahmoodi (2013), and Navarro et al. (2013), by increasing the pH of the solution, the adsorption capacity increases; however, according to the results of Salisu et al. (2015), there is an optimal value of pH for maximum removal efficiency.

Effect of pH on adsorption of MB onto the magnetic alginate beads is shown in Figure 2. It can be found that the pH variation had a slight increasing influence on the adsorption process. Lata et al. (2007), Mahmoodi (2013), and Navarro et al. (2013) reported a same trend for pH effect on adsorption of dye.

Figure 2.

Effect of pH on the adsorption of MB onto magnetic alginate beads (C₀ = 20 mgl⁻¹, dose of Fe₃O₄ in beads = 1 Gy, time = 60 min, temperature = 293.15 K).

MB has a permanent positive charge. At low pH values, the adsorbent is positive charged which result the adsorption of MB is decreased. By increasing the pH value, the surface of the adsorbent becomes anionic and useful for more adsorption of MB on the magnetic alginate beads.

Orthogonal array and analysis of S/N ratio

The orthogonal array of L₁₆ was applied and the replication number of the conducted experiments and S/N values are shown in Table 2. The mean value of dye removal for the orthogonal factors and their levels are presented in Table 3. Figure 3 shows the effects of factors level on the mean value of dye removal.

Table 2.

Orthogonal array of factors at four different levels.

						%Dye Removal
	Initial dye concentration	Dose of Fe₃O₄	Adsorption time	Magnetic field	1st run	2nd run	Average	S/N Ratio
1	1	1	1	1	16.78	16.4	16.59	24.4
2	1	2	2	2	41.81	40.7	41.225	32.31
3	1	3	3	3	78.77	77.2	77.985	37.84
4	1	4	4	4	86.14	87.63	86.884	38.78
5	2	1	2	3	29.45	29.1	29.275	29.33
6	2	2	1	4	35	33.69	34.345	30.71
7	2	3	4	1	63.57	64.19	63.88	36.11
8	2	4	3	2	60.27	61.21	60.739	35.67
9	3	1	3	4	39.38	38.1	38.739	31.76
10	3	2	4	3	66.92	68.33	67.625	36.6
11	3	3	1	2	28.2	28.64	28.42	29.07
12	3	4	2	1	41.52	40.33	40.925	32.24
13	4	1	4	2	34.86	33.74	34.3	30.7
14	4	2	3	1	43.49	42.35	42.92	32.65
15	4	3	2	4	42.15	41.54	41.845	32.43
16	4	4	1	3	24.63	25.32	24.974	27.95

Table 3.

The mean values of dye removal for the levels of the factors.

Factors	Level 1	Level 2	Level 3	Level 4	Δ
Initial dye concentration	55.678	47.059	43.927	36.01	19.668
Dose of Fe₃O₄ in beads	29.726	46.536	53.032	53.381	23.655
Adsorption time	26.082	38.325	55.096	63.172	37.09
INTENSITY of magnetic field	41.078	41.178	49.965	50.453	9.375

Figure 3.

Effects of factors level on mean of dye removal.

ANOVA

ANOVA is used to determine the relative importance of various factors on the experiment response (dye removal percentage). ANOVA results are shown in Table 4. In ANOVA analysis, the values of freedom degree (DOF), sum of squares, variance, F-ratio (F), pure sum, and percent of contribution (P, %) for each factors in response are obtained. It can be observed that the adsorption time has the most contribution (55.358%) among the factors in dye removal and the error percent in the response is very low (1.859%).

Table 4.

Analysis of variance (ANOVA) for the mean of dye removal data.

Factors	DOF (f)	Sum of Sqrs (S)	Variance (V)	F-ratio (F)	Pure sum	Percent P (%)
Initial dye concentration	3	1587.672	529.224	73.654	1566.116	13.054
Dose of Fe₃O₄ in beads	3	2948.987	982.995	136.807	2927.431	24.402
Adsorption time	3	6662.487	2220.829	309.082	6640.931	55.358
Intensity of magnetic field	3	660.66	220.22	30.649	639.105	5.327
Other/error	19	136.518	7.185			1.859
Total	31	11,996.326				100.00%

Optimum conditions for dye removal

The optimum conditions for MB removal can be determined using data reported in Figure 3 and Table 3. According to Figure 3, the value of mean dye removal decreases by increasing the initial dye concentration, and it increases by increasing the dose of Fe₃O₄ in beads and adsorption time. The dye removal increases with Fe₃O₄ dosage due to the increasing of adsorbent surface and the availability of more adsorption sites.

The value of mean dye removal also increases by increasing the intensity of magnetic field. According to Brito et al. (2012), aromatic compounds such as MB have magnetic properties, when the molecules are placed near the magnetic field. The Fe₃O₄ molecules also have magnetic characteristics, therefore the magnetic field is acting on them, and they are good candidates to study the effect of applying magnetic field on the adsorption performance.

By increasing the magnetic intensity, the surface tension and viscosity of the magnetized solution decrease which correspondingly enhances the mass transfer performance. The magnetic field can also cause a weakening of hydrogen bonds of solvent (Brito et al., 2012).

According to the results, initial dye concentration of 20 mg l⁻¹, adsorption time of 60 min, magnetic field intensity of 440 G, and Fe₃O₄ dosage of 1 Gy are the optimum conditions for dye removal.

Prediction of performance and confidence interval (CI)

After determination of the optimum conditions, the mean of dye removal at the optimum conditions (μ_opt) can be predicted. The dye removal under the optimal conditions can be obtained from the following equation (Suresh et al., 2011)

μ_{opt} = \bar{T} + \sum_{i = 1}^{n} (μ_{i} - \bar{T})

(4) where

\bar{T}

is the overall mean of dye removal, μ_i is the individual dye removal at the optimal conditions, and n is the number of factors. According to the data reported in Tables 2 and 3

μ_{opt} = 85.68

It is usual to represent μ_opt within a CI. The expression for computing the CI is (Roy, 2000)

{CI}_{pop} = \sqrt{\frac{F_{α} (1, f_{e}) \times V_{e}}{n_{eff}}}

(5) where F_α(1, f_e) represents the F-ratio at a confidence level of (1 − α) against degree of freedom (DOF = 1) and f_e is DOF of error (from ANOVA), V_e is the error variance (from ANOVA), and n_eff is defined as (Srivastava et al., 2007)

n_{eff} = \frac{N}{1 + [total DOFassociated in theestimate ofthe mean]}

(6) where N is number of results (N = 16*2).

According to ANOVA, f_e = 31–12 = 19, and V_e = 7.185. From tabulate F, the F-value at the 95% confidence level is equal to 4.3808, thus the CI is calculated to be ±3.576.

Confirmation experiments

The confirmation experiments are conducted to verifying the experimental design results based on Taguchi method. The experiments of dye removal under the optimal condition were carried out and it was found that the mean of dye removal is 86.88%. The value of mean dye removal obtained from confirmation experiments within the CI at optimum condition is 85.68 ± 3.576.

Adsorption isotherms

In this study, equilibrium in dye adsorption was modeled by some important isotherms such as Langmuir, Freundlich, Dubinin–Radushkevich, and Temkin. Isotherm experiments were performed at initial dye concentrations of 20–300 mg l⁻¹, pH = 11, Fe₃O₄ dosage = 1 Gy, adsorption time = 90 min, and temperature of 293.15 K. The correlation coefficient (R²) values describe the feasibility of using the isotherm models which is calculated from fitting of equilibrium adsorption data by these models.

Langmuir isotherm

The Langmuir model assumes that a monolayer adsorption of adsorbate is formed on a homogeneous adsorbent surface. The Langmuir model can be expressed as the following linear form (Hashemian et al., 2013)

\frac{C_{e}}{q_{e}} = \frac{C_{e}}{q_{m}} + \frac{1}{k_{L} . q_{m}}

(7) where, q_m (mg g⁻¹) is the maximum capacity of adsorbent and K_L (l mg⁻¹) is the Langmuir constant. Figure 4 shows the values of C_e/q_e versus C_e. The values of q_m and K_L can be obtained from the slope and intercept of the linear plot of C_e/q_e versus C_e.

Figure 4.

Langmuir isotherm for adsorption of MB at T = 293.15 K, C₀ = 20–300 mgl⁻¹, pH = 11, dose of Fe₃O₄ in beads = 1 Gy, and t = 90 min.

Freundlich isotherm

The Freundlich isotherm model is an empirical equation based on multilayer adsorption on a heterogeneous surface of adsorbent. The Freundlich model can be expressed as the following linear form (Sen et al., 2011)

{Lnq}_{e} = \ln K_{f} + \frac{1}{n} \ln C_{e}

(8) where K_f (mg g⁻¹) Freundlich constant indicates adsorption capacity and 1/n Freundlich constant indicates adsorption intensity. As shown in Figure 5, values of K_f and 1/n can be obtained from the slope and intercept of the linear plot of Lnq_e against lnC_e.

Figure 5.

Freundlich isotherm for adsorption of MB at T = 293.15 K, C₀ = 20–300 mgl⁻¹, pH = 11, dose of Fe₃O₄ in beads = 1 Gy, and t = 90 min.

Temkin isotherm

The Temkin model can be expressed as (Osasona et al., 2013)

q_{e} = \frac{RT}{b_{T}} Ln (K_{T} C_{e})

(9)

This can be linearized as

q_{e} = {BLnC}_{e} + {BLnK}_{T}

(10) where B=RT/b_T, K_T (l mol⁻¹) is the Temkin isotherm constant, R is the universal gas constant (8.314 J mol⁻¹K⁻¹), T is the absolute temperature (K), and b_T (J mol⁻¹) is a constant that is related to heat of adsorption. The positive and negative value of b_T indicate that the adsorption process is exothermic and endothermic, respectively. As shown in Figure 6, the values of B and K_T can be obtained from the slope and intercept of the linear plot of q_e versus LnC_e.

Figure 6.

Temkin isotherm for adsorption of MB at T = 293.15 K, C₀ = 20–300 mgl⁻¹, pH = 11, dose of Fe₃O₄ in beads = 1 Gy, and t = 90 min.

Dubinin–Radushkevich isotherm

The linear form of Dubinin–Radushkevich isotherm can be expressed as follows (Osasona et al., 2013)

{Lnq}_{e} = {Lnq}_{D} - β ɛ 2

(11) where q_D is the adsorption capacity of the adsorbent (mg g⁻¹), β is a constant related to the adsorption energy (mol² kJ⁻²), R is the universal gas constant (8.314 J mol⁻¹K⁻¹), T is the absolute temperature (K), and ɛ is the Polanyi potential = RT Ln(1+1/C_e). Ln q_e versus ɛ² is shown in Figure 7. The value of β and q_D can be obtained from the slope and intercept of the linear plot of Lnq_e versus ɛ².

Figure 7.

Dubinin–Radushkevich isotherm for adsorption of MB at T = 293.15 K, C₀ = 20–300 mgl⁻¹, pH = 11, dose of Fe₃O₄ in beads = 1 Gy, and t = 90 min.

According to Table 5, the Langmuir model shows the lower R² values and Freundlich model presented the higher R² values. Therefore, Freundlich model is the most appropriated for the adsorption of the MB onto magnetic alginate beads. Therefore, there is an exponential variation in site energies of the adsorbent, and surface adsorption is not the rate limiting step.

Table 5.

Isotherm parameters for the removal of MB at T = 293.15K, C₀ = 20–300 mg l⁻¹, pH = 11, dose of Fe₃O₄ in beads=1 Gy, and t = 90 min.

Model	Isotherm Constant
Langmuir
	q_m(mg g⁻¹)	K_L(L mg⁻¹)		R²
	106.38	0.00517		0.743
Freundlich
	K_F	n		R²
	0.69	1.1435		0.9819
Temkin
	B	K_T(L mol⁻¹)	b_T(J mol⁻¹)	R²
	11.81	0.168	206.37	0.939
Dubinin-Radushkevich
	q_D(mg g⁻¹)	β(mol² kJ⁻²)		R²
	15.12	11.546		0.751

The maximum capacity of adsorbent obtained from Langmuir isotherm equation at 293.15 K was found to be 106.38 mg g⁻¹. The value of b_T (constant of Temkin isotherm) is 206.37 (J mol⁻¹) which indicates the adsorption process is exothermic. The “n” value in the Freundlich model shows the degree of nonlinearity between MB concentration and adsorption as follows: if n = 1, then adsorption is linear; if n < 1 then adsorption is a chemical process; if n > 1, then adsorption is a physical process, and the values of n within the range of 1–10 represent good adsorption. In this work the constant value in Freundlich equation was found to be 1.1435 (1 < n < 10); it indicates the physical adsorption of MB onto magnetic alginate beads and shows the magnetic alginate beads have a high affinity for MB molecules.

Adsorption kinetics

It is necessary to determine the equilibrium adsorption time for the MB adsorption. The pseudo-first-order, pseudo-second-order, and intraparticle diffusion models were used to evaluate the kinetic parameters for the adsorption process. Kinetic experiments were performed at initial dye concentrations 20, 50, 100 mg l⁻¹; pH 11; magnetic alginate beads with 1 Gy dose of Fe₃O₄; and temperature of 293.15 K.

The pseudo-first-order model

The pseudo-first-order equation is expressed as follows (Han et al., 2011)

\frac{{dq}_{t}}{dt} = K_{1} (q_{e} - q_{t})

(12)

When integrating equation (12) by initial conditions q_t = 0 at t = 0, the linear form of the pseudo-first-order equation is obtained

Ln (q_{e} - q_{t}) = {Lnq}_{e} - K_{1} t

(13) where q_e and q_t are the capacity of adsorbent at equilibrium and at time t (mg g⁻¹), and k₁ is the pseudo-first-order rate constant (min⁻¹). The values of Ln(q_e-q_t) against time are shown in Figure 8 and q_e and K₁ were obtained from the slope and intercept of the plot of Ln(q_e-q_t) against time.

Figure 8.

Pseudo-first-order kinetic of MB adsorption onto magnetic alginate beads for an initial dye concentrations 20, 50, 100 mg l⁻¹, pH 11, dose of Fe₃O₄ in beads=1 Gy at 293.15 K.

The pseudo-second-order model

The pseudo-second-order model is represented as follows (Qiu et al., 2009)

\frac{{dq}_{t}}{dt} = K_{2} (q_{e} - q_{t}) 2

(14)

When integrating equation (14) by initial conditions q_t = 0 at t = 0, the linear form of the pseudo-second-order equation is obtained

\frac{t}{q_{t}} = (\frac{1}{K_{2} q_{e}^{2}}) + \frac{t}{q_{e}}

(15) where K₂ is the pseudo-second-order adsorption rate constant (g mg⁻¹min⁻¹). As shown in Figure 9, the values of q_e and K₂ can be obtained from the slope and intercept of the plot of t/q_t against time.

Figure 9.

Pseudo-second-order kinetic of MB adsorption onto magnetic alginate beads for an initial dye concentrations 20, 50, 100 mg l⁻¹, pH 11, dose of Fe₃O₄ in beads=1 Gy at 293.15 K.

The intraparticle diffusion model

The intraparticle diffusion model explains the diffusion mechanism of adsorption process. The model can be described as (Qiu et al., 2009)

q_{t} = K_{t} t 1 / 2 + C

(16) where K_t is the intraparticle diffusion rate constant (mg g⁻¹min^−1/2) and C is the intercept and as shown in Figure 10, K_t and C can be obtained from the slope and intercept of the plot of q_t against t^1/2.

Figure 10.

The intraparticle diffusion model kinetic of MB adsorption onto magnetic alginate bead for an initial dye concentrations 20, 50, 100 mg l⁻¹, pH 11, dose of Fe₃O₄ in beads=1 Gy at 293.15 K.

All kinetic parameters were calculated from the fits of experimental data with the pseudo-first-order, pseudo-second-order, and intraparticle diffusion models presented in Table 6. By comparing the correlation coefficients (R²) of models in Table 6, it can be seen that the pseudo-first-order model fits the experimental results with higher R² values (0.982–0.9962) than pseudo-second order model (R² from 0.8708 to 0.9985) and intraparticle diffusion model (R² from 0.8871 to 0.9144). The values of adsorption capacity (q_e) calculated from pseudo-first-order model are also close to the values observed experimentally (q_e,Exp) from the pseudo-second-order model. The higher R² values and the accurate estimations of q_e indicate that the adsorption kinetics is represented better by pseudo-first-order model. Similar observation of fitting kinetics data with pseudo-first-order model has been reported by Hameed et al. (2008).

Table 6.

Kinetics parameters for the adsorption of MB onto magnetic alginate bead for an initial dye concentrations 20, 50, 100 mg l⁻¹, pH 11, dose of Fe₃O₄ in beads=1 Gy at 293.15K.

		The pseudo-first-order model			The pseudo-second-order model
Initial dye concentration (mgL⁻¹)	q_e,Exp	q_e,Cal	K₁	R²	q_e,Cal	K₂	R²
20	2.9	2.909	0.0597	0.9871	3.32	0.0248	0.9985
50	7.17	7.279	0.0473	0.9962	9.597	4.04×10⁻³	0.9794
100	15.02	15.6	0.039	0.982	25.707	7.51×10⁻⁴	0.8708
	The intraparticle diffusion model
Initial dye concentration (mgL⁻¹)	K_t	C	R²
20	0.2695	0.6658	0.8871
50	0.8347	0.2262	0.9074
100	1.9639	−1.3851	0.9144

Conclusion

Removal of methylene blue from synthetic wastewater using Fe₃O₄ nanoparticles encapsulated with alginate beads is carried out in a fixed-bed adsorption unit equipped with external magnetic field. The Taguchi method was applied for optimization of operating conditions in adsorption of MB onto magnetic alginate beads. The effects of initial dye concentration, dose of Fe₃O₄ in beads, adsorption time, and intensity of magnetic field on the MB adsorption were investigated. The results showed that by increasing the Fe₃O₄ concentration, adsorption time, and magnetic field intensity, the adsorption rate increases, while the value of dye removal decreases by increasing the initial dye concentration. Effect of pH on the adsorption of MB also was studied and the results showed that by increasing the pH value from 3 to 11, the adsorption of MB increases to 12%. ANOVA was carried out and it can be found that the adsorption time was the most effective factor by higher contribution percent (55.358%) in MB adsorption. The optimum conditions were achieved as 20 mg l⁻¹ dye concentration, 1 Gy dose of Fe₃O₄ in beads, 60 min of adsorption time, and 440 G of magnetic field intensity.

In the second part of the paper, the isotherm experiments were performed under the optimum operating conditions. Equilibrium data fitted very well with Freundlich isotherm model. Kinetic of adsorption obeyed with pseudo-first-order model for entire adsorption period.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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