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Abstract

Diffusional mass transfer models with and without external resistance were applied to represent the adsorption of Acid Red 357 (AR357) and Acid Black 210 (AB210) by tannery solid wastes. The mass transfer parameters, such as, external mass transfer coefficient (k_f), surface diffusion coefficient (D_s), and Biot number (B_i) were estimated and interpreted. It was found that the two models agreed with the experimental data and, very similar values of the parameters were obtained. This indicated that the external mass transfer mechanism can be neglected. Then, the model without external resistance, which is simpler, can be used. The D_s values ranged from 5.01 × 10⁻¹³ to 1.30 × 10⁻¹² m² s⁻¹ for AR357 and from 3.19 × 10⁻¹⁴ to 5.38 × 10⁻¹⁴ m² s⁻¹ for AB210. The high values of the B_i number confirmed that the adsorption of AR357 and AB210 on tannery solid wastes was controlled by surface diffusion.

Keywords

Adsorption decay curves external resistance mass transfer parameters parameters estimation

Introduction

Colored effluents are a direct result of the dyes production, and also, consequence of its use in textile and related industries (Noroozi and Sorial, 2013). It is estimated that about 6–12 L of colored effluents are generated per kilogram of wet blue leather, during the wet finishing process (Piccin et al., 2012). The inadequate release of these colored effluents in aqueous ecosystems is esthetically unpleasant and leads to a reduction of sunlight penetration, which in turn, decreases the photosynthetic activity, dissolved oxygen concentration, and water quality. Furthermore, had acute toxic effects on aquatic flora and fauna, causing severe environmental problems worldwide (Saratale et al., 2011). This scenario shows the importance of the treatment of dye containing effluents prior to their final discharge into the environment.

Several technologies for dyes removal from effluents are presented in the literature (Gupta and Suhas, 2009; Mezohegyi et al., 2013; Saratale et al., 2011; Srinivasan and Viraraghavan, 2010). Among all of these, adsorption has been preferred due to its cheapness and high-quality of the treated effluents, especially for well-designed processes (Dotto et al., 2014; Filipkowska and Rodziewicz, 2012; Jin et al., 2012; Samarghandi et al., 2014). The main adsorbent used for dye removal is activated carbon, but, the use of cheap and eco-friendly materials have been studied as alternative (Ali, 2012; Ali et al., 2012). Recently, tannery solid wastes (TSWs) were successfully employed for dyes adsorption, providing some advantages, for example, the reuse of treated water in leather industry and an extended survival of such waste before reaching its final destination (Piccin et al., 2012, 2013). Moreover, the reduction in color, applying TSW to treat colored tannery wastewater, is able to reduce significantly the presence of organic and inorganic pollutants in wastewater, as well as, toxicity. Also, TSW can be applied to equipments already existing in this type of industrial plant (Gomes et al., 2016; Piccin et al., 2016). However, more detailed studies about the mass transfer mechanism of dyes adsorption onto TSWs are still necessary.

In solid–liquid adsorption systems, the mass transfer mechanism occurs by external mass transfer, intraparticle diffusion (pore volume diffusion, surface diffusion, or a combination of both mechanisms) and adsorption on the active sites (Ruthven, 1984; Suzuki, 1990). The diffusional mass transfer models are constructed on the basis in the above mentioned steps (Dotto et al., 2014; Ocampo-Pérez et al., 2010, 2011, 2012). In this way, these models can be used as realistic physico-mathematical tolls to elucidate the dyes adsorption onto TSWs. It should be highlighted that, interpretations about the mass transfer mechanism of dyes adsorption onto TSWs, based on diffusional models, were not performed yet. This information is fundamental for scale up and design purposes.

This work aimed to develop diffusional mass transfer models with and without external resistance to represent the adsorption of AR357 and AB210 by TSWs. The models were based on the mass transfer principles and used to represent the adsorption decay curves under different temperatures (288, 298, and 308 K). The values of k_f, D_s, and B_i were accurately estimated and its dependence with the temperature was studied. The rate limiting step of the process was elucidated.

Materials and methods

Obtainment of the TSW

TSWs were obtained from chromium-tanned leather shaving operation in a local tannery (Portão-RS, Brazil). These residues were dried under vacuum conditions (−500 mmHg) at 60℃ for 48 h (Piccin et al., 2012). TSW were cut in rectangular shape (3.31 mm × 3.31 mm) with thickness of 0.50 mm.

Characterization techniques

TSW were characterized according to the moisture content (ASTM D3790-79) solid density (ρ_s) (picnometry), void fraction (ε_p), surface area, and pore size distribution (S_BET) (BET method) (Quantachrome Instruments, New Win 2, USA) (Dotto and Pinto, 2012). Scanning electron microscopy (SEM) (Jeol, JSM–6060, Japan) was used to observe the TSW surface. The main elements on the TSW surface were identified by energy dispersive X-ray spectroscopy (Jeol, JSM 5800, Japan). The main groups on the TSW surface were identified by Fourier transform infrared spectroscopy (FTIR) analysis (PerkinElmer, Spectrum 1000, USA) (Piccin et al., 2012).

Dyes

Acid Red 357 (AR357) (azo-dissulphonated Cr organic-complex dye, molecular weight 956.7 g mol⁻¹, CAS 57674-14-3, λ_max = 494 nm) and Acid Black 210 (AB210) (amine dissulphonated triazo organic dye, molecular weight 965.9 g mol⁻¹, CAS 99576-15-5, λ_max = 459 nm) were supplied by the Business Leather Unit of Lanxess Company, with purity higher than 95%. The optimized three-dimensional structural formula of the dyes was obtained from MarvinSketch software, version 14.9.22.0, and is presented in Figure 1. Distilled water was used to prepare all solutions. All reagents were of analytical-grade.

Figure 1.

Optimized three-dimensional structural formula of the dyes: (a) AR357 and (b) AB210.

Adsorption experiments

The adsorption assays were carried out in batch conditions at different temperatures (288, 298, and 308 K) using a thermostated shaker (Nova Ética, 218 MBD, Brazil). Two hundred fifty milligrams of TSW (dry basis) were added to 10 mL of citric acid/sodium diphosphate buffer (0.1 mol L⁻¹) at pH 2.5. After 10 min, 50 mL of dye aqueous solution (with desired concentrations) were added and the system was stirred at 150 r/min under controlled temperature. Aliquots were withdrawn in preset time intervals and the dye remaining concentration was determined by spectrophotometry (Varian, Cary 100, USA) at the maximum wavelength for each dye. The maximum wavelength used to quantify the dyes was obtained by a spectrophotometric scanning in the visible region. For Acid Red 357, λ_max was 494 nm and for Acid Black 210, λ_max was 459 nm. All adsorption experiments were performed in duplicate (n = 2) and blanks were performed. The experimental conditions were based on preliminary tests and literature (Piccin et al., 2012, 2013). The mass of dye adsorbed per gram of TSW at any time (q(t), mg g⁻¹), and the mass of dye adsorbed at equilibrium (q_e, mg g⁻¹) were calculated by the equations (1) and (2), respectively

q (t) = \frac{(C 0 - C (t))}{m} V

(1)

q e = \frac{(C 0 - C e)}{m} V

(2)

where, C₀ is the initial dye concentration in the liquid phase (mg L⁻¹), C(t) is the bulk dye concentration along the time (mg L⁻¹), C_e is the equilibrium dye concentration in the liquid phase, V is the volume of solution (L), and m is the TSW amount (g).

Model development

Some assumptions were made to develop the model: (1) an unidirectional transference was assumed, since the thickness of TSW is very lower than the other dimensions (Table 1); (2) the adsorption process is isothermal; (3) the intraparticle diffusion occurs due surface diffusion; (4) the D_S values are constant for each experiment.

Table 1.

Main characteristics of TSW adsorbent.

Characteristic	Value
Length (mm)	3.31
Width (mm)	3.31
Thickness (mm)	0.50
Moisture content (% wet basis)^a	7.8 ± 0.8
Solid density (kg m⁻³)^a	1450 ± 37
Void fraction (%)^a	15 ± 2
Surface area (m² g⁻¹)^a	1.3325 ± 0.0480
Main elements on the surface	C, N, O, Cr

Mean ± standard error for n = 3.

At first, the mass transfer model with external resistance was developed according to the mass balances in the liquid phase, describing the variation of dye concentration along the time (equation (3)), and in the solid phase, describing the variation of dye concentration along the time and in the solid position (equation (4)) (Ruthven, 1984; Suzuki, 1990). The initial and boundary conditions are presented in the equations (5), (6), and (7)

\frac{dC (t)}{dt} = - \frac{V S}{L V L} k f (C (t) - C S)

(3)

\frac{\partial q (z, t)}{\partial t} = D S \frac{\partial 2 q (z, t)}{\partial z 2}

(4)

t = 0, - L \leq z \leq L \Rightarrow q (z, t) = 0

(5)

\frac{\partial q (z, t)}{\partial z} | z = 0 = 0

(6)

ρ S D S \frac{\partial q (z, t)}{\partial z} | z = L = k f (C (t) - C S)

(7)

being, C_S the liquid phase concentration at solid–liquid interface (mg L⁻¹), q the dye concentration in the solid phase (mg g⁻¹), L the half of the adsorbent thickness (m), V_S and V_L the solid and liquid volumes (m³), k_f the external mass transfer coefficient (m s⁻¹), D_S the surface diffusion coefficient (m² s⁻¹), ρ_S the solid density (g m⁻³), t the time (s), and z corresponds to the solid position (m).

The equations are connected through the external mass transfer from the bulk liquid phase to the solid surface. The liquid concentration at surface C_S was considered to be in equilibrium with the adsorbed phase concentration at solid surface. The equilibrium relations are defined according to the Langmuir isotherm (equation (8)) for Acid Red 357 and BET model (equation (9)) for Acid Black 210. The values of q_m, k_L, q_BET, k₁, and k₂ for different temperatures can be found in Piccin et al. (2012).

q (t, L) = \frac{q m k L C S}{1 + k L C S}

(8)

q (t, L) = \frac{q BET k 1 C S}{(1 - k 2 C S) (1 - k 2 C S + k 1 C S)}

(9)

After, the above model (equations (1) and (3) to (7)) was simplified considering the external mass transfer very fast (model without external resistance). In this case, k_f is very high and C_S is equal to C(t). Then, the equation (7) is reduced to equation (13). Equations (4), (5), and (6) that describe the solid volume are not changed and are rewritten in equations (10), (11), and (12)

\frac{\partial q (z, t)}{\partial t} = D S \frac{\partial 2 q (z, t)}{\partial z 2}

(10)

t = 0, - L \leq z \leq L \Rightarrow q (z, t) = 0

(11)

\frac{\partial q (z, t)}{\partial z} | z = 0 = 0

(12)

C (t) = C S

(13)

The partial differential equations were discretized with respect to z coordinate through finite difference method and, the resulting system of ordinary differential equations was solved using is an integrator based on an adaptive explicit Runge–Kutta of fourth and fifth orders, by a Dormand–Prince pair (Dormand and Prince, 1980).

In order to allow the models evaluation at different temperatures simultaneously, D_S was considered a function of the temperature (T), according to the equation (14) (Schwaab and Pinto, 2007)

D S = D S, Tref \exp [B (\frac{T - T ref}{T})]

(14)

In equation (14), D_S,Tref (m² s⁻¹) is the surface diffusion coefficient at reference temperature T_ref (in this work, T_ref value was equal to 298 K), B is a parameter that describes how surface diffusion coefficient varies with temperature T. The dependence of k_f with T was found to be negligible and a constant value for all temperature was estimated.

The parameters D_S,_Tref, B, and k_f were estimated through minimization of the nonlinear least squares function presented in equation (15)

f (k f, D S, ref, B) = \sum_{i = 1}^{N} (C (t) \exp - C (t)) 2

(15)

The error minimized in equation (15) was the sum of squared residuals, for example, the sum of squared difference between an observed value (experimental value) and the fitted value (model predicted value) provided by a model that is nonlinear. The minimization of equation (15) was performed by the Nelder–Mead simplex algorithm (Lagarias et al., 1998). The computer used for the parameters estimation has an Intel® Core™ i7–3770 with 3.40 GHz processor and 12 GB of RAM memory, running with the Windows 7 64 bits operating system. The software Matlab® was chosen to parameter estimation and model simulation.

Results and discussion

TSW characteristics

The SEM image, N₂ adsorption isotherm, BJH pore size distribution and FTIR spectra of TSW are shown in Figures 2, 3, 4 and 5, respectively. The main characteristics of TSW adsorbent are presented in Table 1. Figure 2 reveals a complex, nonporous, and heterogeneous surface of TSW. Some interlaced fibers can be observed. This interlacement suggests a lower void fraction and surface area, as demonstrated by the BET analysis (Table 1 and Figure 3). The values of length, width, and thickness of TSW ensure that the mass transfer can be considered mainly in z direction (Table 1).

Figure 2.

SEM image of TSW adsorbent.

Figure 3.

N₂ adsorption/desorption isotherms of TSW adsorbent.

Figure 4.

BJH pore size distribution of TSW adsorbent.

Figure 5.

FTIR vibrational spectrum of TSW adsorbent.

The N₂ adsorption/desorption isotherm (Figure 3) presented a type II sigmoid curve (Thommes et al., 2015). The BJH pore size distribution data (Figure 4) revealed that TSW has pores ranging from 100 to 1100 Å. The majority of pores are from 200 to 400 Å. These pore dimensions are extremely desirable for dyes adsorption, since these compounds have large molecular size (Figure 1). Also, comparing the pore size and dye molecules dimensions, it can be proved the diffusion mechanism. In the FTIR analysis (Figure 5), bands were observed near to 3000 cm⁻¹, representing the symmetric stretching vibration of O−H group, which overlaps the NH vibration. Absorption bands at 1960 cm⁻¹ are from the stretching vibration of C−H. Moreover, characteristic bands of the proteinaceous material structure can be seen at 1627 cm⁻¹ (C=O), 1536 cm⁻¹ (C−N−H), 1233 cm⁻¹ (C−N), and 1078 cm⁻¹ (C−O). On the basis of these structural characteristics, it can be inferred that the large dye molecules are transferred mainly by surface diffusion in the solid phase.

Equilibrium isotherms

In order to find the equilibrium relations according to the Langmuir isotherm (equation (8)) for Acid Red 357 and BET model (equation (9)) for Acid Black 210, equilibrium isotherms were constructed. The experimental isotherms were obtained in the same way of Adsorption experiments section, but, the solutions were stirred until the equilibrium. The equilibrium isotherms at 298 K are presented in Figure 6 (similar isotherms were found in the other temperatures). The isotherm parameters, q_m, k_L, q_BET, k₁, and k₂ for different temperatures were estimated by the fitting of the models ((equations (8) and (9)) with the experimental data and are shown in Table 2. Based on the high values of R² presented in Table 2, it can be seen that the Langmuir (equation (8)) and BET models (equation (9)) were able to explain the equilibrium adsorption of Acid Red 357 and Acid Black 210, respectively.

Figure 6.

Equilibrium isotherms for the adsorption of Acid Red 357 (AR357) and Acid Black 210 (AB210) onto TSW at 298 K. Source: adapted from Piccin et al. (2013).

Table 2.

Adsorption isotherm parameters of tannery dyes adsorption by TSW.

Parameter	288 K	298 K	308 K	ΔG (at 298 K) (kJ mol⁻¹ K⁻¹)	ΔH (kJ mol⁻¹)	ΔS (kJ mol⁻¹ K⁻¹)
Acid Red 357
k_L (L mg⁻¹)	0.218	0.142	0.112	−8.66	−18.6	−0.033
q_m (mg g⁻¹)	218.8	232.0	239.9
R²	0.980	0.975	0.953
Acid Black 210
k₁ (L mg⁻¹)	2.907	0.522	0.042	−10.01	−112.9	−0.35
k₂ (L mg⁻¹) × 10³	2.10	1.70	1.50
q_BET (mg g⁻¹)	43.2	108.8	138.1
R²	0.994	0.998	0.996

Source: adapted from Piccin et al. (2013).

Table 2 shows also the thermodynamic parameters, which were estimated by the Van't Hoff's plot (Piccin et al., 2013). The negative ΔG values indicated that the dyes adsorption onto TSW was a spontaneous and favorable process. The negative ΔH values indicated that the dyes adsorption onto TSW was exothermic in nature. Another fact in Table 2 is that the adsorption capacity for AR357 was higher than the adsorption capacity for AB210. This can be occurred because AR357 is a Cr organic-complex dye and its structure is organized around the Cr, becoming more ordered and easy to adsorb. On the contrary, the AB210 molecule is long and its adsorption is hindered by the steric hindrance.

Model validation and parameters estimation

The mass transfer models with and without external resistance were used to represent the experimental data of the adsorption decay curves of Acid Red 357 and Acid Black 210 at different temperatures. During the models resolution and parameters estimation of Acid Black 210, it was observed that the experimental data at 288 K present a strange behavior, since adsorption rate was higher than the values observed at 298 K. For this reason, adsorption data of Acid Black 210 at 288 K were not considered. Figures 7 and 8 show the experimental and modeled data for the adsorption of Acid Red 357 and Acid Black 210 on TSW. It was found that the experimental data presented a typical behavior, with C(t) starting from C₀ and tending to C_e. The models agreed very well with the experimental data. It was also verified that the modeled curves were overlapped. This shows that, in this case, the external mass transfer is very fast and this mechanism can be neglected. As consequence, the model without external resistance, which is simpler, can be used.

Figure 7.

Model fit for the adsorption decay curves of Acid Red 357 at different temperatures.

Figure 8.

Model fit for the adsorption decay curves of Acid Black 210 at different temperatures.

The estimated parameters with intervals of 95% of confidence for batch adsorption of both dyes are presented in Table 3. Several simulations were performed and compared to each set of experimental data to verify its goodness. The Student's t-test was performed to verify if the means of the process variables predicted by the model were correspondent to the experimental means; likewise, the Fisher's exact test was performed to verify if variances of the process variables were also correspondent to experimental variances.

Table 3.

Estimated parameters with intervals of 95% of confidence for the adsorption of both dyes.

Parameter	Acid Red 357	Acid Black 210	Description
k_f (m s⁻¹)	4.06 × 10⁻⁴ ± 2.53 × 10⁻⁴	2.01 × 10⁻⁴ ± 1.61 × 10⁻⁵	External mass transfer coefficient
D_s,ref (m² s⁻¹)	8.45 × 10⁻¹³ ± 8.74 × 10⁻¹⁴	3.18 × 10⁻¹⁴ ± 2.35 × 10⁻¹⁵	Surface diffusion coefficient at reference temperature (298 K)
B	14.09 ± 0.39	16.24 ± 2.32	Parameter that describes how surface diffusion coefficient varies with temperature

Table 4 presents the Student's t-test results, where

\bar{C} (t)

is the mean value of the experimental data for the liquid bulk concentration, C(t). It can be seen that intervals of experimental and model data, for all process variables, intercept each other, meaning that the means of the experimental data for each process variable for all experiments are equivalent to those found through the model simulated data. In addition, intervals are very alike, leading to the conclusion that the experimental and model data are very similar.

Table 4.

Student's t-test for C(t).

	Acid Red 357	Acid Black 210
Experimental	202.89 < $\bar{C} (t)$ < 270.17	409.89 < $\bar{C} (t)$ < 422.27
Model	142.24 < $\bar{C} (t)$ < 197.59	392.48 < $\bar{C} (t)$ < 403.82

Note: $\bar{C} (t)$ is the mean of C(t).

Fisher's exact test was performed to verify if the model variances are also similar to experimental data variances. Table 5 presents the test results, where all variances ratios are contained into the intervals, meaning that model variances are also equivalent to experimental variances.

Table 5.

Fisher's exact test for C(t).

Acid Red 357	Acid Black 210
0.48 < 1.49 < 2.13	0.48 < 1.84 < 2.13

Note: Lower limit < $σ \exp 2 / σ 2$ < upper limit.

In general lines, it can be affirmed that both models (with and without external resistance) were suitable to represent the experimental data. However, the external mass transfer mechanism can be negligible, and then, the model without external resistance, which is simpler, is sufficient to represent the experimental data. From the statistical viewpoint, the parameters D_S,Tref, B, and k_f were significant (95% of confidence) and consistent, allowing the correct physical interpretation of the mass transfer phenomena that occurs in the adsorption of Acid Red 357 and Acid Black 210 on TSW.

Interpretation of the mass transfer parameters

The mass transfer parameters for the adsorption of Acid Red 357 and Acid Black 210 on TSW at different temperatures are presented in Table 6. The Ds values ranged from 5.01 × 10⁻¹³ to 1.30 × 10⁻¹² m² s⁻¹ for AR357 and from 3.19 × 10⁻¹⁴ to 5.38 × 10⁻¹⁴ m² s⁻¹ for AB210. These values are in accordance with the values reported in the literature for surface diffusion coefficient (Dotto et al., 2014; Ocampo-Pérez et al., 2010, 2011, 2012; Ruthven, 1984). It can be noted in Table 6, that the D_s values for Acid Red 357 were higher than the Ds values for Acid Black 210. This probably occurred because the dyes dimensions (Figure 1). The Acid Black 210 has molecular size higher than Acid Red 357, hindering its transference within the adsorbent and leading to lower values of Ds.

Table 6.

Mass transfer parameters for the adsorption of Acid Red 357 and Acid Black 210 on TSW at different temperatures.

Dye	T (K)	k_f (m s⁻¹)	D_S (m² s⁻¹)	Biot
Acid Red 357	288	2.4 × 10⁻⁴	5.01 × 10⁻¹³	320.1
	298	4.2 × 10⁻⁴	8.80 × 10⁻¹³	304.7
	308	4.1 × 10⁻⁴	1.30 × 10⁻¹²	232.8
Acid Black 210	298	2.2 × 10⁻⁴	3.19 × 10⁻¹⁴	5364.8
Acid Black 210	308	2.1 × 10⁻⁴	5.38 × 10⁻¹⁴	2923.1

Table 6 shows that for both dyes, the surface diffusion coefficient increase with the temperature. The mass flux due surface diffusion occurs when one adsorbed molecule is desorbed from an active site and then, is diffused in the solid surface to another adsorption site (Medved and Cerný, 2011). So, the dependence of Ds against T can be explained as follows: At lower temperatures, the adsorbed dye molecules had lower internal energy, so, desorption and diffusion to another site is hindered. When the temperature was increased, the adsorbed dye molecules had higher internal energy. Then, the dye molecules required less energy to be desorbed from a site and diffused to another site. Similar trend was found by Ocampo-Pérez et al. (2010) in the adsorption of pyridine onto granular activated carbon. They found that the surface diffusion coefficient increased from 4.6 × 10⁻¹² to 6.9 × 10⁻¹² m² s⁻¹, when the temperature increased from 288 to 308 K.

The surface diffusion modified B_i was calculated by the equation (16) in order to verify the predominance of surface diffusion in relation to the external mass transfer (Weber and Di Giano, 1995)

B i = \frac{k f L C 0}{2 ρ s D s q 0}

(16)

It is accepted that, for B_i < 0.5, it exists a complete dominance of the external mass transfer, while for B_i > 10 a considerable dominance of the surface diffusion exists (Costa and Rodrigues, 1985). The B_i values obtained in this work are presented in Table 6. It was found that the B_i values were higher than 200, confirming that the surface diffusion is the rate limiting step in the adsorption of Acid Red 357 and Acid Black 210 on TSW. This statement is in accordance with the model assumptions and TSW characteristics.

Comparison with other adsorbents

The maximum adsorption capacities obtained in this work were 239.9 and 138.1 mg g⁻¹, for Acid Red 357 and Acid Black 210, respectively. For these specific dyes, consistent comparisons were not found. However, for dyes, in general, the adsorption capacities using waste materials as adsorbents can be from 0.75 to around 1500 mg g⁻¹, depending of the experimental condition (Anastopoulos and Kyzas, 2014; Salleh et al., 2011; Yagub et al., 2014). In this way, it can be concluded that TSW has adequate adsorption capacity for the studied dyes.

Conclusion

In this work, mass transfer models were used to represent the adsorption data of Acid Red 357 and Acid Black 210 dyes onto TSWs. Experiments were performed at three different temperatures. Diffusional models with and without external resistance were employed to fit the experimental data. The results showed that external mass transfer resistance is negligible. In this way, the model without external resistance, which is simpler, can be used. The estimated values for surface diffusion coefficient ranged from 5.01 × 10⁻¹³ to 1.30 × 10⁻¹² m² s⁻¹ for AR357 and from 3.19 × 10⁻¹⁴ to 5.38 × 10⁻¹⁴ m² s⁻¹ for AB210. These values are in accordance with literature and were dependent of the dye and temperature. The B_i numbers were higher than 200, indicating that the internal mass transfer due surface diffusion was the rate limiting step in the adsorption of Acid Red 357 and Acid Black 210 onto TSW.

Footnotes

Acknowledgements

The authors thank to Chemaxon for furnishing an Academic Research license for the software MarvinSketch Version 14.9.22.0 () that was used for obtaining the dyes properties.

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) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by Coordination for the Improvement of Higher Education Personnel (CAPES) and National Council for Scientific and Technological Development (CNPq).

Appendix

References

Ali

(2012) New generation adsorbents for water treatment. Chemical Reviews 112: 5073–5091.

Ali

Asim

Khan

(2012) Low cost adsorbents for the removal of organic pollutants from wastewater. Journal of Environmental Management 113: 170–183.

Anastopoulos

Kyzas

(2014) Agricultural peels for dye adsorption: A review of recent literature. Journal of Molecular Liquids 200: 381–389.

Costa

Rodrigues

(1985) Intraparticle diffusion of phenol in macroreticular adsorbents: Modeling and experimental study of batch and CSTR adsorbers. Chemical Engineering Science 40: 983–993.

Dormand

Prince

(1980) A family of embedded Runge–Kutta formulae. Journal of Computational and Applied Mathematics 6: 19–26.

Dotto

Buriol

Pinto

LAA

(2014) Diffusional mass transfer model for the adsorption of food dyes on chitosan films. Chemical Engineering Research and Design 92: 2324–2332.

Dotto

Pinto

LAA

(2012) Analysis of mass transfer kinetics in the biosorption of synthetic dyes onto Spirulina platensis nanoparticles. Biochemical Engineering Journal 68: 85–90.

Filipkowska

Rodziewicz

(2012) Analysis of the sorption efficiency of acid, basic and direct dyes using chitosan, fly ashes immobilized onto chitosan and modified sawdust immobilized onto chitosan as sorbents. Adsorption Science & Technology 30: 461–472.

Gomes

Piccin

Gutterres

(2016) Optimizing adsorption parameters in tannery-dye-containing effluent treatment with leather shaving waste. Process Safety and Environmental Protection 99: 98–106.

10.

Gupta

Suhas

(2009) Application of low–cost adsorbents for dye removal: A review. Journal of Environmental Management 90: 2313–2342.

11.

Jin

Zhu

Xing

(2012) Adsorptive removal of cationic dyes from aqueous solutions using graphite oxide. Adsorption Science & Technology 30: 437–448.

12.

Lagarias

Reeds

Wright

(1998) Convergence properties of the Nelder–Mead Simplex Method in low dimensions. SIAM Journal of Optimization 9: 112–147.

13.

Medved

Cerný

(2011) Surface diffusion in porous media: A critical review. Microporous and Mesoporous Materials 142: 405–422.

14.

Mezohegyi

Van der Zee

Font

(2013) Towards advanced aqueous dye removal processes: A short review on the versatile role of activated carbon. Journal of Environmental Management 102: 148–164.

15.

Noroozi

Sorial

(2013) Applicable models for multi component adsorption of dyes: A review. Journal of Environmental Sciences 25: 419–429.

16.

Ocampo-Pérez

Leyva-Ramos

Alonso-Davila

(2010) Modeling adsorption rate of pyridine onto granular activated carbon. Chemical Engineering Journal 165: 133–141.

17.

Ocampo-Pérez

Leyva-Ramos

Mendoza-Barron

(2011) Adsorption rate of phenol from aqueous solution onto organobentonite: Surface diffusion and kinetic models. Journal of Colloid and Interface Science 364: 195–204.

18.

Ocampo-Pérez

Rivera-Utrilla

Gómez-Pacheco

(2012) Kinetic study of tetracycline adsorption on sludge-derived adsorbents in aqueous phase. Chemical Engineering Journal 213: 88–96.

19.

Piccin

Feris

Cooper

(2013) Dye adsorption by leather waste: Mechanism diffusion, nature studies, and thermodynamic data. Journal of Chemical and Engineering Data 58: 873–882.

20.

Piccin

Gomes

Feris

(2012) Kinetics and isotherms of leather dye adsorption by tannery solid waste. Chemical Engineering Journal 183: 30–38.

21.

Piccin

Gomes

Mella

(2016) Color removal from real leather dyeing effluent using tannery waste as an adsorbent. Journal of Environmental Chemical Engineering 4: 1061–1067.

22.

Ruthven

(1984) Principles of Adsorption and Adsorption Processes, New York: John Wiley & Sons.

23.

Salleh

MAM

Mahmoud

Karim

WAWA

(2011) Cationic and anionic dye adsorption by agricultural solid wastes: A comprehensive review. Desalination 280: 1–13.

24.

Samarghandi

Hadi

McKay

(2014) Breakthrough curve analysis for fixed-bed adsorption of azo dyes using novel pine cone-derived active carbon. Adsorption Science & Technology 32: 791–806.

25.

Saratale

Chang

(2011) Bacterial decolorization and degradation of azo dyes: A review. Journal of the Taiwan Institute of Chemical Engineers 42: 138–157.

26.

Schwaab

Pinto

(2007) Optimum reference temperature for reparameterization of the Arrhenius equation. Part 1: Problems involving one kinetic constant. Chemical Engineering Science 62: 2750–2764.

27.

Srinivasan

Viraraghavan

(2010) Decolorization of dye wastewaters by biosorbents: A review. Journal of Environmental Management 91: 1915–1929.

28.

Suzuki

(1990) Adsorption Engineering, Tokyo: Kodansha.

29.

Thommes

Kaneko

Neimark

(2015) Physisorption of gases, with special reference to the evaluation of surface area and pore size distribution (IUPAC Technical Report). Pure Applied Chemistry 87: 1051–1069.

30.

Weber

Jr Di Giano

(1995) Process Dynamics in Environmental Systems, New York: John Wiley & Sons.

31.

Yagub

Sen

Afroze

(2014) Dye and its removal from aqueous solution by adsorption: A review. Advances in Colloid and Interface Science 209: 172–184.

Mass transfer models for the adsorption of Acid Red 357 and Acid Black 210 by tannery solid wastes

Abstract

Keywords

Introduction

Materials and methods

Obtainment of the TSW

Characterization techniques

Dyes

Adsorption experiments

Model development

Results and discussion

TSW characteristics

Equilibrium isotherms

Model validation and parameters estimation

Interpretation of the mass transfer parameters

Comparison with other adsorbents

Conclusion

Footnotes

Acknowledgements

Declaration of Conflicting Interests

Funding

Appendix

References