Introduction

Dyes are classified as non-ionic (disperse), anionic (direct, acid, and reactive), and cationic (basic) compounds (Kuppusamy et al. 2016). Chemically, the anionic dyes consist of anthraquinone acid, triphenylmethane, xetonimina, azin, xanthenes, and nitro compounds. These dyes are used in the fiber industries like wool, silk, nylon, and acrylic-modified fibers (Silva et al. 2012). Currently, there are more than 100,000 types of dyes commercially available in the textile industry (Abbas and Trari 2015; Boudechiche et al. 2016). About 130 t of dyes is ejected daily into the aquatic environment without any control, and the cost to remove dyes remains high (Kuppusamy et al. 2016). In this respect, many methods are employed to reach the regulatory standards for treating wastewaters such as biological treatment (Aytar et al. 2013; Mozia et al. 2016), coagulation and flocculation (Verma et al. 2012), precipitation (Šimek et al. 2016), solvent extraction (El-Ashtoukhy and Fouad 2015), adsorption onto activated carbon (Noorimotlagh et al. 2014), membrane filtration (Mozia et al. 2016), electrochemical treatment (Mook et al. 2017), sonochemical degradation (Ferkous et al. 2015), photocatalysis using nanoparticles and nanocomposites (Yola et al. 2014a; Gupta et al. 2015), and advanced oxidation process (AOP) (Aytar et al. 2013; Mozia et al. 2016). However, these techniques have some disadvantages like the high energy and product consumption, incomplete removal, and generation of toxic sludge and other waste products, which require further treatments (de Luna et al. 2013). Among the physicochemical methods, biosorption using natural materials remains attractive, because of its efficiency, low cost, simplicity (Yola et al. 2014b; Gupta et al. 2016), elimination of various pollutants, abundance in nature, and biodegradability (Silva et al. 2012; Oladipo et al. 2014). Many biosorbents and waste materials have been tested for the removal of hazardous dyes and heavy metals in aqueous media such as the leaves of Posidonia oceanica (El Khames et al. 2014), Inula viscosa (Kebir et al. 2015), Citrus limetta peel (Pathak and Mandavgane 2015), rice husk (Li et al. 2016), Luffa cylindrica (Boudechiche et al. 2016; Kesraoui et al. 2016), jujube shell (El Messaoudi et al. 2016), olive stones (Albadarin and Mangwandi 2015), and de-oiled karanja seed cake (Varala et al. 2016). Agricultural wastes consist of cellulose, hemicelluloses, and lignin, which make them effective biosorbents due to their different functional groups. In this context, the new genus Crataegus, belonging to the Rosaceae family, is one of the most important genera. Crataegus species are available in many countries especially in North Africa (Khiari et al. 2014). The Crataegus azarolus (CA) wild fruits are known as pome, which are local and abundant in Algeria. They are used as a medicinal herb in the pharmaceutical and food industries; the seeds and their boney endocarps are termed stones which can degrade in 5–10 years. So, the objective of this study concerns the valorization of C. azarolus stones (CAS) as a new biosorbent for water depollution. To our knowledge, there are no published reports on CAS for dye removal and CAS can be attractive to replace high-cost biosorbents.

The response surface methodology (RSM) is a combination of statistical and mathematical methods used to develop, improve, and optimize the processes and to evaluate the relative significance of various process parameters in the presence of complex interactions (Jain et al. 2011). RSM was used in chemistry, physics, biology, and water treatment. Dye biosorption using RSM permits us to fit the mathematical models to the experimental data using a minimal number of experiments to get the optimal parameters; this was undertaken with the goal of realizing the water treatment in less time and at low cost (Jain et al. 2011; Gorgulu and Celik 2013; Akar et al. 2014; Asfaram et al. 2016; Salehi et al. 2016; Varala et al. 2016). RSM is a powerful tool for the prediction of engineering processes and is applied in many common designs such as Box–Behnken, Doehelrt, and central composite rotatable designs (CCRD). The CCRD method includes factorial points from a full factorial (2k), axial points (2k), and center points (cp). The number of experiments is estimated by N = 2k + 2k + cp), where k is the factor number and cp is the replicate number of central points (Jain et al. 2011; Ahmadi et al. 2012). Central composite design (CCD) is a RSM design which proposes a series of experiments with the least number of tests (Mazaheri et al. 2015). However, in some cases, the first-order and quadratic models developed by RSM do not fit well the experimental data (Afshar et al. 2015). Despite the fact that the cubic regression functions (X i 3) have rarely been applied to the experimental data, when the responding variable is sensitive to changes of variables, the interaction between the parameters is deemed to be of vital importance; a third-order model provides a broader understanding of the process’ nature (Bazrafshan et al. 2015). Podstawczyk et al. (2015) studied the effect of operating parameters for Cu2+ removal in the concentration range 20–200 mg L−1, biosorbent dose 1–10 g L−1, and pH 2–5 which were modeled by the comparison of three designs: CCD, Box–Behnken design (BBD), and full factorial design (FFD). The second-order polynomial equation extended with additional cubic effects was used as an objective function. The authors showed that CCD turned out to be the best design among the experiments for modeling the effect of the process conditions in terms of correlation coefficient (R 2 = 0.99) and ANOVA (Fisher value of 276 with p value lower than 0). The obtained model was further used to get the optimal conditions, which maximize the biosorption yield expressed by the metal removal.

The main goals of the present work include the following steps: (i) preparation and characterization (MEB/EDS, FTIR, and pHPZC) of C. azarolus stones (CAS) as a novel biosorbent for DB86 anionic dye removal, used in Algeria for dyeing in the textile and clothing industries; (ii) application of CCRD based on a cubic polynomial module for the optimization of the operating parameters that affect the DB86 removal such as the solution pH, biosorbent dose, initial DB86 concentration, and temperature; and (iii) evaluation of appropriate biosorption isotherms and kinetic models for describing the DB86 biosorption.

Materials and method

Preparation of C. azarolus powder

Stones of C. azarolus were collected from the region of Mila (east Algeria), repeatedly washed with hot distilled water to eliminate the impurities, and dried at 80 °C for 24 h. Afterward, CAS samples were crushed and ground by a stainless steel grinder to get sizes smaller than 315 μm by standard sieves. The resultant powder was stored in airtight glass bottles for further experiments (Fig. 1).

Fig. 1
figure 1

Images of the Crataegus azarolus. a Fruits. b Stone. c Powder (<315 μm)

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Preparation of aqueous DB86 solution

DB86 was obtained from TEXALG textile unit of Boufarik (Algiers area). The stock solution was prepared by dissolving 1 g of DB86 in 1 L of distilled water. The solutions at different concentrations (20–100 mg L−1) were prepared by dilution. DB86 is anionic in nature, and its maximum absorption wavelength (λ max) is 620 nm; other characteristics are reported in Table 1.

Table 1 Molecular properties of direct blue 86
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Determination of zero-charge pH

The zero-charge pH (pHPZC) of CAS was determined by the technique described elsewhere (Boudechiche et al. 2016). Fifty milliliters of KNO3 solutions (×10−2 M) was transferred into 100-mL beakers. The initial pH (pHinitial) of the solutions was adjusted in regions 2–12 by addition of NaOH or HCl. Then, 0.5 g of CAS was added to the beakers, which was magnetically stirred for 48 h to reach the equilibrium, and the pHfinal was measured. The difference (pHinitial − pHfinal) was plotted against pHinitial. The intersection point of the resulting curve with the abscissa axis, for which ΔpH = 0, gives pHPZC = 5.06 (Fig. 2).

Fig. 2
figure 2

The determination of the pHPZC

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Scanning electron microscopy–energy-dispersive X-ray spectroscopy

The surface morphology of CAS was analyzed by scanning electron microscopy (SEM), JEOL-JSM 6360, combined with the energy-dispersive X-ray spectroscopy (EDS) to determine the chemical composition.

FTIR analysis

The FTIR spectroscopy was used to detect the surface functional groups of the biosorbent. The spectrum was recorded in the range 4000–650 cm−1 using a Fourier transform infrared spectrometer (Thermo Scientific™ OMNIC™ series software).

Central composite rotatable design and batch experimental program

CCRD is well-suited for fitting the polynomial surface and works well for the process optimization; it was used for the experimental design to obtain the optimal biosorption conditions (Sun et al. 2014). To evaluate the influence of the variables on the response functions and to establish the optimal conditions of dye removal, we have used CCRD for the experiment design. In this study, 31 runs for the four-parameter experimental design were required to calculate the response function and to assess the design performance through the analysis of the experiment data. Moreover, the optimization process includes the evaluation of coefficients, thus predicting and verifying the response of the adjusted model. Therefore, four process variables, namely, pH of the solution (X 1), biosorbent dose (X 2), initial DB86 concentration (X 3), and temperature (X 4), were chosen, each at five levels (−α, −1, 0, +1, +α) (Table 2). CCRD for the four parameters consists of 16 factorial points, 6 axial points, and 7 replicates at the center point, with a total number of 31 experiments designed by JMP 11.0.0 (SAS Institute) software (Demim et al. 2013). The coded values (X i ) of the process variables were obtained from Eq. (1) (Kousha et al. 2015):

$$ {X}_i=\frac{X_{i\ \mathrm{real}}-{X}_{0\ \mathrm{real}}}{\Delta X} $$
(1)
Table 2 Experimental factors and their ranges and standard deviations
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where X i is the dimensionless coded value of the independent variable i, X i real is the real value, X 0 real is the value of X i at the center point, and ΔX is the step change value. The empirical third-order polynomial model defines the behavior of the system using RSM, a cubic polynomial equation (Soo et al. 2004; Xie et al. 2011). Equation (2) was developed for the response prediction as a function of the main factors and their interactions. CCRD consists of a group of empirical techniques for establishing the relationship between a cluster of independent variables and the measured responses for the optimization of independent variables:

$$ \begin{array}{l} Y\ \left(\%\right)={a}_0+\sum_{i=1}^4{a}_i{X}_i+\sum_{i=1}^4{a}_{i i}{{X_i}_i}^2+\sum_{i=1}^4{a}_{i i i}{{X_{i i}}_i}^3+\sum_{i=1}^3\sum_{j= i+1}^4{a}_{i j}{X}_i{X}_j+\sum_{i=1}^2\sum_{j= i+1}^3\sum_{k= j+1}^4{a}_{i j k}{X}_i{X}_j{X}_k\\ {}+\sum_{i=1}^1\sum_{j= i+1}^2\sum_{k= j+1}^3\sum_{l= k+1}^4{a}_{i j k l}{X}_i{X}_j{X}_k{X}_l\end{array} $$
(2)

where Y is the predicted response (% removal), a 0 is a constant, a i is the linear term coefficients, a ii is the quadratic term coefficients, a iii is the cubic term coefficients, and a ij , a ijk , and a ijkl are the cross-product term coefficients. X i , X j , X k , and X l represent the independent variables in the form of coded values. The coded and real values of the independent variables are listed in Tables 2 and 3. Using the developed model, the predicted responses are compared with the observed values.

Table 3 Central composite rotatable design matrix with experimental and predicted values
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The residual DB86 concentrations were analyzed using UV/Vis spectrophotometer (Optizen 2120UV). The kinetic and equilibrium studies were investigated by using the optimum biosorption conditions. The amount of biosorbed DB86 q t (mg g−1) and DB86 removal (%) were calculated from Eqs. (3) and (4):

$$ {q}_t=\frac{\left({C}_0-{C}_t\right)}{m} V $$
(3)
$$ \%\mathrm{Removal}=\frac{\left({C}_0-{C}_t\right)}{C_0}100 $$
(4)

where C 0 is the initial DB86 concentration (mg L−1), C t is the DB86 concentration at time t (mg L−1), m is the biosorbent mass (g), and V is the volume of the solution (L).

Results and discussion

Characterization of the biosorbent

FTIR analysis of the biosorbent

The FTIR spectrum of CAS is plotted in the range 4000–650 cm−1 to get information on the functional groups on the biosorbent surface. The spectrum (Fig. 3) shows a strong peak at 3350 cm−1 assigned to the O–H stretching vibration of OH groups involved in hydrogen bonds. The bands centered at 2929 and 2855 cm−1 are assigned to C–H bond of alkyl groups. The peaks at 1733, 1644, and 1234 cm−1 are attributed to the stretching of C=O and COO− functions (Vijayaraghavan et al. 2008) while the large band at 1644 cm−1 is due to OH bending vibrations. The peak at 1504 cm−1 is attributed to amine salt (N–H) while the one at 1460 cm−1 corresponds to vibrations of –CH3 bending (Gorgulu and Celik 2013). The band absorption at 1421 cm−1 corresponds to C–O stretching. The band at 1372 cm−1 is related to the vibration of the –CH2 bending (Gorgulu and Celik 2013) while that at 1320 cm−1 is assigned to C–O groups on the CAS surface. The band at 1154 cm−1 corresponds to antisymmetric bridge C–OR–C stretching (Wang and Shen 2012). The absorption peak at 1033 cm−1 is due to the stretching vibrations of CO, whereas the band at 896 cm−1 is assigned to antisymmetric out-of-ring stretching (Boudechiche et al. 2016). Consequently, the FTIR result indicates that CAS present functional groups that are potential adsorbing and exchanging sites for the interaction with DB86 during biosorption.

Fig. 3
figure 3

FTIR spectrum of CAS

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SEM/EDS analysis

The SEM morphology of CAS is given in Fig. 4a–d at different magnifications. The surface of CAS exhibits a smooth and non-porous texture; we also note the presence of cavities which are more or less homogeneous with different geometries (Fig. 4c). The EDS spectrum and the content of each element are given in Fig. 4e. A qualitative chemical composition of CAS was obtained by microanalysis (SEM/EDS); it mainly consists of carbon (69.74%) and oxygen (27.66%), suggesting the existence of the groups C–O, C=O, C–O–C, and O–H and indicating that the predominant functions are of aromatic cycles and alcoholic types: cellulose, lignin, and hemicellulose. Trace elements like Ca, Mg, and P exist between 0.24 and 1.59%.

Fig. 4
figure 4

SEM micrographs of CAS (a–d) and EDS spectrum (e)

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Experimental design

Main interaction effects and Student’s t test

The results were analyzed using the JMP release 11.0.0 software, provided by SAS Institute, and the main effects and interactions between the factors were determined. The effect of any factor is defined as the response change produced by a variation of the factor level (Soo et al. 2004). The regression coefficients, associated standard errors, Student’s t values, and their effects are shown in Tables 3 and 4. By substituting the coefficients in Eq. (2) by their values taken from Tables 3 and 4, one obtains

$$ \begin{array}{l} Y\ \left(\%\right)=15.72-7.374\ {X}_1+7.032\ {X}_2-4.856\ {X}_3+4.499\ {X}_4+5.336\ {X_1}^2 - 0.926\ {X_2}^{2\ }\\ {}+0.958\ {X_3}^2 + 0.509\ {X_4}^2 - 1.309{X_1}^3-0.69\;{X_2}^3-0.519\ {X_3}^3-0.646\ {X_4}^3-2.516\ {X}_1{X}_2\\ {}+1.695\ {X}_1{X}_3+1.361\ {X}_1{X}_4-1.629\ {X}_2{X}_3+1.987\;{X}_2{X}_4-1.673\ {X}_3{X}_4+0.385\ {X}_1{X}_2{X}_{3\;}\\ {}+0.607\ {X}_1{X}_2{X}_4-1.137\ {X}_1{X}_3{X}_4-1.103\ {X}_2{X}_3{X}_4-1.104\ {X}_1{X}_2{X}_{3\;}{X}_4\end{array} $$
(5)
Table 4 Statistical analysis of coefficients from the cubic model
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This equation includes all terms regardless of their significances. The coefficient sign (±) defines the direction of the relationship between the related effect and its response. The positive sign indicates that as the value of one effect changes, the response changes in the same direction, while for the negative sign, the response operates in the opposite direction. The absolute coefficients measure the strength of the relationship (Demim et al. 2013). Table 4 summarizes the regression coefficients accompanied with their standard errors, Student’s t values, and corresponding p values. The p and Student’s t values permit us to know the significance of the model coefficients; the larger the Student’s t value, the lower the p value, and one can obtain a very significant coefficient (Liu and Chiou 2005). The extremely significant effects are X 1 2 (pH2: quadratic effect) followed by X 1 (pH: main factor) and X 3 (initial DB86 concentration) because |Student’s t value| < critical Student’s t value with probability p < 0.01% (Wu et al. 2010; Kogkaki et al. 2016). The second effects highly significant (|Student’s t value| < critical Student’s t value with p < 1%) (Wu et al. 2010; Kogkaki et al. 2016) are X 2 (biosorbent dose), X 4 (temperature), interaction X 1 X 3 (pH–initial DB86 concentration), X 1 3 (pH3: cubic effect), and interactions X 3*X 4, X 1*X 2, X 2*X 4, and X 2*X 3. The significant third effects (|Student’s t value| < critical Student’s t value with p < 5%) (Kogkaki et al. 2016) are X 1*X 4, X 2 2 (quadratic effect), X 3 2 (quadratic effect), X 3 3 (cubic effect), X 4 3 (cubic effect), X 1*X 2*X 4, X 2*X 3*X 4, and X 1*X 2*X 3*X 4. Based on the Student’s t test and p value (|Student’s t value| > critical Student’s t value with p value >5%) (Campos et al. 2014), some effects were discarded, because they do not exhibit any statistical significance such as X 2 3 (cubic effect), X 4 2 (quadratic effect), X 1*X 3*X 4, and X 1*X 2*X 3. Equation (4) is used to visualize the effects of experimental parameters of DB86 removal (Fig. 5). The actual values are determined from the experiments while the predicted ones are obtained from Eq. (5). Both actual and predicted dye removals shown in Fig. 5, the R 2 values (=0.996), and the R 2 adj (=0.9827) indicate a good adjustment between the experimental and predicted responses. The result also suggests that the selected cubic model is adequate for predicting the response variables for the studied parameters.

Fig. 5
figure 5

Actual and predicted values for DB86 removal

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Analysis of variance

The mathematical cubic models are often unsuitable to describe the experimental data, and a more reliable model is required to evaluate the quality of the fitting using ANOVA and to compare the variation sources with the Fisher distribution (Fisher test). This statistical test is based on the ratio of two sums of squares (the error and regression sums of squares). Therefore, the significance of regressions is evaluated by the ratio between the mean square of regression and the mean square of residuals (difference between observed and predicted values) (Almeida et al. 2011).

The ANOVA results for the cubic equation (Table 5) show that the Fisher values for all regressions are higher. A large Fisher value indicates that the cubic model can explain the variation in the DB86 removal. The associated p value is used to estimate whether the Fisher value is large enough to indicate statistical significance. p values lower than 5% (i.e., α = 0.05: error or 95%: confidence) indicate a significant model (Tripathi et al. 2009). The calculated Fisher value 74.86 (which is higher than critical Fisher23,7 = 3.42) with very low probability values (p value of the model <0.0001) demonstrates that the regression models are significant at 95% of confidence interval for the DB86 removal.

Table 5 ANOVA for response surface cubic model
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Optimization of independent parameters

RSM combined with CCRD is used to optimize the factors and to describe the nature of the response surface in the experiment using three-dimensional (3D) response surface plots. This combination is helpful for understanding the main factors, and their interactions can provide a simple examination on the effects of independent variables on the removal percentage (Sivarajasekar and Baskar 2014). Therefore, the 3D response surface plots for the measured removal percentage are based on the cubic polynomial model (Eq. 4). Figure 6a–f presents the 3D response surface plots as a function of two simultaneous parameters, maintaining the other parameters at a fixed central level (X = 0). As observed, these plots display reasonable interactions between each of the independent factors and the DB86 removal percentage. Figure 6a gives the response surface plots of pH and biosorbent dose. The DB86 removal increases drastically from 3 to 77% with decreasing pH from 6 to 2 and increasing the biosorbent dose from 0.8 to 4 g L−1. This can be explained by the fact that in an acidic medium, DB86 is dissociated to polar groups (R–SO3 −). Moreover, low pH is favorable for the biosorption of anionic DB86 on CAS because the biosorbent is acidic and increases the H+ concentration on its surface. In addition, the CAS amount is very significant (biosorbent dose = 4 g L−1), which induces electrostatic interactions between its surface and R–SO3 − from the solution (Cheng et al. 2015). At a low pH (< pHPZC = 5.06), the exchange sites on the biosorbent are positive, thus favoring the biosorption of anions (R–SO3 −) (Cheng et al. 2015). According to Mahmoodi et al. (2011) who have used direct red 23 and acid green 25 as anionic dyes at pH 2, strong Coulomb attractions exist between the positively charged surfaces of the biosorbent (due to the ionization of functional groups of biosorbent) and the negatively charged anionic dyes. Aksu and Isoglu (2006) studied the pH’s effect on the removal of Gemazol turquoise blue G, as an anionic reactive dye, on sugar beet pulp; they noticed that the adsorption peaks at pH 2 with an adsorption capacity of 83.7 mg g−1 and decreases with further pH increase to reach zero at pH 6. Figure 6b presents the response surface plots in the pH range 2–6 and initial DB86 concentration from 20 to 100 mg L−1; the biosorbent dose and temperature are maintained at a fixed central level, 2.4 g L−1 and 30 °C, respectively. The results showed that DB86 removal percentage remarkably increases with decreasing pH to reach 87% at pH 2 at low initial DB86 concentration (=20 mg L−1). This phenomenon can be attributed to the acidic medium favorable for the biosorption, at low DB86 concentration and high biosorbent dose (2.4 g L−1). However, for higher DB86 concentrations, the removal percentage decreases because of the saturation of CAS sites on the surface (Sivarajasekar and Baskar 2014; Abbasi and Habibi 2016). The surface plot (Fig. 6c) indicates the evolution of DB86 removal by varying the pH simultaneously from 2 to 6 and the temperature from 10 to 50 °C, maintaining the other factors at their fixed central levels (initial DB86 concentration = 60 mg L−1 and biosorbent dose = 2.4 g L−1). From this response surface plot, we note a maximum DB86 removal of 66% at pH 2 and 10 °C; similar results were reported elsewhere (Arunachalam and Annadurai 2011). Figure 6d illustrates the surface plot of the variation of DB86 removal for the biosorbent dose (0.8–4 g L−1) and initial DB86 concentration (20 to 100 mg L−1) with appropriate values of other parameters at center levels (pH 4 and temperature 30 °C). From this response surface plot, a maximum DB86 removal of 45% was obtained for an initial DB86 concentration of 20 mg L−1 and a biosorbent dose of 4 g L−1. The low removal is attributed to pH (=4) which plays a crucial role in the biosorption. Similar results were reported by Cheng et al. (2015) who have studied the congo red and direct red 80 adsorptions onto activated carbon–surfactant from aqueous solutions by using the RSM–Box–Behneken design where the optimal values are 20 mg L−1 and 50 °C. It can be concluded that these results indicate the optimum conditions for DB86 removal on CAS (theoretical maximum removal) using CCRD by a cubic model (minimum level of X 1, X 3, X 4 = −α, and maximum level of X 2 = +α). Theoretical DB86 removal of 123% was found under optimum conditions: pH 2, biosorbent dose of 4 g L−1, initial DB86 concentration of 20 mg L−1, and temperature of 10 °C (Fig. 6e, f). The experience was performed from these optimized parameters, and the result shows that DB86 removal was 100%.

Fig. 6
figure 6

Response surface plots (3D) of DB86 removal versus the effects (pH of solution, biosorbent dose, initial DB86 concentration, and temperature)

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Biosorption isotherm

The Langmuir, Freundlich, and Temkin models have been applied to determine the nature of DB86 biosorption isotherms on CAS. The Langmuir model based on a biosorption monolayer on the biosorbent surface, with no interaction between adsorbed molecules (Hosseini et al. 2011), is expressed by

$$ {q}_e=\frac{q_{\max }{K}_{\mathrm{L}}{C}_e}{\left(1+{K}_{\mathrm{L}}{C}_e\right)} $$
(6)

The linearized form is represented by

$$ \frac{C_e}{q_e}=\frac{1}{q_{\max }{K}_L}+\frac{C_e}{q_{\max }} $$
(7)

where q max and K L are, respectively, the maximum biosoption capacity to form a complete monolayer on the surface (mg g−1) and the Langmuir constant related to the biosorption energy (L mg−1).

The empirical Freundlich model describes the biosorption on heterogeneous surface through a multilayer biosorption mechanism (Hosseini et al. 2011):

$$ {q}_e={K}_{\mathrm{F}}\;{C_e}^{\frac{1}{n}} $$
(8)

The linearized form is expressed by Eq. (9)

$$ \ln {q}_e= \ln {K}_{\mathrm{F}}+\frac{1}{n} \ln {C}_e $$
(9)

where K F [(mg g−1) (L mg−1)1/n] is the Freundlich constant and 1/n is the heterogeneity factor, related to the capacity and biosorption intensity.

The Temkin isotherm contains a parameter, which does not neglect the adsorbate–biosorbent interactions and supposes that (i) the biosorption heat of DB86 molecules in the layer decreases linearly with increasing the coverage and (ii) the biosorption is characterized by a homogeneous distribution of binding energies (Ghaedi et al. 2014).

$$ {q}_e=\left(\frac{RT}{b_{\mathrm{T}}}\right) \ln \left({A}_{\mathrm{T}}{C}_e\right) $$
(10)

The linear form of Eq. (10) gives

$$ {q}_e=\frac{RT}{b_{\mathrm{T}}} \ln \left({A}_{\mathrm{T}}\right)+\frac{RT}{b_{\mathrm{T}}} \ln \left({C}_e\right) $$
(11)

where b T (J mol−1) is the Temkin constant related to the biosorption heat of DB86 and A T (L mg−1) the equilibrium binding constant.

The equilibrium data were obtained at different concentrations (20–100 mg L−1) during 180 min of fixed contact time at constant pH (=2), a biosorbent dosage of 2 g L−1, and a temperature of 20 °C. The parameters of all isotherm models are gathered in Table 6. Accordingly, the R 2 value for the Langmuir model (close to 1) is greater than that of Freundlich and Temkin models (Table 6 and Fig. 7a–c) and this indicates that the homogeneous biosorption sites are occupied by one layer of DB86 molecules (Noorimotlagh et al. 2014) with a maximum biosorption capacity (q max) of 24.02 mg g−1 (Table 6 and Fig. 7a). The graphical analysis (Fig. 7d) confirms the best fit of the experimental data by the Langmuir model. Sayğılı and Güzel (2016) explored the adsorption isotherm of yellow anionic acid on a low-cost activated carbon using ZnCl2 for chemical activation. The equilibrium data are well-fitted by the Langmuir model (R 2 = 0.997) compared to the Freundlich one. El Nemr et al. (2009) confirmed the successful application of the Langmuir model to the experimental data for DB86 adsorption on activated carbon prepared from orange peel. The Langmuir isotherm fits suitably the experimental data with the q max value close to those obtained with other adsorbents using anionic dyes. It is clear that CAS used in this work have an acceptable maximum biosorption capacity of the Langmuir model compared to other adsorbents reported in the literature (Table 7).

Table 6 Constants of isotherm models for the biosorption of DB86
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Fig. 7
figure 7

The biosorption isotherm plots: a Langmuir, b Freundlich, c Temkin, and d graphical analyses

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Table 7 Comparison of the q max of various adsorbents used for anionic dye removal from aqueous solutions
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Biosorption kinetics

The kinetic study of DB86 biosorption on CAS was undertaken for different initial DB86 concentrations; it provides information for biosorption modeling and predicts the biosorption rate. For this purpose, the pseudo-first-order, pseudo-second-order, and intraparticle diffusion models were used.

The Lagergren first-order model is given by

$$ \log \left({q}_{\mathrm{e}}-{q}_t\right)= \log {q}_{\mathrm{e}}-\frac{k_1 t}{2.303} $$
(12)

where q t and q e are the biosorption capacities, respectively, at time t and at equilibrium (mg g−1) and k 1 (min−1) is the biosorption rate constant.

The pseudo-second order model is expressed by

$$ {\frac{t}{q}}_t=\frac{1}{k_2{q_{\mathrm{e}}}^2}+\frac{1}{q_{\mathrm{e}}} t $$
(13)

where k 2 (g mg−1 min−1) is the pseudo-second-order rate constant. The initial biosorption rate h (mg g−1 min−1) is given by (Arunachalam and Annadurai 2011)

$$ h={k}_2{q_{\mathrm{e}}}^2 $$
(14)

Figure 8a, b presents the plots for the pseudo-first-order and pseudo-second-order kinetic models, respectively, and the model constants are gathered in Table 8. The biosorption kinetic of DB86 follows a pseudo-second-order model in the concentration range 20–100 mg L−1 with very high correlation coefficients R 2 > 0.99, and the calculated equilibrium biosorption capacities (q e cal) are much closer to the experimental ones (q e exp). By contrast, the pseudo-first-order model does not give a good agreement with the experimental data (R 2 = 0.504–0.947), and the experimental biosorption capacities are different from the calculated ones (Table 8). Sadaf and Bhatti (2011) reported similar results for the removal of anionic dye Foron turquoise SBLN by using fungal biomass as biosorbent. The pseudo-second-order rate constant (k 2) decreases with increasing the DB86 concentration (Table 8), and this can be attributed to the competitive biosorption of DB86 molecules on available surface area (Albadarin et al. 2011).

Fig. 8
figure 8

The kinetic plots, pseudo-first-order (a) and pseudo-second-order (b) models

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Table 8 Kinetic parameters for the DB86 biosorption
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The Weber–Morris equation is used to describe the intraparticle diffusion. If the plot of q t versus t 1/2 is linear and passes by the origin, then the intraparticle diffusion is the sole rate-limiting step (Albadarin et al. 2011) and the rate constant (k int, mg g−1 min–½) is given by the equation (Abbas and Trari 2015)

$$ {q}_t={k}_{\mathrm{int}}{t}^{1/2}+ C $$
(15)

where C (mg g−1) is the intercept due to the presence of the boundary layer thickness (Albadarin et al. 2011; Boudechiche et al. 2016). A non-zero value for the intercept indicates that a mass transfer limits the diffusion rate across the boundary layer (Albadarin et al. 2011). The plots q t versus t 1/2 (Fig. 9) are multilinear (R 2 = 0.92–0.98), and the straight lines do not pass by the origin (boundary layer effect) (Table 8). This characterizes some degree of boundary layer control, which clearly indicates that the intraparticle diffusion is not the rate-determining step. So, other kinetic models control the biosorption of DB86 on CAS which can operate simultaneously (Albadarin et al. 2011).

Fig. 9
figure 9

The intraparticle diffusion model at various initial DB86 concentrations

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Conclusion

In the present work, RSM combined with CCRD was used to examine the effects of four operating parameters, namely, the initial solution pH (X 1), biosorbent dose (X 2), initial DB86 concentration (X 3), and temperature (X 4), for DB86 removal by a novel biosorbent: C. azarolus. The cubic model was found to be a suitable mathematical model which provides an adequate prediction of DB86 removal (R 2 = 0.996 and R 2 adj = 0.983). According to this model, the Student’s t test results showed that all coefficients are significant except X 2 3, X 4 2, X 1*X 3*X 4, and X 1*X 2*X 3. Additionally, the optimal conditions resulting in the highest DB86 removal of theoretical and experimental values, 123 and 100%, respectively, were obtained for a solution of pH 2, a biosorbent dose of 4 g L−1, an initial DB86 concentration of 20 mg L−1, and a temperature of 10 °C. The equilibrium data of DB86 biosorption onto CAS are well-fitted by the Langmuir model with a maximum monolayer biosorption capacity of 24.02 mg g−1. The kinetic study showed that the pseudo-second-order model describes adequately the DB86 biosorption, and the intraparticle diffusion model is not the rate-limiting step which governs the biosorption mechanism; other kinetic models may control the biosorption rate.