Removal of Metals by Biomass Derived Adsorbent in Its Granular and Powdered Forms: Adsorption Capacity and Kinetics Analysis

: Among the various existing metals, zinc and copper are predominant metals in several efﬂuents from industries such as electroplating, plastics production and mining. Technical methods have been applied in the treatment of efﬂuents containing metals, including chemical removal, adsorption, ion exchange, membrane technologies and electrochemistry. However, it is necessary to develop technologies that minimize costs and increase treatment quality while reducing residual sludge generation. Adsorption using biological materials stands out for removing metals, a low-cost technique and high efﬁciency. Thus, this study evaluated metal adsorption using an adsorbent from granular and powdered anaerobic sludge, followed by a kinetic analysis, aiming at a new alternative for wastewater treatment. Evaluation of the copper and zinc adsorption process using granular and powdered biomass resulted in maximum removals of 72.9% and 62.7% for zinc, respectively, and 92.8% and 85.0% for copper, respectively. Analyzing the kinetic models, the pseudo-second-order model ﬁtted the data better. Applying the kinetics of other studies in the literature for copper and zinc removal by other adsorbents, the pseudo-second-order model was the most representative model. In this context, kinetic modeling allowed the determination of the solute removal rate, estimating the adsorption mechanism.


Introduction
Accelerated growth combined with poor management, especially in waste generation, brings severe environmental and public health challenges. Among the significant environmental impacts is an increase in concentration of metals in the soil and water resulting from human activities such as mining, metallurgy and agricultural production [1]. Metal ions are toxic components. Therefore, they cause environmental damage [2]. In addition, their presence in surface and groundwater has become an environmental concern due to their toxicity and tendency to bioaccumulate, especially when combined with accelerated industrial and economic development [3].
Zinc-containing effluents result from industrial activities such as electroplating, paint, battery, cosmetic, rubber, plastic, pharmaceutical production, and mine wastewater. High concentrations of this metal in the human body can cause disease emergence, skin irritation, and vomiting, among other effects [4]. Another relevant metal is copper, used in industrial activities such as metal finishing, electroplating, plastic production and corrosion. Copper is a toxic and harmful metal even at low concentrations. Therefore, effluents containing this metal must be treated before being discharged into the environment [5]. the solute removal rate, estimating the adsorption mechanism and sizing reactors and effluent treatment systems.
The kinetic models of the adsorption mechanism are classified into reaction models and diffusion models [20]. The reaction models can be pseudo-first-order, pseudo-second-order, or Elovich. However, they may not represent the experimental data, requiring other models, such as the Weber and Morris model (diffusion model). Diffusion models assume that intraparticle diffusion is the rate-limiting step of biosorption, and reaction models assume that the rate-limiting step of biosorption occurs due to chemisorption [21]. Therefore, this study evaluated metal adsorption systems (Cu 2+ and Zn 2+ ) using granular and powdered anaerobic sludge as adsorbent. Kinetic analysis of the adsorption process considered the pseudo-first-order, pseudo-second-order, Elovich, and Weber and Morris model.

Biomass Derived Adsorbent and Adsorbate Solution
The BDA was a biological sludge from an anaerobic sludge blanket reactor used to treat effluents from poultry slaughterhouses (Aviculture Dacar, Tietê-SP, Brazil). Thermal and physical treatments were applied to modify the cell surface, inactivate the sludge, and increase its adsorption performance. First, the process removed excess water in the sludge using a commercial household sieve. Subsequently, the sludge was dried in an oven for 48 h at 100 • C. Next, the material was transferred to a commercial sieve, where the material retained in the sieve was called granular biomass, and the filtered particles were considered powdery biomass. Finally, the powdered biomass was macerated with a pestle to reduce the particle size. The mass of BDA used in the adsorption process was defined as a function of the determination of total solids (ST) and fixed and volatile total solids (FTS and VTS), according to the Standard Methods for Examination of Water and Wastewater-2540 Solids [22].
The adsorbate solution was prepared from salt and ZnCl 2 for a final zinc concentration of 14.5 mg L −1 ; the pH of the medium did not change, presenting a value of 5.29 ± 0.01. Finally, the 10 mg L −1 copper solution was prepared using CuCl 2 . Again, the pH of the solution did not change, with a value equal to 4.66 ± 0.01. The pH measurement was performed using a digital bench pH meter (Bel Engineering, PHS3BW).

Fourier Transform Infrared Spectroscopy Analysis
FTIR analyses were performed on an Agilent ® model Cary 630 FTIR Spectrometer, in attenuated total reflectance mode with a sweep between 4000 and 500 cm −1 and resolution of 4 cm −1 .

Experimental Procedure
All the materials used in the experimental setup were immersed for 24 h in a solution of HNO 3 10% (v/v) and then washed with distilled water to protect from the removal of residual trace metals. Subsequently, the materials were sterilized in an autoclave at 121 • C for 30 min, as suggested by Mogensen et al. [23]. The tests were performed under conditions of complete asepsis. Antibiotic-type glass vials with a reaction volume of 100 mL were used. The vial was filled with 5 g L −1 of dry BDA (59.5 g SV L −1 ) and subsequently autoclaved. Then, 80 mL of the copper or zinc solution was added to the flask containing the dry BDA. The reactors were closed with a butyl cap and metal seal. All experiments were performed in triplicate. The flasks were stored in a shaker incubator with constant orbital shaking (170 rpm), heating and a controlled temperature (30 • C). The kinetic analyses of adsorption were performed at different times: 0, 2, 4, 24, 48, and 72 h.
For analysis of the metal concentration in the liquid phase, samples were collected at regular intervals at the end of each adsorption period. First, a sterilized set of syringes and needles was used to remove the sample (18 mL), which was transferred to a Falcon tube, where 30 µL of an HNO 3 solution (10%) was added. Then, the samples were frozen for further analysis of the metal concentrations in the solution.

Determination of Metal Concentration
For each sample, the concentrations of Cu 2+ and Zn 2+ were analyzed. First, the copper and zinc adsorption test aliquots were centrifuged at 3500 rpm for 10 min and vacuum filtered for clarification. Then, at 24, 48, and 72 h in the copper samples, a solution of aqua regia (HCl + HNO 3 ) was added, and the samples were placed in a biodigester for 15 min at 150 • C; a longer contact time between the BDA and the copper solution produces a darker color in the samples. Finally, the Cu and Zn concentrations were determined by high-resolution continuous source atomic absorption spectrometry (model 300, Analytik Jena-HR CS-AAS).

Kinetic Modeling
The ability of BDA to remove Zn 2+ and Cu 2+ ions from the adsorption system was determined by the amount of metal adsorbed per mass of BDA over time. Equation (1) describes the adsorption capacity (q t ) at time t: where q t is the adsorbed amount of zinc or copper per mass of BDA (mg g −1 ), V-solution volume (L), C 0 -initial concentration of metal ions in the solution (mg L −1 ), C t -concentration of metal ions in the solution at time t (mg L −1 ), and m-dry mass of the BDA (g).

Pseudo-First-Order Model
Equation (2) expresses the pseudo-first-order model developed by Lagergren. It is used when the rate of adsorption to binding sites is proportional to the number of unoccupied sites in the BDA. Adsorption systems on solid surfaces immersed in a liquid solution containing a solute also follow this model. Its use is suitable for initial biosorption times, up to 20% solute adsorption. However, after this surface charge, there are changes in the solute concentration in the aqueous solution, and the number of active sites available for incorporation of the adsorbate decreases, making the model not very applicable [24].
where k 1 -pseudo-first-order adsorption rate constant (min −1 ), q e and q t -adsorbed quantities per gram of adsorbent biomass at equilibrium and at time t, respectively (mg g −1 ). By integrating Equation (2) and applying the following boundary conditions, q t = 0 and t = 0, Equation (3) is obtained: The pseudo-first-order adsorption rate constant can be obtained from the ln (q e − q t ) versus t graph.

Pseudo-Second-Order Model
Equation (4) describes the pseudo-second-order model. It is used when the occupancy rate of the adsorbent sites is proportional to the square of the number of unoccupied sites [25]: where k 2 -pseudo-second-order adsorption rate constant (g mg −1 min −1 ), and q e and q t -adsorbed quantities per gram of adsorbent biomass at equilibrium and at time t, respectively (mg g −1 ). After integration and linearization, Equation (5) is obtained: The intercept and slope of the t/q t versus t curve give the pseudo-second-order adsorption rate constant and the amount adsorbed per gram of adsorbent biomass at equilibrium. The constant considers that chemisorption is the limiting step of the adsorption process. Therefore, the system depends on the adsorption capacity of the BDA related to the number of active sites available.

Weber and Morris Model
The adsorption rate-limiting mechanism is a step in the diffusion of molecules in the fluid into the pores. Therefore, the Weber and Morris model states that adsorption varies almost proportionally with half of the time power (t 0.5 ), as described by Equation (6).
where q t -amount of adsorbate adsorbed on the solid phase (mg g −1 ) at time t (min), K d -intraparticle diffusion coefficient (mg g −1 min −1 ), and C-constant related to the diffusion resistance (mg g −1 ). The slope of the line and the intersection of the curve qt versus t 0.5 provides the values of k d and C. They can help interpret the process as the thickness of the boundary layer since the value of C is directly proportional to the layer effect limit in the adsorption system. The model describes that during the initial adsorption steps, the linear coefficient is zero, indicating that intrapore diffusion controls the adsorption process. However, for a non-zero linear coefficient, the film diffusion controls adoption, and the thickness of this boundary layer may be related to the linear coefficient value.

Elovich Model
The Elovich kinetic model, according to Equation (8), was initially described for the process of chemical adsorption of a gas on the surface of a solid material. However, this model also describes the adsorption processes of various substances in a liquid medium.
The curve q versus ln(t) provides the parameters α and β. The Elovich equation describes the chemical adsorption mechanism, representing the interaction between the adsorbent and the adsorbate as a chemical reaction (chemisorption) [26]. The Elovich model is accurate, fitting the kinetic data properly throughout almost the entire adsorption period, with errors only at the end of the process due to slow adsorption [27]. Table 1 displays data on metal ion removal during zinc and copper adsorption by powdered and granular inactive anaerobic biomass. The constant adsorbate concentration in the fluid medium or the insignificant amount of adsorbate removed determines the equilibrium of the adsorption process. For zinc adsorption systems, equilibrium occurred within 48 h. For copper, equilibrium was reached for granular biomass in 24 h and powdered biomass in 48 h. Figure 1 displays the amount of adsorbed ions (Zn 2+ and Cu 2+ ) from the aqueous solution by the granular and powdery biomass. adsorbent and the adsorbate as a chemical reaction (chemisorption) [26]. The Elovich model is accurate, fitting the kinetic data properly throughout almost the entire adsorption period, with errors only at the end of the process due to slow adsorption [27]. Table 1 displays data on metal ion removal during zinc and copper adsorption by powdered and granular inactive anaerobic biomass. The constant adsorbate concentration in the fluid medium or the insignificant amount of adsorbate removed determines the equilibrium of the adsorption process. For zinc adsorption systems, equilibrium occurred within 48 h. For copper, equilibrium was reached for granular biomass in 24 h and powdered biomass in 48 h. Figure 1 displays the amount of adsorbed ions (Zn 2+ and Cu 2+ ) from the aqueous solution by the granular and powdery biomass. The adsorption process presents phases associated with the steps of adsorption kinetics. It depends on the initial transport of metal ions from the aqueous solution to the outer surface of the BDA. The ions diffuse to the surface of the pores. Then, they are adsorbed on the active sites within the pores, reaching equilibrium. The quantification of metal ions adsorbed by the granular biomass was superior to that of the powdered BDA, contrary to expectations since the powdered biomass presented a greater external surface area. For zinc removal, granular biomass reached a final removal of 72.9% and powder-58.3%. For copper, the removal for granular biomass was 91.8%, and for powder -80.9%. The performance efficiency of the adsorbent depends on its selectivity and affinity for the The adsorption process presents phases associated with the steps of adsorption kinetics. It depends on the initial transport of metal ions from the aqueous solution to the outer surface of the BDA. The ions diffuse to the surface of the pores. Then, they are adsorbed on the active sites within the pores, reaching equilibrium. The quantification of metal ions adsorbed by the granular biomass was superior to that of the powdered BDA, contrary to expectations since the powdered biomass presented a greater external surface area. For zinc removal, granular biomass reached a final removal of 72.9% and powder-58.3%. For copper, the removal for granular biomass was 91.8%, and for powder-80.9%. The performance efficiency of the adsorbent depends on its selectivity and affinity for the respective ion compared to competing ion, ionic properties and ion concentration. Likewise, adsorbent characteristics, metal ion properties and liquid medium characteristics are parameters that impact adsorbent performance [28,29]. In addition, the acidic property of the metal influences the adsorption of metals. A more acidic heavy metal reacts easily with a protonated site compared to a weaker acidic heavy metal. Different experimental adsorption analyses indicate that the adsorbent affinity follows the order Cu > Zn [30]. The significance test of the variables indicated that there was a significant difference (p < 0.05) for the adsorption time for both metals. The biomass granulometry was significant for the Cu 2+ adsorption (p < 0.05). On the other hand, for Zn 2+ adsorption, the significance test indicated p = 0.48 for biomass granulometry, showing no effect on adsorption.

Removal of Metal Ions
Norton et al. [31] evaluated the removal of Zn 2+ ions in aqueous solutions from the application of biosolids collected from an activated sludge system of an effluent treatment plant. Zinc removal occurred at different concentrations, including the concentration of 19.6 mg L −1 , a value close to that evaluated in this study. Equilibrium was reached after 5 h, with a maximum removal of 86.7%. In another study, Shanmugaprakash and Sivakumar [32] evaluated a biosorption system using an oil cake derived from the extraction of biodiesel oil as a biosorbent. The ion removal efficiency ranged from 68.42% to 81.45% for different metal concentrations. Yang et al. [33] reported that a zinc ion biosorption system using dry activated sludge had removal efficiencies ranging from 17.6% to 89%.
Terry and Stone [34] studied a copper biosorption system from green algae species Scenedesmus abundans. The authors obtained a reduction in the copper concentration from 10 mg L −1 to 0.1 mg L −1 in 36 h. Pavasant et al. [35] investigated the sorption of Cu 2+ by the dry green macroalgae Caulerpa lentillifera. The removal efficiency increased to a specific pH value, reaching a range in metal removal between 50% and 85%. Finally, Lacerda et al. [36] evaluated a copper biosorption system using the dead biomass of a filamentous fungus (Penicillium ochrochloron). The authors observed 75% removal of Cu 2+ ions for a system with an initial copper concentration of 50 mg L −1 .

Characterization of the Biomass Composition
FTIR spectra were obtained for the granular biomass treated at 100 • C, as shown in Figure 2.
Likewise, adsorbent characteristics, metal ion properties and liquid medium characteristics are parameters that impact adsorbent performance [28,29]. In addition, the acidic property of the metal influences the adsorption of metals. A more acidic heavy metal reacts easily with a protonated site compared to a weaker acidic heavy metal. Different experimental adsorption analyses indicate that the adsorbent affinity follows the order Cu > Zn [30]. The significance test of the variables indicated that there was a significant difference (p < 0.05) for the adsorption time for both metals. The biomass granulometry was significant for the Cu 2+ adsorption (p < 0.05). On the other hand, for Zn 2+ adsorption, the significance test indicated p = 0.48 for biomass granulometry, showing no effect on adsorption.
Norton et al. [31] evaluated the removal of Zn 2+ ions in aqueous solutions from the application of biosolids collected from an activated sludge system of an effluent treatment plant. Zinc removal occurred at different concentrations, including the concentration of 19.6 mg L −1 , a value close to that evaluated in this study. Equilibrium was reached after 5 h, with a maximum removal of 86.7%. In another study, Shanmugaprakash and Sivakumar [32] evaluated a biosorption system using an oil cake derived from the extraction of biodiesel oil as a biosorbent. The ion removal efficiency ranged from 68.42% to 81.45% for different metal concentrations. Yang et al. [33] reported that a zinc ion biosorption system using dry activated sludge had removal efficiencies ranging from 17.6% to 89%.
Terry and Stone [34] studied a copper biosorption system from green algae species Scenedesmus abundans. The authors obtained a reduction in the copper concentration from 10 mg L −1 to 0.1 mg L −1 in 36 h. Pavasant et al. [35] investigated the sorption of Cu 2+ by the dry green macroalgae Caulerpa lentillifera. The removal efficiency increased to a specific pH value, reaching a range in metal removal between 50% and 85%. Finally, Lacerda et al. [36] evaluated a copper biosorption system using the dead biomass of a filamentous fungus (Penicillium ochrochloron). The authors observed 75% removal of Cu 2+ ions for a system with an initial copper concentration of 50 mg L −1 .

Characterization of the Biomass Composition
FTIR spectra were obtained for the granular biomass treated at 100 °C, as shown in Figure 2. The band referring to water was observed at 3250 cm −1 . Likewise, methyl and methylene groups were identified at 2960 and 2925 cm −1 , respectively. Primary amides The band referring to water was observed at 3250 cm −1 . Likewise, methyl and methylene groups were identified at 2960 and 2925 cm −1 , respectively. Primary amides were observed at 1634 and 1627 cm −1 . At 1540 cm −1 two bands referring to secondary amide groups were observed. C-O bond groups referring to carbohydrates and alcohols are assigned in the region between 1250 and 1000 cm −1 . Thus, polysaccharides and cellulose carbohydrates were assigned to bands at 1034 and 1024 cm −1 . Furthermore, bands attributed to -OH groups of mineral compounds were identified between 1070 and 1000 cm −1 . Yang et al. [33] reported a similar FTIR spectra for Zn 2+ biosorption using dry activated sludge with a particle size of 250 µm as BDA. The authors observed a decrease in the adsorption intensity of the amide group at 1637 and 1543 cm −1 , demonstrating that this group played an important role in zinc binding. The vibration of -C-O-C and -OH from polysaccharides resulted in a band at 1036 cm −1 . In addition, the -OH group was involved in zinc binding. Table 2 displays the parameters of the pseudo-first-order kinetic model based on Equations (1) and (2). Table 2. Parameters of the pseudo-first-order kinetic model.

Metal Parameters 1 Granular Biomass Powdered Biomass
Zinc q e exp (mg g −1 ) The linear regression coefficient (R 2 ) and the similarity between the experimental and adjusted value of the adsorbed amount of metal per adsorbent mass at equilibrium allowed evaluation of the representativeness of the model. For the zinc system, the granular biomass data had a good fit to the pseudo-first-order model (R 2 = 0.95), with values close to q e exp and q e adj. For the copper system, the powder biomass also indicated a good correlation with the model (R 2 = 0.95); however, with a greater difference between the values of q e exp and q e adj.
High values of R 2 for the pseudo-first-order model in the metal biosorption systems have been reported in the literature [20,[37][38][39]. Furthermore, the adsorption data fitted to a pseudo-first-order model indicate that a chemical phenomenon may limit the sorption kinetics since the chemical reactions and/or the diffusion of the liquid film in the boundary layer is responsible for the resistance to the mass transfer [40]. Table 3 displays the parameters of the pseudo-second-order kinetic model based on Equations (4) and (5). Table 3. Parameters of the pseudo-second-order kinetic model.

Metal Parameters Granular Biomass Powdered Biomass
Zinc q e exp (mg g −1 ) Data from both systems using powdered and granulated biomass fit well with the pseudo-second-order model, demonstrating high linear regression coefficients (R 2 ≥ 0.993). For all conditions, the amount of metal adsorbed per mass of adsorbent in the experimental and adjusted equilibrium were close. According to Tan and Hameed [41], pseudo-first and pseudo-second-order models are commonly applied to adsorption systems. However, the pseudo-first-order model generally presents data with less adjustability than the pseudo-second-order model due to mathematical factors during linearization since the random errors in the values of q e are less expressive in the pseudo-second-order model [42]. Furthermore, these models are more descriptive than predictive due to the ease of curve fitting [41]. Several authors have reported the representativeness of the model in metal biosorption systems [43][44][45]. The systems point out that chemical sorption is the binding mechanism. The bond between the metal ions and the biosorbent occurs through an exchange of ions or covalent bonds [46]. Table 4 displays the parameters of the Weber and Morris kinetic model. The parameter C is related to the thickness of the boundary layer formed on the surface of the adsorbent particle. As it increases, the limiting effect of the layer is also enhanced. The granular biomass (R 2 = 0.99) fits better for the zinc adsorption systems than the powdered biomass. In contrast, the powdered biomass (R 2 = 0.91) presented a better representation of the model with copper than the granular biomass. Studies have reported that the Weber and Morris model adjusted to metal biosorption with high values for the linear regression coefficient [25,37]. In most adsorption systems, the model presents multiple control mechanisms, in which the initial step consists of adsorption on the surface of the adsorbent. Subsequently, intraparticle diffusion becomes the process control mechanism, and in the third stage, the system tends to approach equilibrium [41]. Table 5 displays the parameters α and β obtained by the Elovich model. The first is related to the initial rate of sorption, and the second to the size of the binding surface and the activation energy for chemisorption [47]. The Elovich kinetics for zinc and granular biomass showed a good correlation (R 2 = 1.00). For copper, the powdered biomass indicated an R 2 = 0.97. Studies have reported this model for metal adsorption systems [26,48]. The adsorption system adjusted to the Elovich model indicates that the sorption tends to be controlled by chemisorption. The interaction between the biosorbent and the adsorbate occurs through a chemical bond [47].

Evaluation of Zn and Cu Adsorption Systems and Application of Kinetic Modeling
A broader kinetic study of zinc and copper adsorption processes considered data from several previous studies. The kinetic study of biosorption systems seeks to identify the time required to reach adsorption equilibrium and evaluate how the system responds to different parameters such as pH, temperature, sorbate concentration and biosorption concentration. Therefore, kinetic modeling was performed in the experimental system (S0). It evaluated the binding rate of metal ions on the surface of the BDA, being a process control step and probable binding mechanism.

Zinc Adsorption Systems
Zinc system 1 (S1-Zn), published by Melčáková and Růžovič [49], analyzed the performance of the filamentous green seaweed (Spirogyra sp.) and parts (root, stem and leaves) of a plant (Reynoutria japonica) in the biosorption process of an aqueous solution of zinc with a Zn 2+ concentration of 10 mg L −1 . Zinc system 2 (S2-Zn) developed by Rodrigues et al. [50] evaluated the potential of using water lettuce (Pistia stratiotes) dry biomass for zinc biosorption, and the biomass performance was analyzed by varying the initial metal concentration. Finally, zinc system 3 (S3-Zn), published by Norton et al. [31], evaluated the potential of applying dry biosolids to remove Zn 2+ ions from aqueous solutions. The BDA was collected from the activated sludge system of a wastewater treatment plant. Figure 3 exhibits the adsorption curves of the Zn 2+ ion for the three evaluated systems.
For the S2-Zn system (Table S2), the adsorption capacity curve revealed that the samples with higher concentrations of zinc had a greater amount of adsorbed zinc per mass of biosorbent. The water lettuce dry biomass reached equilibrium at different times, according to the initial zinc concentration. For lower concentrations, equilibrium was reached in 6 h (q e = 0.045 mg g −1 ), for median concentrations it occurred in 36 h (q e = 0.846, 2.192, and 2.358 mg g −1 for concentrations of 21.04, 51.98 and 61.91 mg L −1 , respectively), and at higher concentrations −72 h (q e = 3.701 mg g −1 ). Furthermore, the removals varied according to the initial zinc concentration, following the ascending order of concentration with maximum removals of 79.3%, 86.1%, 85.9%, 80.3% and 70.8%.
The S3-Zn system (Table S3) reached equilibrium with a period of 4 h for the initial zinc concentration of 2 mg L −1 (q e = 0.327 mg g −1 ), 8 h-5 mg L −1 (q e = 1700 mg g −1 ) and 24 h-98.1 mg L −1 (q e = 7.846 mg g −1 ). As observed in the previous study, the adsorption capacity was higher for higher initial concentrations of zinc. The maximum removals in ascending order of the initial Zn concentration were 91.5%, 86.7%, and 84%.

Copper Adsorption Systems
Copper system 1 (S1-Cu) investigated by Peng et al. [51] analyzed the efficiency of Cu 2+ biosorption from an aqueous solution of (CuSO 4 ·5 H 2 O) by immobilizing the fungus Saccharomyces cerevisiae (active cells) on the surface of chitosan-coated magnetic nanoparticles from an aqueous solution. Copper system 2 (S2-Cu) was described by Ianis et al. [52]. The authors analyzed the biosorption of an aqueous copper solution with a concentration of 100 mg L −1 by the fungus Penicillium cyclopium (active cells). Finally, copper system 3 (S3-Cu) was studied by Khormaei et al. [53]. The authors investigated the biosorption of copper by sour orange residues. The copper metal concentration during the biosorption process was 150 mg L −1 . Figure 4 exhibits the adsorption curves of the Cu 2+ ion for the three evaluated systems.
The S1-Cu system (Table S4) indicated the high adsorption capacity of copper by the fungus Saccharomyces cerevisiae during the initial 20 min. Equilibrium was reached in 60 min (q e = 131 mg g −1 ). The maximum copper removal by the fungal biomass was 66.5%. For the S2-Cu system (Table S5), the biomass rapidly adsorbed copper ions by the biomass in the first five minutes at both biosorbent concentrations. However, the biosorption started to stabilize in 25 min. It reached equilibrium in 60 min, with q e = 57.49 mg g −1 for the biosorbent concentration of 0.9915 g L −1 and q e = 20.42 mg g −1 for the biosorbent concentration of 3.9660 g L −1 . For high concentrations of biosorbent, the biosorption capacity decreases as diffusional limitations may occur. The mass transfer rate slows down and begins to limit the overall reaction rate [52]. The maximum copper removal by the fungal biomass of Penicillium cyclopium was 57%, with a biosorbent concentration of 0.9915 g L −1 and 3.9660 g L −1 -81%. Therefore, increasing the concentration of the biosorbent resulted in the greater removal of metal ions.
For the S3-Cu system (Table S6), both biosorbent particle sizes rapidly biosorbed copper ions by orange residues within the first few minutes of analysis. Equilibrium times were different for each particle size: particles from 0.15 to 0.35 mm took 20 min (q e = 13.59 mg g −1 ), while from 0.7 to 1.0 mm required 80 min (q e = 13.21 mg g −1 ). The difference in equilibrium times is related to the high agitation speed (300 rpm) to overcome the diffusion resistance of the film resulting from intraparticle diffusion [53]. The removal of copper ions for the biosorbent with granulometry between 0.15 and 0.35 mm indicated a maximum value of 90.63%, and the particles of 0.7-1.0 mm were slightly smaller at approximately 88.08%. The removal efficiency was higher for smaller sizes of biosorbent particles. Cu 2+ biosorption from an aqueous solution of (CuSO4·5 H2O) by immobilizing the fungus Saccharomyces cerevisiae (active cells) on the surface of chitosan-coated magnetic nanoparticles from an aqueous solution. Copper system 2 (S2-Cu) was described by Ianis et al. [52]. The authors analyzed the biosorption of an aqueous copper solution with a concentration of 100 mg L −1 by the fungus Penicillium cyclopium (active cells). Finally, copper system 3 (S3-Cu) was studied by Khormaei et al. [53]. The authors investigated the biosorption of copper by sour orange residues. The copper metal concentration during the biosorption process was 150 mg L −1 . Figure 4 exhibits the adsorption curves of the Cu 2+ ion for the three evaluated systems. Figure 4. Adsorption curve of the Cu 2+ ion for the systems: (a) S1-Cu-with Saccharomyces cerevisiae [51]; (b) S2-Cu-with different concentrations of biosorbent [52]; and (c) S3-Cu-with different biomass particle sizes [53].
The S1-Cu system indicated the high adsorption capacity of copper by the fungus Saccharomyces cerevisiae during the initial 20 min. Equilibrium was reached in 60 min (qe = 131 mg g −1 ). The maximum copper removal by the fungal biomass was 66.5%. For the S2-Cu system, the biomass rapidly adsorbed copper ions by the biomass in the first five minutes at both biosorbent concentrations. However, the biosorption started to stabilize in 25 min. It reached equilibrium in 60 min, with qe = 57.49 mg g −1 for the biosorbent concentration of 0.9915 g L −1 and qe = 20.42 mg g −1 for the biosorbent concentration of 3.9660 . Adsorption curve of the Cu 2+ ion for the systems: (a) S1-Cu-with Saccharomyces cerevisiae [51]; (b) S2-Cu-with different concentrations of biosorbent [52]; and (c) S3-Cu-with different biomass particle sizes [53].

Representativeness of the Pseudo-Second-Order Model in Metal Adsorption Systems
In addition to the experimental system, kinetic modeling of the zinc and copper systems was performed for the studies discussed above, considering the four kinetic models. Tables 6 and 7 show that the pseudo-second-order model indicated a more representative fit. Data for the adjustments considering the other models are available in the supplementary material.
As illustrated in Table 6, most systems showed high values for R 2 . Only the systems that operated with a low initial concentration of zinc resulted in data that did not fit the model well, according to the S2-Zn and S3-Zn systems with different biosorbents. For all copper adsorption systems shown in Table 7, the R 2 value was 1.00, demonstrating the full fit of the experimental data to the model. The experimental and adjusted adsorption capacity was similar for all adsorbent materials.
The adsorption system data fitted to the pseudo-second-order model suggest that the interaction between the system components occurred through an exchange of electrons between the adsorbate (metal ions) and the adsorbent through the chemisorption process [54]. The data also showed a good fit to the Elovich model, where the limiting mechanism of the process occurs due to chemical reactions. Therefore, zinc and copper adsorption are mainly limited by chemisorption mechanisms. Table 6. Pseudo-second-order model parameters for zinc systems: S0-Zn, S1-Zn, S2-Zn and S3-Zn.  Table 7. Pseudo-second-order model parameters for copper systems: S0-Cu, S1-Cu, S2-Cu, and S3-Cu.

Conclusions
The experimental system of adsorption of Zn 2+ and Cu 2+ ions by granular and powdered biomass proved efficient. The adsorption reached maximum removals of 72.9% (granular) and 62.7% (powder) for zinc, and 92.8% (granular) and 85.0% (powder) for copper. The evaluation of the kinetic models through the linear regression coefficient indicated that the pseudo-second-order model presented a high capacity for adjustment to the experimental data for the zinc and copper adsorption systems. Thus, as the kinetic model was based on chemical reactions, the adsorption rate-limiting step occurred due to chemisorption. In addition, the adsorption allowed the regeneration of the BDA and the possibility of recovering the metal. Therefore, investment in studies involving the kinetic analysis of the process becomes valid since the studies assist in development of projects and more efficient responses to the treatment of effluents. In addition, these actions contribute to the 6 th Sustainable Development Goal, reducing pollution and improving water quality.