Journal of Colloid and Interface Science 232, 64–70 (2000) doi:10.1006/jcis.2000.7186, available online at http://www.idealibrary.com on
Isotherm Model Analysis for the Adsorption of Cd (II), Cu (II), Ni (II), and Zn (II) on Anaerobically Digested Sludge Adriana Artola, Maria Martin, MaDolors Balaguer, and Miquel Rigola Laboratori d’Enginyeria Qu´ımica i Ambiental, Departament d’Enginyeria Qu´ımica, Agr`aria i Tecnologia Agroaliment`aria, Facultat de Ci`encies, Universitat de Girona. Campus de Montilivi, 17071-Girona, Spain Received March 29, 2000; accepted August 28, 2000
bind. The second might be the entrance of metals inside the cell. As the contribution of the second step has been demonstrated negligible when compared with the first one, biosorption is considered mainly a physico-chemical process, independent of the metabolic processes (11). As in physical processes, equilibrium conditions between adsorbed metal ions in solid phase and free ions remaining in solution are rapidly attained (12). Thus, equilibrium data obtained experimentally in biomass–metal systems has been modeled using the classical adsorption isotherm models with Langmuir and Freundlich equations as the most widely applied (8, 13, 14). The formation of metal complexes by ligands present in biological material has also been described (15, 16). Weakly acidic functional groups present in the cell wall are involved in the mechanism proposed above. In addition to those groups, polysaccharides and amino acids constituting the basic structure of the cell wall provide amino, sulfate, and phosphate groups which also contribute to the biomass heavy metal binding capacity (17, 18). All these groups are intended as the biomass binding sites. In previous work, the behavior of a welldefined amino acid–metal system (glycine–Cu (II)) and that of the sludge–Cu (II) system were studied and compared establishing a parallelism in some aspects of their behavior. This fact suggests the participation of amino and acid groups in metal adsorption (19). Metal desorption has also been demonstrated to be feasible. Hydrochloric acid and EDTA are the desorbing agents most commonly used for this purpose (20–22). Metal desorption has been attributed to high concentrations of protons made available by HCl which compete with heavy metals for the biomass binding sites. EDTA desorption was explained in terms of direct competition between ligands present in biomass and EDTA for heavy metal ions since EDTA forms strong metal complexes with strong stability constants. Even if EDTA can also be adsorbed onto bacterial cell surfaces at low pH values (pH < 3), the formation of ternary surface–metal–EDTA complexes has not been reported (23). Consequently, adsorbent regeneration as conducted with traditional adsorbents seems also possible when biological material is used in adsorption processes. The use of waste biomass as heavy metal adsorbent may result in an inexpensive and effective heavy metal polluted wastewater treatment. The adsorptive capacity of nonbiological low cost
Adsorption of Cd (II), Cu (II), Ni (II), and Zn (II) from aqueous solutions on anaerobically digested sludge has been investigated. Experimental data has been fit to Langmuir, Freundlich, and Redlich-Peterson isotherms to obtain the characteristic parameters of each model. Based on the maximum adsorption capacity obtained from the Langmuir and the Redlich-Peterson isotherm the affinity of the studied metals for the sludge has been established as Cu (II) > Cd (II) > Zn (II) > Ni (II). Adsorption tests from multimetal systems confirm the affinity order obtained in the individual metal tests. The adsorption capacity for Cu (II) measured in individual tests is not reduced by the presence of the other above referred metals. Desorption of Zn (II) and Cd (II) previously bound to the sludge in front of Cu (II) and HCl solutions is also reported. C
2000 Academic Press
Key Words: heavy metals; digested sludge; metal affinity; adsorption isotherms; multimetal system; desorbing agent.
INTRODUCTION
Heavy metals are considered as hazardous pollutants due to their toxicity even at low concentration. Public awareness has increased in recent years relating to the long-term toxic effects of water containing dissolved heavy metal ions (1). The concentration of such pollutants in wastewater has to be reduced to meet increasing legislative standards. Precipitation and ion exchange are the conventional methods applied for heavy metal removal (2, 3). Adsorption on activated carbon surface is one of the alternatives proposed to these methods (3). More specific treatments like electrodialysis or reverse osmosis have also been developed with their high costs as the main drawback for their generalized application (3, 4). In addition to classical wastewater detoxification treatments, heavy metals as well as other compounds and particulates, can be removed from wastewater by biological material in a process named biosorption (5–7). Heavy metal removal or uptake by biological material is a consequence of the interaction between metals in the aqueous solution and bacterial, algae, yeast, and fungi cell surface (8). Biosorption was interpreted by means of a two-step mechanism (9, 10). The first step relates to the surface characteristics of biological material to which metal can 0021-9797/00 $35.00
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ADSORPTION OF HEAVY METALS ON DIGESTED SLUDGE
materials (i.e., red muds and fly ashes, natural zeolites, bentonite, and lignite) has also been investigated in order to decrease wastewater treatment costs (1, 24–26). The recoverability of heavy metals by its concentration in the proposed adsorbents has also been the goal of those investigations. The biosorptive capacity of the biological sludge excess from conventional sewage treatment plants has been widely investigated (15, 27–29). The ability of the different types of biological sludge to adsorb heavy metals was confirmed and compared in previous work. Anaerobically digested sludge has been selected as the most convenient for its use as a heavy metal biosorbent (30, 31). In this study, experimental equilibrium data obtained for the adsorption of Cu (II), Cd (II), Ni (II) and Zn (II) on anaerobically digested sludge has been analyzed by the Langmuir, Freundlich, and Redlich-Peterson isotherm equations in order to determine which of them can better represent metal biosorption on sludge. The values of the isotherm parameters obtained in each case by best fitting experimental data have been used to compare sludge affinity for the four metals under study. Metal affinity has also been assessed using individual metal adsorption data from Cd (II), Cu (II), Ni (II), and Zn (II) four metal mixtures. Desorption tests for Cd (II) and Zn (II) are also presented when discussing metal–sludge affinity. MATERIALS AND METHODS
Sludge Characteristics Anaerobically digested sludge was obtained from the sewage treatment plant in the city of Girona (Spain). The characteristics of the sludge used in the tests were the following: pH 7.2–7.6; total solids, 17.5–26.2 kg/m3 ; volatile solids, 9.4–14.8 kg/m3 ; [Cu], 0.30–0.38 g Cu/kg TS; [Zn], 0.37–0.40 g Zn/kg TS; [Cd] and [Ni] were below detection limits. Analytical Methods Total and volatile solids (TS, VS) were measured according to Standard Methods (32). A commercial electrode was used to measure pH (CRISON, 52-02). Metal concentration in the samples was determined by flame atomic absorption spectrophotometry (AA) using a VARIAN SPECTRAA-300 instrument. Metal content in the original sludge was also measured by flame atomic absorption with prior acidic digestion of the samples as described below. Digestion of Sludge Samples Acid digestion was used for the determination of the sludge metal content. Thirty milliliters of concentrated HNO3 plus 10 ml of concentrated HCl were added to a 50-ml sludge sample. Three sludge samples were used in each test. The sludge–acid mixture was digested under reflux during 2 h at a temperature of 100◦ C. After this period, each sample was filtered through a microfiber filter (WHATMAN GF/C) and diluted for its AA
65
analysis. A blank test was also undertaken following the same procedure but substituting the sludge sample by 50 ml of distilled water. Determination of the Sludge Heavy Metal Binding Capacity Heavy metal binding capacity was determined in batch experiments. A 30-ml sample of original sludge was added to 200 ml of metal chloride solution in a 250-ml open Erlenmeyer flask. The concentration of total solids in the adsorption media was 3–3.4 g/L. A magnetic stirrer was used to maintain well-mixed conditions and to minimize mass transfer resistance. When adsorption tests were performed for multimetal systems, each initial solution was equimolar for all metals. After 1 h of contact, a sample was taken from the flask and filtered through a microfiber filter (WHATMAN GF/C). In previous work it was determined that practical attainment of equilibrium was achieved in 1 h (30). Filtrates were diluted as required so as to lie within the linear range of spectrophotometric measurements. The tests were repeated at different initial metal concentration maintaining a constant sludge concentration. Blanks were also prepared to determine the starting metal concentration in each test. The objective of the blank tests is the determination of the initial metal concentration with the same experimental error gained in the preparation and analysis of the sludge–metal samples. The pH of the adsorption media remained around neutral in all the tests performed. This value of pH was attained by the metal–sludge system after the addition of the sludge to the metal solution due to the buffer capacity of anaerobically digested − sludge where CO2− 3 /HCO3 species are present. Desorption Tests Four 0.78-g identical portions of anaerobically digested sludge which had previously adsorbed Cd (II) (0.73 mmol/g TS) and Zn (II) (0.48 mmol/g TS) from a mixture of the two metals at an initial concentration of 8 mmol/L of each of them were taken. One of the portions was used for the determination of the total solids content. A second one was digested to determine its metal content as described above. A third portion was resuspended in 200 ml of 4 mmol/L Cu (II) solution. The fourth portion was resuspended in 200 ml of distilled water to which concentrated HCl was added to reach a pH of 2. The contact between sludge and metal or acid solution was maintained during 19 h. Samples were taken after 1 and 2 h of contact and at the end of the contact time. RESULTS AND DISCUSSION
Equilibrium data obtained for Cu (II), Cd (II), Ni (II), and Zn (II) in adsorption tests against anaerobically digested sludge are presented in Figs. 1 to 4. In these figures, the adsorption capacity, X , in mmol of metal/g of total solids in the sludge, is plotted against equilibrium free metal concentration, Ceq , in mmol/L. Molar units were chosen for the adsorption capacity instead of mass units to allow direct comparison of the affinity
66
ARTOLA ET AL.
FIG. 1. Equilibrium adsorption isotherm for Cd (II) on anaerobically digested sludge: , experimental data; —, adjustment to the Redlich-Peterson isotherm.
FIG. 3. Equilibrium adsorption isotherm for Ni (II) on anaerobically digested sludge: , experimental data; —, adjustment to the Redlich-Peterson isotherm.
of the four metals for the sludge. Solid lines in Figs. 1 to 4 compare the experimental data points to the best fit theoretical lines for the Redlich-Peterson equation. Experimental data in Figs. 1 to 4 have been analyzed using the Langmuir, Freundlich, and Redlich-Peterson isotherm models. Values obtained for the different equation parameters are presented in Tables 1 to 3. Langmuir and Freundlich isotherms have been commonly used to model data obtained in wastewater adsorption treatment systems (1, 9, 18, 26, 33). The Redlich-Peterson isotherm has been scarcely applied in the above-mentioned systems (1), but it has been found to better fit the experimental data obtained in this work. The isotherm profiles obtained for Cu (II), Cd (II), and Zn (II) show the pattern of strongly favourable isotherms while the profile obtained for Ni (II) corresponds to a favourable isotherm (34, 35). This fact shows the lower affinity of Ni (II) for the sludge binding sites when compared to those of the other three metals under study. The values obtained for the characteristic parameters of the different isotherm equations confirmed that observation. Isotherm constants obtained by polynomial fit of the experimental data to the Langmuir model are presented in Table 1
together with the correlation coefficient, r 2 . On the basis of the correlation coefficient values, the best adjustment is obtained for Ni (II). The highest value obtained for X m (maximum adsorption capacity) corresponds to Cu (II) (1.5 mmol metal/g TS) followed in decreasing order by Cd (II) (1.17 mmol metal/g TS), Zn (II) (0.51 mmol metal/g TS), and Ni (II) (0.43 mmol metal/g TS). The parameter X m reflects the metal affinity for the sludge binding sites. Thus, copper can be considered as the metal showing the highest affinity for the sludge closely followed by cadmium. Similar X m values for cadmium were obtained by Holan et al. working with two different biosorbents: 1.17 mmol Cd (II)/g for S. natans and 1.18 mmol Cd (II)/g for A. nodosum (33). Chang et al. found X m values for Cu (II) and Cd (II) in front of P. aeruginosa: 0.38 mmol Cd (II)/g and 0.30 mmol Cu (II)/g (9). Results obtained when Freundlich isotherm is used to model experimental data are presented in Table 2. Again, the isotherm equation and the correlation coefficient obtained for each metal are given. The correlation coefficient values calculated in this case are lower than those obtained for the Langmuir equation for all metals except Ni (II) (Table 1). Cu (II) is the metal system with the lowest correlation value. In the case of the Freundlich isotherm the affinity of the adsorbent for a metal can be measured
FIG. 2. Equilibrium adsorption isotherm for Cu (II) on anaerobically digested sludge: , experimental data; —, adjustment to the Redlich-Peterson isotherm.
FIG. 4. Equilibrium adsorption isotherm for Zn (II) on anaerobically digested sludge: , experimental data; —, adjustment to the Redlich-Peterson isotherm.
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ADSORPTION OF HEAVY METALS ON DIGESTED SLUDGE
TABLE 1 Langmuir Parameters for the Adsorption of Cd (II), Cu (II), Ni (II), and Zn (II) on Anaerobically Digested Sludge X=
TABLE 3 Redlich–Peterson Parameters for the Adsorption of Cd (II), Cu (II), Ni (II), and Zn (II) on Anaerobically Digested Sludge
X m bCeq 1 + bCeq
X=
X m bCeq B 1 + bCeq
Metal
Xm (mmol metal/g TS)
b (L/mmol)
Correlation coefficient (r 2 )
Metal
Xm (mmol metal/g TS)
b (L/mmol)
B
Correlation coefficient (r 2 )
Cd (II) Cu (II) Ni (II) Zn (II)
1.17 1.50 0.43 0.51
18.45 18.00 1.14 20.75
0.921 0.893 0.945 0.921
Cd (II) Cu (II) Ni (II) Zn (II)
1.03 1.46 0.28 0.50
34.48 19.34 3.50 32.90
0.91 0.98 0.72 0.93
0.945 0.894 0.955 0.939
Note. X m , Maximum adsorption capacity (mmol metal/g TS); b, Adsorption energy related constant (L/mmol).
Note. X m , Maximum adsorption capacity (mmol metal/g TS); b, Adsorption energy related constant (L/mmol); B, Empirical parameter.
by the parameter K . Values obtained for K follow the same order than those obtained for the maximum adsorption capacity when using the Langmuir model (Cu (II) > Cd (II) > Ni (II) > Zn (II)). McKay considers the parameter n in the Freundlich isotherm as a measure of the heterogeneity of the adsorbent binding sites (36). Values of n range from 0 to 1 for decreasing heterogeneity. Following that statement, the heterogeneity of the binding sites is higher for Cu (II), Cd (II), and Zn (II) (for which n is approximately equal to 0.2) than for Ni (II) (n = 0.44). This fact supports the possibility of the existence of some site specificity for Ni (II) stated by Gould and Genetelli when justifying the lower affinity of this metal for the sludge compared with the other metals appearing in their study (37). The Redlich-Peterson isotherm equation is given in Table 3. In this case, the isotherm equation implies three parameters: X m , b, and B. The values obtained simultaneously by curve fitting for these parameters are summarized in Table 3. Correlation coefficients are also listed for the four metals studied. In the present case, X m represents the maximum adsorption per unit weight of adsorbent, not restricted to a monolayer of molecules as it was in the Langmuir isotherm. The Redlich-Peterson model considers, as the Freundlich model, heterogeneous adsorption surfaces as well as the possibility of multilayer adsorption. When B = 1 the Redlich-Peterson equation converges with the Langmuir
isotherm. This is the case of Cu (II) for which B = 0.98. The correlation coefficient value for this metal (0.8939) is the same for the two isotherm models (see Tables 1 and 3). Values of X m calculated using the Redlich-Peterson isotherm show the same metal–sludge affinity order that was deduced from the application of Langmuir and Freundlich models. In this case, X m = 1.46 mmol metal/g TS for Cu (II), close to the value of 1.50 obtained from the Langmuir isotherm. The lowest value is X m = 0.28 mmol metal/g TS obtained for Ni (II). The Redlich-Peterson equation provides the best fit for Cu (II), Cd (II), and Zn (II) when the values obtained for the correlation coefficient in the three isotherm models used are compared. The Freundlich model gives the best adjustment only in the case of Ni (II). The Freundlich equation predicts that the amount of metal adsorbed per unit weight of adsorbent will increase as long as metal ion concentration in the liquid phase increases. Data obtained experimentally indicates that an isotherm plateau is reached at X m value for all the metals studied except for Ni (II). This fact explains the suitability of the Freundlich model in this case. Relating to the shape of the curve presented for Ni (II) it should be pointed that the same metal initial concentration in solution rang was maintained for all the metals tested. In spite of the invalidity of the classical Langmuir assumptions, i.e., site-specificity and uniformly energetic adsorption confined to a monolayer of molecules, heavy metals adsorption on heterogeneous adsorbents has been interpreted with slightly better results by the Langmuir isotherm than by the Freundlich equation (24). From the values obtained for X m in the Langmuir and RedlichPeterson models an affinity order in the metal-anaerobically digested sludge system can be established:
TABLE 2 Freundlich Parameters for the Adsorption of Cd (II), Cu (II), Ni (II), and Zn (II) on Anaerobically Digested Sludge n X = K Ceq
Metal
K
n
Correlation coefficient (r 2 )
Cu (II) > Cd (II) Zn (II) > Ni (II).
Cd (II) Cu (II) Ni (II) Zn (II)
0.86 1.14 0.21 0.46
0.19 0.17 0.44 0.17
0.867 0.741 0.972 0.803
The affinity of the sludge for the studied metals has been suggested to be related both to the solubility of the metal hydroxides and to the electronegativity of the metal ions. Table 4 summarizes the values of these two parameters for the four metals under study. Apak et al. pointed that surface metal precipitation in form of metal hydroxide occur simultaneously to metal adsorption,
Note. K, Empirical constant related to the adsorption capacity of the adsorbent against a specific metal; n, Freundlich exponential parameter.
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ARTOLA ET AL.
TABLE 4 Metal Properties Related to Metal-Sludge Affinity Order Metal propertiesa Metal
Electronegativity (Pauling)
PKs M(OH)2
Cd (II) Cu (II) Ni (II) Zn (II)
1.90 1.70 1.90 1.60
18.8 14.4 13.3 14.8
a Burriel, F., Lucena, F., Arribas, S., and Hern´ andez, J., “Qu´ımica anal´ıtica cualitativa.” Paraninfo, Madrid, 1989.
even if partial contribution of the two phenomena to the final adsorption capacity value could not be determined (24). The relationship between adsorption capacity and the electronegativity of the metal ions is applicable in the group of metals studied except in the case of nickel. Following the electronegativity order, nickel should show an affinity for the sludge similar to that obtained for copper. As stated above, some site specificity for Ni (II) was pointed by other investigators to justify the lower affinity of this metal for the sludge (37). The mentioned investigators found the same affinity order for the same four metals in front of anaerobically digested sludge (37). Holan and Volesky found that the affinity of Cu (II) for R. arrhizus was higher than the affinity of Cd (II) for the same biomass (38). Kapoor and Viraraghavan (39) studied the adsoption of different metals on A. niger establishing the highest affinity for Cu (II) followed by Cd (II) and Ni (II). The results of the investigation of Chong and Volesky (40) on metal adsorption by A. nodosum agree with those presented above: the metal–biomass affinity order was Cu (II) > Cd (II) > Zn (II). To confirm the higher affinity that the sludge has for Cu (II) when compared with the three other metals under study, a set of competitive experiments was undertaken. The adsorption tests were performed from mixtures of the four metal ions at the same initial concentration. Tests were undertaken for different initial concentrations of the four metals (from 0.5 to 8 mmol/L). Total solids concentration in the test was the same than that used in the individual adsorption experiments (3–3.4 g/L). The results obtained are presented in Fig. 5. The total length of the bars in Fig. 5 represents the total metal adsorbed. The contribution of each metal to this amount has been marked in different colour. As shown in Fig. 5, there is a clear predominance of Cu (II) over the other metals for the adsorption on sludge binding sites. The highest affinity of sludge for Cu (II) is more evident at high initial metal concentration in solution. While values of adsorption capacity at low initial metal concentration (0.5 mmol/L) are very similar for all the metals tested (around 0.1 mmol metal/g TS), at 3 mmol/L the adsorption capacity of Cu (II) doubles the capacity found for Cd (II). At higher initial metal concentration, the amount of Cu (II) adsorbed is higher than the sum of the quantities of the other adsorbed metals. The amount of Cd (II)
adsorbed at an initial metal concentration of 8 mmol/L decreases compared with the amount of Cd (II) adsorbed at 5 mmol/L. As a consequence of that fact the total metal adsorption also decreases. This can be due to the presence of a high concentration of Cl− (chloride salts of the metals were used to prepare metal solutions) which form the complex CdCl+ . At pH values lower than 8.5 and in the absence of sludge, if the ratio Cl− /Cd2+ is greater than 4, 60% of the cadmium present forms the mentioned complex (CdCl+ ) while only a 30% remains as Cd2+ (41). Cu (II) almost reaches in multimetal tests the maximum adsorption capacity found in individual metal tests (1.35 and 1.5 mmol Cu (II)/g TS, respectively). The high affinity of Cu (II) for the sludge binding sites implies Cu (II) adsorption is not affected by the presence of Cd (II), Ni (II), and Zn (II) in solution at the same concentration. The total sludge adsorption capacity obtained for the four-metal system (around 2 mmol/L) is higher than the maximum adsorption capacity found for the different metals in individual tests (1.5 mmol/L, the maximum value found corresponding to copper). This fact can be due to the existence of a variety of binding sites on the sludge that are partially specific for individual metals species (42). Following the results obtained in multi-metal–sludge systems, another test was conducted in order to determine if the higher affinity of the sludge for Cu (II) enables this metal to act as a metal desorbing agent. A solution of Cu (II) was used to desorb Cd (II) and Zn (II) previously bound to anaerobically digested sludge. The results of desorption experiment are presented in Fig. 6. Both Cd (II) and Zn (II) desorb against Cu (II). After 19 h of contact all the Cd (II) present in the sludge passed to the solution as well as an 80% of the Zn (II) initially bound to the sludge (0.09 mmol Zn(II)/g TS remain). At the same time, the concentration of Cu (II) in the sludge raised to 0.436 mmol Cu (II)/g TS. The desorption rate for Cd (II) and Zn (II) was lower than the adsorption rate determined in previous work where a sludge–metal contact time of 1 h for maximum adsorption was established (30). Consequently, the adsorption rate of Cu (II)
FIG. 5. Competitive adsorption of Cd (II), Cu (II), Ni (II), and Zn (II) from equimolar mixtures of the four metals.
ADSORPTION OF HEAVY METALS ON DIGESTED SLUDGE
69
CONCLUSIONS
The Redlich-Peterson isotherm equation was found to best represent the experimental adsorption data obtained in anaerobically digested sludge–metal systems. The Langmuir isotherm also provided a satisfactory fit to the experimental data while the worst correlation was obtained for the Freundlich model. Ni (II) was the only exception presenting the best fit of experimental data when Freundlich equation is used. This was supported by the comparison of the correlation coefficients obtained by polynomial curve fitting. The affinity order of the metals studied for the sludge binding sites was determined based on the maximum adsorption capacity values obtained in the isotherm model adjustment. Cu (II) was the metal presenting the highest value of the maximum adsorption capacity followed by Cd (II), Zn (II), and Ni (II). The same affinity order was maintained when metal adsorption was performed from different four metal equimolar solutions. The high affinity of Cu (II) for anaerobically digested sludge was emphasized by its capacity to desorb Zn (II) and Cd (II) previously bound to the sludge in a similar extend to that obtained using HCl at pH 2 as the desorbing agent. REFERENCES FIG. 6. Desorption of Cd (II) and Zn (II) against time for: (a) Cu (II) 4 mmol/L solution; (b) HCl pH 2 solution (, desorbed Cd (II); , desorbed Zn (II); , adsorbed Cu (II)).
was also lower than in the individual or simultaneous metal adsorption tests summarized above. As can be deduced from the stoichiometry (when the number of mmols of metal adsorbed and desorbed are balanced), the adsorption of Cu (II) is not the only promoter of the desorption of Cd (II) and Zn (II). Results not shown herein had demonstrated that metal desorption using pure distilled water is negligible. The same results were obtained by other investigators (20). Figure 6b also summarizes the results of the desorption of Cd (II) and Zn (II) using HCl at pH 2. Chang et al. determined this pH value as the optimum for metal desorption from biomass using HCl as the desorbing agent (8). When HCl was used as the desorbing agent, the maximum amount of metal desorbed was reached after 1 h of contact with the acid solution both for Cd (II) and Zn (II). Zn (II) desorption was almost complete against HCl (only 0.025 mmols Zn (II)/g TS were bound to the sludge after 19 h contact), while the amount of Cd (II) desorbed (0.63 mmol Cd (II)/g TS) was lower than the quantity desorbed in the presence of the Cu (II) solution (0.73 mmol Cd (II)/g TS) leaving 0.102 mmol Cd (II)/g TS bound to the sludge at the end of the sludge–acid contact time. The affinity of Cu (II) for the sludge confers to this metal a desorption capacity similar to the capacity of HCl at pH 2 (against other metals with lower affinity), even if the desorption rate is lower with the Cu (II) solution.
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