Introduction

Azo dyes, such as Orange II (OII), are widely used in various industries, including textiles and manufacturing1. Due to their persistence, toxicity, and carcinogenicity, azo dyes pose significant environmental and health risks2. These dyes can absorb light, disrupting photosynthesis in aquatic ecosystems and reducing dissolved oxygen levels3. With 10–15% of dyes produced globally ending up in wastewater4, their removal is a critical concern.

Conventional wastewater treatments combine physical, chemical, and biological processes to remove pollutants5. However, many dyes are not fully eliminated by these methods6, necessitating additional treatment approaches like adsorption, enzymatic catalysis, and advanced oxidation processes5. Among these, adsorption is particularly promising due to its high efficiency and use of non-toxic reagents compared to processes like the Fenton reaction7. Recent developments in adsorbent materials, including ceramics and composites, have shown efficacy in removing dyes and toxic metals from aqueous media8,9,10,11,12. However, the valorisation of agro-food waste remains a challenge for developing eco-friendly and economically viable adsorbents13.

Globally, one-third of food produced for human consumption is wasted or lost, amounting to 1.3 billion tons annually14. This waste arises from factors such as overproduction and market influences (surplus), intentional food waste at the end of the supply chain (waste), and unintentional food loss during processing or transportation (loss)15,16. The management of these food wastes, often through incineration or landfilling, can lead to environmental issues such as greenhouse gas emissions and toxic leachates17,18.

Potatoes are among the most widely cultivated tubers, with a global yield of 359 million tons in 2020 and projected production reaching 500–750 million tons by 2025 and 2030, respectively19. Composed of lignin, cellulose, and hemicellulose, potatoes offer physical adsorption sites for dye molecules (Stavrinou et al., 2018). While several authors have reported the utilization of potato peels (loss) for dye adsorption20,21,22,23, there is limited research on the efficacy of potato surplus in dye removal. Potato surplus refers to tubers that have no commercial value due to factors like market conditions.

In this study, surpluses of potato were used as eco-friendly adsorbents for Orange II (OII), presenting an innovative approach to valorising agro-food waste. A kinetic model was developed to understand adsorption dynamics and optimize adsorbent use and contact time, balancing efficiency and cost. This approach is crucial for designing sustainable batch adsorption processes for treating coloured wastewater.

Materials and methods

Raw materials and reagents

The surplus of potato tubers (Solanum tuberosum) was kindly donated by a local market (Duitama, Boyacá, Colombia). The potato tubers used were collected according to Colombian legislation. Orange II (OII) sodium salt (96%) was acquired from Biopack (Buenos Aires, Argentina). The structure of OII and some of its chemical characteristics are shown in Table 1. The inorganic salts used for the preparation of the buffer solutions were NaH2PO4 (99%) and Na2HPO4 (99%). These salts were sourced from Loba Chemie PVT. LIDA (Maharastra, India). All methods, including experiments and analyses, were performed in accordance with relevant national and international protocols, guidelines, and regulations.

Table 1 Chemical structure and general characteristics of Orange II (adapted from Sabnis, 2010).
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Preparation of potato surplus-based adsorbent

Figure 1 shows the schematic representation of the preparation of potato surplus-based adsorbent. The surplus of potato tubers was conditioned according to a previous work25. Briefly, 1 kg of tubers was peeled and cut into cubes of approximately 30 mm. Then, potato cubes were immersed in an ascorbic acid solution (1% w/v, pH 5.0) for 1 h as an anti-browning treatment. Finally, these cubes were frozen at − 20 °C for 12 h and then dried in a BUCHI Lyovapor L-200 freeze dryer (Flawil, Switzerland) operated at − 55 °C at a chamber pressure of 0.1 mbar for 48 h. The obtained potato surplus-based adsorbent (PSBA) was grounded to obtain a powder with an average diameter of 1 mm and stored in a hermetic flask until use.

Fig. 1
figure 1

Schematic representation of the preparation of potato surplus-based adsorbent.

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Characterization of potato surplus-based adsorbent (PSBA)

Scanning electron microscopy (SEM–EDS)

The morphology of the absorbent samples was studied using a scanning electron microscope (SEM) operated at a voltage of 20 kV (Thermo Fisher Scientific, Apreo 2 S LoVac model). Elemental identification was performed using an energy dispersive X-ray spectrometry (EDS) probe (Fisher Scientific, ANAX-30P-B model).

Fourier transform infrared spectroscopy (FTIR)

FTIR analysis was performed using a Perkin-Elmer Spectrum TwoTM IR spectrometer (Waltham, MA, USA) equipped with an attenuated total reflectance (ATR) module. Infrared (IR) spectra were recorded between 4400 and 400 cm−1 with 20 scans and a spectral resolution of 2 cm−1.

Point of zero charge (PZC) of adsorbent (PSBA)

PZC was determined using the technique proposed by Bakatula et al. (2018). 0.2 g of PSBA was mixed with 40 mL of 0.1 M NaNO3 solutions at initial different pH values (pHi = 3–9). Then, these mixtures were stirred at 150 rpm for 24 h and the final pH values (pHf) were measured. The pHpzc was determined as the point of intersection where the pHi versus ΔpH (pHf–pHi) plot intersects with ΔpH = 0. All determinations were performed in duplicate.

Orange II (OII) adsorption assays

The capability of PSBA to remove OII was tested according to a previous work25. Adsorption assays were performed by mixing OII solutions (7–525 mg L−1) with PSBA suspensions (3.8–7.6 g L−1) at pH values ranging from 4 to 9 until the equilibrium was achieved (Fig. 2). The temperature of the test was controlled at 22 °C (INGELAB, I-122PF). All determinations were performed in duplicate. At predetermined intervals, 2 mL from the reaction mixture were centrifuged for 20 min at 5000 rpm (Benchmark Scientific, MYFUGE 12) to remove the PSBA. Then, the absorbance of the supernatant was measured at 485 nm in a spectrophotometer X-ma 1200 (Human Corporation, Loughborough, UK). The OII concentration in the supernatant was calculated using a molar attenuation coefficient of 19.6 ± 0.2 a.u. mM−1 cm−127. Finally, the OII concentration was converted from mmol L−1 to mg L−1 using the corresponding molecular weight (Table 1).

Fig. 2
figure 2

Schematic representation of the adsorption assays of Orange II solutions (OII).

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Once the equilibrium between aqueous and adsorbed OII was reached, the equilibrium adsorption capacity of OII onto PSBA (qe, mg g−1) was calculated as follows:

$$q_{e} = \frac{{C_{0} - C_{e} }}{{\left[ {PSBA} \right]}}$$
(1)

where C0 and Ce (mg L−1) are the initial and equilibrium OII concentrations, respectively, and [PSBA] (g L−1) is the tested PSBA concentration. Note that the term \(C_{0} - C_{e}\) represents the amount of OII adsorbed per unit volume of the liquid phase.

Langmuir (Eq. 2) and Freundlich (Eq. 3) models were fitted to equilibrium adsorption capacity (qe) as a function of the equilibrium OII concentration (Ce):28

$$q_{e} = q_{m} \frac{{C_{e} }}{{K_{L} + { }C_{e} }}{ }$$
(2)
$$q_{e} = K_{F} C_{e}^{1/n}$$
(3)

where qm (mg g−1) is the maximum adsorption capacity of the tested adsorbent, KL (mg L−1) is the semisaturation constant, and KF and n are the constants corresponding to the Freundlich adsorption isotherm.

Ethical approval

No manipulation of human or animal tissue was performed in this work. The tubers used were collected according to Colombian protocols, guidelines, and regulations.

Results and discussion

Microstructure analysis of adsorbent

Figure 3 shows the microstructure of the adsorbent before (Fig. 3a) and after (Fig. 3b) being used for the removal of Orange II. In general, the microstructure of the starch is observed in spherical and oval. Also, no pores were observed in the images, suggesting that the material is not naturally porous.

Fig. 3
figure 3

Microstructure of the adsorbent before (a) and after (b) being used for the removal of Orange II.

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Table 2 shows the EDS elemental analysis of the adsorbent before and after OII removal assays. The predominant elements in the adsorbent were carbon (46.5% w/w) and oxygen (46.6% w/w). Bouhadjra et al.20 reported similar results in potato peels. These carbon and oxygen compositions are associated with the cellulose, hemicellulose, and lignin in potatoes23. Additionally, a significant increase in oxygen, sodium, and nitrogen was observed post-adsorption. Orange II (Table 1) likely contributed to these increased levels, but the rise in potassium, sodium, and oxygen could also be due to the use of sodium phosphate salts as buffer solutions.

Table 2 EDS elemental analysis of the adsorbent before and after Orange II removal.
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FTIR analysis of adsorbent

Figure 4 shows the FTIR spectrum of the adsorbent before and after the OII adsorption assays. The adsorbent exhibited characteristic absorption bands at 1733 cm−1, corresponding to C = O bonds, and at 1637 cm−1, associated with C = C vibrations of polyphenolic compounds20,23. The IR spectrum also showed characteristic bands at 2911 cm−1 (C–H2 asymmetric stretching) and 3266 cm−1 (O–H stretching), indicating the presence of methoxyl groups in cellulose, hemicellulose, and lignin. Figure 4 (inset) also shows changes in the FTIR spectrum after the OII adsorption assays. New bands at 1284 cm−1 and 1459 cm−1 correspond to symmetric stretching vibrations of S(= O)2 in the group -SO32− group and the stretching vibration of –N = N–, respectively29,30. Jin et al. (2014), observed these peaks during FTIR analysis of OII, while Kali et al.30, identified these bands after the adsorption of an azo dye on almond shells. It must be mentioned that after the OII removal assays, the adsorbent was colored orange. Considering that O–H moieties are known active sites for the adsorption of organic dyes23, this result suggests that the adsorbent is effective for OII removal.

Fig. 4
figure 4

FTIR spectra of adsorbent before (black line) and after (red line) the Orange II (OII) removal assays. The inset shows a detail of the spectra before (black line) and after (red line) the OII removal assays, highlighting the new peaks at 1459 cm−1 and 1284 cm−1 due to dye adsorption.

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Point of zero charge (PZC) of adsorbent

By definition, the point of zero charge (PZC) of a material is the pH value at which the surface charge of the tested material is zero under a given experimental condition (Bakatula et al.26). At this point, both positive and negative surface charges are equal. In principle, at pH values higher than the PZC, the adsorbent surface has a net negative charge. Conversely, the solid surface is positively charged in the cases when pH is lower than the PZC. Figure 5 shows the experimental curve of ΔpH as a function of pHi corresponding to PSBA. The PZC of adsorbent (PSBA) was identified at pH = 4.7 ± 0.2. Hence, the PSBA surface will exhibit positive and negative global charges at pH values below and above pH = 4.7, respectively. The obtained PZC value was lower than those reported by Jeddou et al.21, and Stavrinou et al.23 for potato peels (about 6). However, it must be noted that in the present work, pulp instead of potato peels was studied.

Fig. 5
figure 5

PZC determination of adsorbent (PSBA). Different symbols indicate independent experiments, line represents the linear regression (r2 = 0.9891).

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OII adsorption assays

Figure 6 shows the effect of the initial concentrations of adsorbent ([PSBA], g L−1) and orange II(OII, mg L−1) on dye removal (ROII, %) at pH 4. When the adsorbent concentration was doubled, the ROII values increased by approximately 1.4-fold. This behaviour was attributed to an increase in surface area and the number of available active sites for dye adsorption30,31. Additionally, the ROII values increased with adsorbate concentrations, reaching a maximum at around 25 mg L−1. Beyond this concentration, a noticeable decrease in ROII values was observed, likely due to the saturation of the PSBA surface by OII molecules. This behaviour has been previously reported by several authors21,23.

Fig. 6
figure 6

Effect of the initial concentrations of adsorbent ([PSBA], g/L) and dye (OII, mg L−1) on the OII removal (ROII, %) at pH4. Barr lines indicate the standard deviation.

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Before performing an equilibrium adsorption isotherm, it is crucial to evaluate the time necessary to achieve equilibrium. Figure 7 shows examples of OII adsorption onto PSBA as a function of time at different initial pH values. Kinetic assays demonstrated that in all cases, adsorption equilibrium was reached within the tested time interval. Equilibrium conditions were attained after at least 48 h, regardless of the tested pH. Under the experimental conditions in Fig. 7, the maximum OII removals at pH 4, 7, and 9 were 38%, 12%, and 18%, respectively. These results suggest that low pH values favour the adsorption of OII onto PSBA.

Fig. 7
figure 7

Typical examples corresponding to the adsorption of Orange II (OII, mg L−1) onto adsorbent (7.58 g L−1) as a function of time at different initial pH values. In all cases, bars represent the standard deviation, and lines correspond to the proposed model (Eqs. 4–6) using the coefficients shown in Table 5.

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As a general rule, pH is a key factor that strongly affects the maximum adsorption capacity (qm) of natural adsorbents20,26. Because the change in adsorption capacity as a function of pH depends on both the adsorbate and the adsorbent, it is crucial to evaluate the effect of pH on the adsorption process of new materials such as PSBA. Figure 8 shows the equilibrium adsorption isotherms of OII onto PSBA at the tested pH values. As a general trend, the adsorption capacity (qe) increased with the equilibrium concentration of OII (Ce), reaching a plateau that varied with pH.

Fig. 8
figure 8

Equilibrium adsorption isotherms of Orange II onto adsorbent at different pHs. Bars indicate the standard deviation. Continuous lines represent the Langmuir model (Eq. 2), dashed lines correspond to the Freundlich model (Eq. 3). Fitting results are shown in Table 3.

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Langmuir (Eq. 2) and Freundlich (Eq. 3) models were fitted to the data presented in Fig. 8. According to the coefficients of determination (r2) shown in Table 3, the adsorption isotherms are more accurately described by the Langmuir equation (Eq. 2) than by the Freundlich model (Eq. 3) within the tested pH range. The maximum adsorption capacities were determined to be 21.4 ± 1.8 mg g−1 (Langmuir) and 0.54 ± 0.13 mg g−1 (mg L−1)−1/n (Freundlich). Table 4 compares these values with those reported in the literature for dyes adsorption using waste and loss of potato. Notably, these studies employed adsorbent powders derived from potato peels, leaves, and stems through dehydration at temperatures near 100 °C, whereas the current study used lyophilized pulp from potato surpluses. Table 4 shows that, except for methylene blue, the maximum adsorption capacities for these adsorbents generally align with the range observed in this study. The discrepancy for methylene blue may be attributed to its smaller molecular size compared to the other dyes.

Table 3 Results corresponding to the fit of Langmuir (Eq. 2) and Freundlich (Eq. 3) models to the data shown in Fig. 8.
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Table 4 Comparison of the highest adsorption capacity values reported in the literature using waste, loss, and surplus of potato as dyes adsorbents.
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From the data presented in Table 3, it was calculated that the maximum adsorption capacity (qm) of the PSBA at pH = 4 was only 1.1 and 2.3 times higher than at pH = 7 and 9, respectively. Despite this, the main difference occurred at low OII equilibrium concentrations (Ce), as seen in Fig. 8. In this context, azo dyes such as Orange II typically exhibit a broad absorption band within the visible spectrum32. Generally, these dyes have maximum molar attenuation coefficients ranging from 1.6 (methyl red) to 182 (p-ethoxychrysoidine) a.u. mM−1 cm−133,34. Consequently, even relatively low concentrations of azo dyes can produce colored wastewater with high absorbance values. Furthermore, adsorption processes are often employed as a final step in effluent polishing to reduce specific pollutants to very low concentrations. This implies that such adsorption processes generally operate within a low concentration range35,36. Under these conditions, calculations demonstrate that the adsorption of OII by PSBA is significantly favored at pH = 4 compared to higher pH values. Several studies have reported similar findings regarding the effect of pH on the adsorption capacity of dyes onto potato peels and leaves20,21,23,31.

Considering that the PZC corresponding to PSBA is 4.7 (Fig. 5), the maximum value of qm was obtained when the solid surface was positively charged (pH 4). Conversely, results demonstrate that at pH values higher than PZC, the adsorption of OII was not favoured by the negatively charged PSBA surface. A similar trend has been reported by Jeddou et al.21 and Stavrinou et al.23 during the adsorption of anionic dyes on potato peel at room temperature. At this point, it is worth mentioning that OII is a diprotic acid with pKa1 = 8.26, and pKa2 = 11.4 (Table 1), corresponding to the deprotonation of the –SO3H moiety of the benzene ring, and the –OH of the naphthalene ring, respectively24,37. Using these pKa values, the fraction corresponding to each dye species as a function of pH can be calculated (Supporting Information, Item 1). According to Fig. S1, for pH values lower than 6 the undissociated OII was the main dye species (99.99%). Then, the monovalent form of OII increases as a function of the pH. However, at pH = 7, the undissociated fraction is still higher than the monovalent species, being for 95%, and 5%, respectively. The monovalent OII species becomes the main form of OII when the pH value increases to 9. In this case, undissociated and monovalent species are about 15%, and 85%, respectively. Thus, within the tested pH range in the present work (4–9), undissociated or monovalent OII are the dominant species. Considering that the highest qm value was obtained at pH = 4 (Fig. 8, Table 3) and then, qm decreased for higher pH values, the low OII adsorption capacity of pH values above the PZC of the PSBA could be due to the result of the electrostatic repulsion between the monovalent form of OII and the negatively charged surface of the PSBA.

Modelling the adsorption kinetics of Orange II (OII) onto adsorbent (PSBA)

In order to select the best operating conditions in full-scale batch processes, the knowledge of the adsorption kinetics of a given adsorbate onto an adsorbent is crucial. Several kinetic models, such as pseudo-first and pseudo-second-order, Weber–Moris, and Elovich, are available in the literature. Among these models, the pseudo-first and the pseudo-second-order kinetic equations are the most used ones38. It is important to note that these semi-empirical models focused attention on the evolution of the adsorption capacity (q) instead of the aqueous adsorbate concentration as a function of time. Unfortunately, in most cases, the conciliation between these models and the experimental adsorption equilibrium isotherm cannot be achieved. For example, pseudo-first and pseudo-second-order models contain two coefficients, a kinetic constant, and an asymptotic q value that represents the adsorption capacity at long contact times (e.g., the equilibrium condition). As a general rule, these coefficients strongly depend on the tested initial conditions. Furthermore, in most cases, there is no theoretical link between these kinetic coefficients and the experimental adsorption equilibrium isotherm.

In the present work, the adsorption kinetics was represented by the model proposed by Ferro Orozco et al. (2010). According to several authors, the total concentration of adsorption sites (TS) is proportional to the adsorbent concentration30,31. In the present model, α (mmol g−1) represents the proportionality constant between the amount of the adsorbent (PSBA in this work) and adsorption sites. To simplify the model, Ferro Orozco et al.39 assumed that all adsorption sites are equal and independent of each other. Thus, the occupation of a free site does not affect other sites. Accordingly, a free adsorption site (FS) can be occupied by an adsorbate molecule to produce an occupied site (OS):

$$C + FS\begin{array}{*{20}c} {\to ^{{k_{a} }} } \\ {\mathop \leftarrow \limits_{{k_{d} }} } \\ \end{array} OS$$
(4)

where C represents the adsorbate (e.g., OII), FS and OS are free and occupied adsorption sites, and ka (mM−1 h−1) and kd (h−1) are the adsorption and desorption kinetic constants, respectively. Besides, for a given concentration of the adsorbent (PSBA in this work), the balance of adsorption sites is as follows:

$$\left[ {TS} \right] = \alpha \left[ {PSBA} \right] = \left[ {FS} \right] + \left[ {OS} \right]$$
(5)

According to Eq. (4), rates corresponding to C, FS, and OS are as follows:

$$\frac{d\left[ C \right]}{{dt}} = \frac{{d\left[ {FS} \right]}}{dt} = - \frac{{d\left[ {OS} \right]}}{dt} = - k_{a} \left[ C \right]\left[ {FS} \right] + k_{d} \left[ {OS} \right]$$
(6)

It is important to note that the equalities represented by Eq. (6) are valid only if the variables are expressed in mol but not in weight. For this reason, the use of mol-based units instead of weights to express concentrations facilitates the development of kinetic models.

By definition, the adsorption equilibrium occurs when adsorption and desorption rates are equal:

$$k_{a} C_{e} \left[ {FS} \right]_{e} = k_{d} \left[ {OS} \right]_{e}$$
(7)

where the subindex e refers to the equilibrium condition. Then, combining eqs.(6) and (7), the following expression can be obtained:

$$\frac{{\left[ {OS} \right]_{e} }}{{\left[ {PSBA} \right]}} = \alpha \frac{{C_{e} }}{{\left( {\frac{{k_{d} }}{{k_{a} }}} \right) + C_{e} }}$$
(8)

The term \(\frac{{\left[ {OS} \right]_{e} }}{{\left[ {PSBA} \right]}}\) (mmol g−1) represents the amount of OII adsorbed (mmol) per unit mass (g) of PSBA in equilibrium with the aqueous phase OII concentration (Ce). Considering that Eqs. (2) and (8) represent the equilibrium between adsorption between the adsorbent (PSBA) and the adsorbate (OII), from the comparison between Eqs. (2) and (8), it can be concluded that \(\frac{{\left[ {OS} \right]_{e} }}{{\left[ {PSBA} \right]}} = q_{e}\), \(\alpha = q_{m}\), and \(\frac{{k_{d} }}{{k_{a} }} = K_{L}\). Thus, Eq. (8) demonstrates that the Langmuir equation (Eq. 2) can be derived from the kinetic model proposed by Ferro Orozco et al.39. Moreover, these relations are very useful for reducing the number of parameters to fit. In particular, because Langmuir coefficients were known (Table 3), using the above-mentioned relations, only one parameter of the model (ka in this work) is necessary to fit. This approach ensures compatibility between the fitting results of the Langmuir equation with the results obtained by fitting the tested kinetic model to the change in the OII concentration as a function of time.

The kinetic model (Eqs. 4–6) was fitted to the experimental data (OII concentration as a function of time for different initial OII and PSBA concentrations) at the three tested pH values using the software package Gepasi 3.3040. To integrate the system of differential equations, the routine LSODA (Livermore Solver of Ordinary Differential Equations) was selected. Briefly, the LSODA algorithm measures the stiffness of the equations and switches the integration method dynamically according to this measure. For non-stiff regions, the Adams integration method with variable step size and variable order up to 12th order is used; for stiff regions the Gear (or BDF) method with variable step size and variable order up to 5th order is used. Additionally, the Multistart Optimization algorithm (with Levenberg–Marquardt local optimization) was selected as the optimization method. Multistart is a hybrid stochastic–deterministic optimization method that runs several simple local optimizations using the gradient descent method, each time starting from a different initial guess. While the first start takes for initial guess of the parameter values entered by the user, subsequent starts are generated randomly within the boundaries for the adjustable parameters selected by the user. According to Mendes & Kell41, the Multistart Levenberg–Marquardt method is one of the most efficient gradient optimizers among the available ones in Gepasi.

Fitting results corresponding to the tested kinetic model (Eqs. 4–6) are shown in Table 5. As a general rule, a satisfactory agreement between experimental and model data was obtained (Fig. 5; Fig. 9, left panel). For all the tested pH, coefficients of determination (r2) were higher than 0.99 (Table 5). Moreover, Fig. 9 (right panel) demonstrates that 50% of the simulated data had absolute errors less than 0.006 mM for all the tested pH values. Table 5 also showed a strong decrease of ka for pH values higher than 4. This behaviour is in accordance with the above-mentioned electrostatic repulsion effect between the negatively charged PSBA surface at pH values above the PZC, and the OII monovalent anionic species (see Sect. "OII adsorption assays").

Table 5 Fitting results corresponding to the tested kinetic model (Eqs. 4–6).
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Fig. 9
figure 9

Parity plots (left panel) between experimental data and the adsorption kinetic model (Eqs. 4–6), and cumulative distribution of absolute fitting errors (right panel). Continuous lines represent the perfect correlation. Dashed lines correspond to a cumulative probability of 50%.

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Adsorption processes are often used as a final polishing step to meet discharge criteria of certain compounds, such as azo dyes, that could not be fully removed by conventional methods35,42,43. In the case of textile wastewater, the main problem is the high and unnatural color due to the presence of dyes after the treatment44. Once a given adsorbent is selected, the key point in designing a batch adsorption process is to estimate the adsorbent concentration (PSBA in this work) necessary to meet a certain effluent discharge limit. For example, the true colour (e.g., the colour after removing suspended solids and turbidity) discharge limit in Taiwan is 400 ADMI units44, while in India is 150 ADMI units45. These discharge limits correspond to maximum OII concentrations (CL) of 0.042 (14.7 mg L−1), and 0.016 mM (5.6 mg L−1), respectively. Details concerning the transformation of OII concentrations to ADMI units can be found in Supplementary Information, Item 2.

Suppose you want to design a batch adsorption process as the final polishing process for a certain wastewater, for example. For long contact times, adsorbate and adsorbent eventually will reach the adsorption equilibrium. So, the aqueous concentration of the adsorbate (OII in this work) represents the outlet concentration of OII of this adsorption system. Assuming that the discharge limit (CL) represents the concentration of dye in equilibrium with the adsorbent, the minimum concentration of the adsorbent \(\left( {\left[ {{\text{PSBA}}} \right]_{{{\text{min}}}} } \right)\) necessary to meet the discharge limit can be calculated as a function of the initial (e.g., wastewater) OII concentration (C0) by combining and rearranging Eqs. (1) and (2) as follows:

$$\left[ {PSBA} \right]_{min} = \frac{{\left( {C_{0} - C_{L} } \right)\left( {K_{L} - C_{L} } \right)}}{{q_{m} C_{L} }}$$
(9)

For example, considering a wastewater containing 0.1 mM of OII (35 mg L−1) at pH = 4, and assuming a discharge limit of 400 ADMI units (OII = 0.042 mM = 14.7 mg L−1), according to Eq. (9) the concentration of PSBA to reach the discharge limit is 11.37 g L−1. However, it is important to note that equilibrium conditions were assumed in Eq. (9). Accordingly, this assumption implies an infinite contact time between the adsorbent and the solution to be treated, which is not technically feasible. In fact, due to kinetic restrictions, the adsorbent concentration necessary to achieve the discharge limit within a practical contact time must be higher than the calculated one employing Eq. (9). In this sense, for a given adsorbent concentration, the kinetic model used in this work (Eqs. 4–6) can be employed to obtain the critical contact time (tC) necessary to attain the discharge limit. Figure 10a shows some simulated OII profiles as a function of time corresponding to different PSBA concentrations. From the intersection between these curves and the assumed discharge limit (dashed line in Fig. 10a), tC values as a function of PSBA concentrations can be obtained. Figure 10b demonstrates that as PSBA decreases to the minimum PSBA concentration obtained by Eq. (9) (dashed line in Fig. 10b), tC increases and tends to infinity, which represents the equilibrium condition. Conversely, the higher the PSBA, the lower the tC. For example, when the PSBA concentration is increased from 12 to 40 g L−1, the contact time necessary to achieve the discharge limit decreases from 26 to 3.35 h. Although lower contact times either represent smaller adsorption tanks or a higher treatment capacity, it must be noted that higher PSBA concentrations also increase the cost associated with the adsorbent. In this sense, the availability of a low-cost adsorbent, such as PSBA, favours the selection of a high adsorbent concentration, reducing the cost associated with higher adsorption tanks, for example. However, it must be noted that the optimum solution depends on many factors, such as land availability and cost, primary and secondary treatments, wastewater characteristics, inlet dye concentration, type of dye, local discharge limits, and others. In this sense, the adsorption model used in the present work can be useful for designers to find the most suitable solution for each particular case.

Fig. 10
figure 10

(a) Simulated Orange II (OII) profiles as a function of time, and b) critical time necessary to achieve a discharge limit of 400 ADMI units (14.7 mg L−1 of OII, dashed line in a) for different adsorbent concentrations (PSBA). Dashed line in (b) represents the minimum PSBA concentration to achieve the discharge limit (Eq. 9). For all simulations, coefficients corresponding to pH = 4 (Table 5) were used.

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Conclusions

This study evaluated the use of potato surpluses as adsorbents for the removal of Orange II from aqueous media. Characterization of the adsorbents confirmed effective Orange II adsorption. The results indicated that the Langmuir model provided a better fit than the Freundlich model. The maximum adsorption capacity was significantly higher at pH 4, attributed to favourable electrostatic interactions between the cationic adsorbent surface and the anionic dye. The developed kinetic model demonstrated high accuracy, aligning well with Langmuir isotherm results and providing a strong theoretical foundation for predicting adsorption kinetics. The critical contact time required to achieve the minimum adsorbent concentration for a discharge limit of 14.7 mg/L was determined, with simulation profiles revealing that contact times decreased as the adsorbent concentration was increased from 12 to 40 g L−1. This study offers a cost-effective and environmentally sustainable solution for wastewater treatment, advancing the use of potato surpluses in dye removal processes and optimizing batch adsorption processes to meet discharge criteria for coloured wastewater.