Trimethoprim Removal from Aqueous Solutions via Volcanic Ash-Soil Adsorption: Process Modeling and Optimization

: Antibiotic contamination of water sources is a significant environmental and public health concern. This contamination is classified among the most dangerous types of pollution currently because of their harmful effects. Therefore, it is essential to identify effective and environmentally friendly ways to deal with those dangerous compounds. Within this context, this work looked into whether soils made from volcanic ash could be used as cost-effective adsorbents to remove the antibiotic trimethoprim (TRM) from aqueous solutions. To examine the impacts of the main operating parameters on TRM removal, which are the initial antibiotic concentration (C), contact time (t), stirring speed (S), and solid-to-liquid ratio (R), a Central Composite Design (CCD) based on the Response Surface Methodology (RSM) was employed. Full quadratic polynomial models were used to correlate the experimental data, allowing for the estimation of each factor’s influence. With a predicted removal efficiency of 77.59%, the removal process optimization yielded the following set of optimal conditions: C = 4.5 mg/L, t = 45.5 min, S = 747 rpm, and R = 0.04 g/mL. Experiments conducted under predicted ideal conditions supported both the result and the previously developed model’s capacity for prediction. Additionally, the adsorption mechanism was also proposed based on the characterization of the adsorbent before and after the treatment. The study’s findings provide the possibility of using soils formed from volcanic ash as a cost-effective adsorbent material for the removal of TRM and likely other similar pollutants from contaminated waters.


Introduction
The health of all living organisms and ecosystems depends on protecting natural water sources from harmful pollution [1].Antibiotics, as a class of pharmaceuticals, account for 15% of all medication use and represent a major risk to aquatic ecosystems and human health [2].Their presence in water systems harms bacteria or limits their growth, frequently resulting in the propagation of antibiotic-resistance genes, which, in turn, promotes bacterial-resistant illnesses and causes prolonged contamination of water resources [3].Increasing populations of living organisms and new infectious diseases have contributed significantly to a 65% rise in antibiotic consumption worldwide in the last few years, with the risk of further increasing, nearly doubling by 2030 [4].
Trimethoprim (TRM) is extensively utilized as an antibiotic on a global scale due to its exceptional effectiveness and accessibility [5].TRM belongs to a category of chemotherapeutic agents that exhibit synergistic antibacterial activity; it is used for treating infections, treating enterocolitis, and enhancing animal growth in the livestock sector, including in feed supplements [6].TRM can only be metabolized by approximately 20% in humans and animals and is excreted through feces and urine, with significant amounts of effluent in the sewage system [7].Due to its high resistance to biodegradation and widespread use and application, TRM has become ubiquitous in various water sources, including rivers, groundwater, lakes, seawater, drinking water, tap water, wastewater, and irrigation water, in concentrations between ng/L and µg/L [8].Research has also detected it in soil, sewage sludge, and sediment at amounts reaching up to nanograms per gram (ng/g) [9].Multiple studies have emphasized that TRM has harmful consequences for non-target aquatic creatures, such as phytoplankton, zooplankton, and fish.These effects include increased mortality, impaired development and reproduction, as well as the emergence of antibiotic-resistant genes and infections in the environment [10].For this reason, it is classified as one of the fourteen pharmaceuticals that pose a high risk in hospital wastewater [11].As a result, there is an urgent need for approaches allowing the efficient removal of TRM from water, both for human consumption and industrial or agricultural applications.
Various methods have been used to remove antibiotics from water, including reverse osmosis, ion exchange, coagulation, co-precipitation, extraction, membrane filtration, electrochemical oxidation, and adsorption [10].In order to select the best approach, it is essential to take into account multiple factors, including the features of the removal technology, the optimization of the process, and its associated costs [12].TRM can be effectively eliminated via adsorption, and this method is preferred over others due to its simplicity, relatively low cost, eco-friendliness, and the absence of transformation during treatment [13].Various adsorbents, including graphene oxide, chitin/bentonite composite, and activated carbon, have been studied for their ability to absorb TRM [14].However, more adsorbents need to be tested to enhance the efficiency of adsorption.
Recent studies have shown that volcanic ash-derived soils (VADS) can exhibit significant adsorption capabilities for various substances from water, with adsorption capacities up to 40 times higher than those of nonvolcanic soils [15,16].VADS have excellent physical, chemical, and biological properties, such as high stability, low bulk density, soil aggregation, high permeability, high water storage, significant anion sorption capacity, and excellent resistance to water erosion [17,18].These soils also show that they are easily available in natural environments.VADS constitute about 1% of the Earth's surface and can be found in regions characterized by predominant geochemical features associated with currently active or recently dormant volcanoes [19].Despite their vast quantity, only 10% of these soils are currently used for agricultural activities, leaving the majority available for other potential uses [20].
As it is known, the effectiveness of an adsorption process relies on various factors, including initial solute concentration, contact time, stirring speed, and solid-to-liquid ratio.In the majority of published works, the effect of each factor was examined individually while holding the other factors constant [21].This approach is not the most efficient, as it involves huge experimental efforts and high research costs, and, above all, it does not allow for identifying the presence of synergistic or antagonistic effects between the factors [22].Recently, there has been a growing trend in using new approaches to enhance the optimization and modeling of the adsorption process [23].Response surface methodology (RSM) is a widely used approach for conducting experimental designs, modeling, evaluating independent variables, and optimizing process parameters [24,25].It uses graphical technology to visualize mathematical function connections, reducing experiment time and cost [26].RSM has been proven effective in improving process parameters for contaminant removal [27,28].
To our knowledge, there is still a lack of published research on the use of volcanic ash soils as an adsorbent for removing pollutants from water.Additionally, no studies have been conducted to model and optimize this process using response surface approaches.Furthermore, determining ideal operating parameters for TRM removal provides useful insights for future applications, as does assessing the properties of volcanic ash soils postadsorption to illustrate its potential for reuse in subsequent adsorption processes.For this purpose, the main objective of this study is to investigate the potential of volcanic ash-derived soils as adsorbents for the removal of trimethoprim from aqueous solutions.Through the utilization of a Central Composite Design (CCD) approach and response sur-Water 2024, 16, 2209 3 of 14 face methodology, the effects of key operating parameters on TRM removal and optimized the adsorption process were analyzed.The results were correlated by a polynomial model, which was used to evaluate the optimal operating conditions.The study highlighted the advantages offered by soils derived from volcanic ash, showcasing their potential for use as a valuable adsorbent, which is also valorization.

Chemicals
Reagents used in this research include TRM (>99% purity), acetonitrile (analytical grade), ultra-pure water, and so on.They were all obtained from Sigma-Aldrich.The volcanic sand was sampled on Vulture Mount (40 • 57 ′ 02.4 ′′ N 15 • 37 ′ 52.9 ′′ E), which is located 56 km north of the city of Potenza in the Basilicata region (Italy).Volcanic sands naturally form morphological features and physical behavior similar to quartz-rich sands.They exhibit a greater variety of mineral compositions and textures qualitatively because they seem more complicated and have less documentation than the much more prevalent sand sheets that are rich in quartz [29].

XRD Characterization
X-ray powder diffraction (XRPD) analysis was employed to determine the mineralogical composition, providing rapid phase identification and information on unit cell dimensions.The technique involves finely grinding and homogenizing the material, then directing focused X-rays onto the powdered sample.The study utilized a powder diffractometer (Philips X'Pert PW3040, Almelo, The Netherlands) equipped with Cu-Kα radiation, operating at 40 kV, 30 mA, and a 0.02 • (2θ) step size configuration for whole-rock mineralogy determination of the analyzed minerals.

Determination of Antibiotic Concentration
The TRM concentration was determined using an Agilent Technologies High-performance liquid chromatography (HPLC) 1200 system equipped with a photodiode array detector set a λ = 271 nm.The column used was a Luna C18 (150 mm × 4.6 mm × 5 µm particle size) provided by Phenomenenex (Madrid, Spain) and a pre-column (4 mm × 2 mm; 5 µm particle size) packed with the same material as the column.The injection volume was 20 µL, and the flow rate was 0.8 mL min −1 .The mobile phase consists of a biphasic gradient, ultrapure water with 0.1% formic acid (solvent A) and acetonitrile (solvent B), structured as follows: 0-3 min, 5% B; 3-7 min, 40% B; 7-8 min, 40% B; 8-9 min, 100% B; 11-12 min, 5% B; 12-15 min, 5% B. The method used in this study was similar to [30], and the limits of detection and quantification of trimethoprim were found to be 0.008 mg/L and 0.0242 mg/L, respectively.

Batch Study
In this study, a known quantity of volcanic ash (between 0.01 and 0.05 g/mL) was added to a 250 mL beaker containing 100 mL of TRM solution, and the mixture was magnetically stirred at a fixed rate.After the desired time for the adsorption process, volcanic ash was separated via filtration (0.2 µm polytetrafluoroethylene polymer filters PTFE), and the residual TRM concentration in the solution was analyzed using HPLC at the wavelength of 271 nm.All experiments were made in water at its natural pH (7.5 ± 0.2) in order to obtain results of interest for a hypothetical wastewater treatment in which the pH was not varied.During the adsorption process, the pH was monitored and found to be substantially constant, with percentage differences between initial and final values of the order of 2-4%.

Experimental and Modeling Design
A CCD was used to evaluate the effects of initial antibiotic concentration (C), contact time (t), stirring speed (S), and solid-to-liquid ratio (R) on TRM removal.These factors were selected as input variables for RSM because preliminary tests on this system showed that they exerted a significant effect on adsorption.The CCD consisted of a full two-level factorial design (24 points), eight axial points at a distance ±α from the central point, and six replicates at the center of the domain.The value of α was taken as (2 4 ) 1/4 = 2 to ensure the orthogonality and rotatability of the design [31].Factor levels were chosen based on preliminary experiments and the need to cover a range of values of practical interest.They are reported in real and dimensionless coded values in Table 1.The coded values (x i ) were calculated from the real ones (X i ) using Equation (1) [32]: where X i,0 is the central point value, i is the factor, and ∆X i is the step change value.The percentage of antibiotic removal from the aqueous solution was taken as the response variable (y).It was calculated using Equation ( 2): where c 0 is the initial TRM concentration in the liquid (mg/L) and c is the concentration at the end of the adsorption process (mg/L).The overall experimental design consisted of 30 runs, which were performed in random order to minimize the effects of uncontrolled factors (Table 2).For the statistical analysis of the results, the Design-Expert ® software (version 7.0.0,Stat-Ease, Inc., Minneapolis, MN, USA) was used.
Table 2. Experimental design layout.x i is the dimensionless coded values for the i-th factor, y is the observed response, SO is the standard order, and RO is the run order of experiments.

Adsorbent Characterization
X-ray diffraction analysis of the volcanic ash powder sample was performed as shown in Figure 1.The XRD peaks show the presence of both crystalline and amorphous phases.This aligns with the expected composition of volcanic ash, which is primarily a mixture of oxides such as SiO 2 , Al 2 O 3 , and Fe 2 O 3 with minor amounts of MgO and K 2 O [33,34].The crystalline phases identified were dominated by olivine, including forsterite (Mg 2 SiO 4 , PDF 87-10619) and fayalite (Fe 2 SiO 4 , ICDD 20-1139), followed by augite (Ca, Mg, Fe, Al) (Si, Al) 2 O 6 , PDF 70-3753).This finding is consistent with previous studies on volcanic ash composition [35].

Adsorbent Characterization
X-ray diffraction analysis of the volcanic ash powder sample was shown in Figure 1.The XRD peaks show the presence of both crystalline an phases.This aligns with the expected composition of volcanic ash, which mixture of oxides such as SiO2, Al2O3, and Fe2O3 with minor amounts of [33,34].The crystalline phases identified were dominated by olivine, inclu (Mg2SiO4, PDF 87-10619) and fayalite (Fe2SiO4, ICDD 20-1139), followed by a Fe, Al) (Si, Al)2O6, PDF 70-3753).This finding is consistent with previous s canic ash composition [35].The amount of mineral oxides contained in volcanic ash is shown i olivine group minerals are silicate minerals, and in particular nesosilicates.T olivine atomic structures are quite similar since in pyroxenes the SiO4 tetra single chains, in olivine minerals (forsterite and fayalite) these tetrahedron The amount of mineral oxides contained in volcanic ash is shown in Table 3.The olivine group minerals are silicate minerals, and in particular nesosilicates.The augite and olivine atomic structures are quite similar since in pyroxenes the SiO 4 tetrahedrons form single chains, in olivine minerals (forsterite and fayalite) these tetrahedrons are isolated.The shift in hump intensity before (18 and 45 • , 2θ) indicates that there is a significant amount of silica in the reactive phase of volcanic ash [35].These minerals' existence in the examined sample suggests that the rock was formed by volcanic activity [36].When volcanic ashes are produced during phreatic eruptions, they are mostly composed of mineral components and hydrothermally altered lithic material within a clay matrix [37].

Model Fitting
Several polynomials, including linear, two-factor interaction, quadratic, and cubic models, were tested for their ability to fit the data listed in Table 2.The best result was obtained with a full quadratic model containing linear, quadratic, and interaction terms following Equation (3): where y is the response, x i is the coded independent variables, a 0 is the intercept, and a i , a ii , and a ij are the linear, quadratic, and interaction coefficients.The model was then reduced to include only the statistically significant terms.To this end, a stepwise procedure with entrance and removal levels of 0.1 was used.This procedure led to the equation ( 4): Statistical analysis by ANOVA indicated that the model was statistically significant (p < 0.0001) while the lack-of-fit was not (p = 0.3599) (Table 4).Furthermore, internally studentized residuals were randomly scattered between −3 and +3, with no outliers detected (Figure 2).The estimated coefficients, together with their standard errors, t-statistics, and p-values, are reported in Table 5.The estimated coefficients, together with their standard errors, t-statistics, and p-val ues, are reported in Table 5.

Evaluation of the Influencing Parameters
The Pareto chart shown in Figure 3 provides a clear indication of the effect of eac factor, alone or in combination, on TRM removal.All the factors had a significant effect o TRM removal.Two of them, t and R, affected the process response through both a linea and a quadratic term, while C and S had only a linear effect.Concerning the linear terms the initial antibiotic concentration (C) made a negative contribution to the response vari able, i.e., an increase in its value had a negative effect on the removal efficiency.The linea effects of the other parameters were positive and increased as follows: S < R < t.There wer no interactions between factors, indicating that each factor exerted its effect independentl of the others.

Evaluation of the Influencing Parameters
The Pareto chart shown in Figure 3 provides a clear indication of the effect of each factor, alone or in combination, on TRM removal.All the factors had a significant effect on TRM removal.Two of them, t and R, affected the process response through both a linear and a quadratic term, while C and S had only a linear effect.Concerning the linear terms, the initial antibiotic concentration (C) made a negative contribution to the response variable, i.e., an increase in its value had a negative effect on the removal efficiency.The linear effects of the other parameters were positive and increased as follows: S < R < t.There were no interactions between factors, indicating that each factor exerted its effect independently of the others.
Perturbation plots and response surfaces were examined in order to better understand the effects of the factors that were explored.Perturbation plots were generated by changing the value of each factor over the range [−1, 1] while setting the other factors to their central values (0).They are shown in Figure 4, from which it can be seen the non-monotonic variation of the response variable with contact time (t) and solvent-to-liquid ratio (R), consistently with the presence of non-zero quadratic terms in the model equation.Perturbation plots and response surfaces were examined in order to better understand the effects of the factors that were explored.Perturbation plots were generated by changing the value of each factor over the range [−1, 1] while setting the other factors to their central values (0).They are shown in Figure 4, from which it can be seen the nonmonotonic variation of the response variable with contact time (t) and solvent-to-liquid ratio (R), consistently with the presence of non-zero quadratic terms in the model equation.Perturbation plots and response surfaces were examined in order to better understand the effects of the factors that were explored.Perturbation plots were generated by changing the value of each factor over the range [−1, 1] while setting the other factors to their central values (0).They are shown in Figure 4, from which it can be seen the nonmonotonic variation of the response variable with contact time (t) and solvent-to-liquid ratio (R), consistently with the presence of non-zero quadratic terms in the model equation.

Optimization and Model Validation
An evaluation of the model structure (Equation ( 4)) and the values of the model coefficients indicates that the removal of TRM from aqueous solutions can be maximized by selecting the proper process conditions.Maximizing the response variable was used to get the optimal value across the entire explored domain (−α ≤ xi ≤ α).This was accomplished using the gradient descent approach with numerous randomly chosen starting points.The following results were obtained: C = 4.5 mg/L; t = 45.5 min; S = 747 rpm; R = 0.04 g/mL.

Optimization and Model Validation
An evaluation of the model structure (Equation ( 4)) and the values of the model coefficients indicates that the removal of TRM from aqueous solutions can be maximized by selecting the proper process conditions.Maximizing the response variable was used to get the optimal value across the entire explored domain (−α ≤ xi ≤ α).This was accomplished using the gradient descent approach with numerous randomly chosen starting points.The following results were obtained: C = 4.5 mg/L; t = 45.5 min; S = 747 rpm; R = 0.04 g/mL.

Optimization and Model Validation
An evaluation of the model structure (Equation ( 4)) and the values of the model coefficients indicates that the removal of TRM from aqueous solutions can be maximized by selecting the proper process conditions.Maximizing the response variable was used to get the optimal value across the entire explored domain (−α ≤ x i ≤ α).This was accomplished using the gradient descent approach with numerous randomly chosen starting points.The following results were obtained: C = 4.5 mg/L; t = 45.5 min; S = 747 rpm; R = 0.04 g/mL.The predicted response rate was 77.59%, with a 95% confidence interval of 74.35-80.83%.Additional tests were conducted to validate the model under optimal conditions and at places both within and outside the factorial domain.The findings are presented in Table 6.All model predictions were found in good agreement with the experimental values, the average percentage error being 2.98%.This clearly supports the reliability of the developed model and its ability to provide a good description of the antibiotic removal process under the investigated conditions.

Adsorbent Characterization after Adsorption
Figure 7 highlights the significant changes in the XRD spectrum of the volcanic ash after trimethoprim (TRM) adsorption.These changes include variations in peak intensity, peak shifts, disappearance of existing peaks, and emergence of new peaks.The decrease in intensity of some crystalline peaks suggests a potential conversion of some crystalline material to a more amorphous state upon TRM adsorption [38].This could indicate interactions between TRM and the crystalline phases of the volcanic ash.Additionally, the presence of new peaks after adsorption might be attributed to the presence of adsorbed TRM or its interaction products with the volcanic ash.However, due to the amorphous nature of TRM, these new peaks most likely reflect low-intensity peaks as TRM is amorphous, instead of the sharp high-intensity peaks usually seen for crystalline materials [39].Actually, XRD has limits when it comes to identifying amorphous phases.The observed peak intensity changes, peak shifts, and the appearance of novel peaks in the XRD pattern after adsorption all provide proof for the effective interaction of TRM with volcanic ash, hence validating that volcanic ash has potential as an adsorbent for the removal of trimethoprim by chemisorption.

Adsorbent Characterization after Adsorption
Figure 7 highlights the significant changes in the XRD spectrum of the volca after trimethoprim (TRM) adsorption.These changes include variations in peak in peak shifts, disappearance of existing peaks, and emergence of new peaks.The d in intensity of some crystalline peaks suggests a potential conversion of some cry material to a more amorphous state upon TRM adsorption [38].This could indicat actions between TRM and the crystalline phases of the volcanic ash.Additiona presence of new peaks after adsorption might be attributed to the presence of ad TRM or its interaction products with the volcanic ash.However, due to the amo nature of TRM, these new peaks most likely reflect low-intensity peaks as TRM is phous, instead of the sharp high-intensity peaks usually seen for crystalline materi Actually, XRD has limits when it comes to identifying amorphous phases.The ob peak intensity changes, peak shifts, and the appearance of novel peaks in the XRD after adsorption all provide proof for the effective interaction of TRM with volcan hence validating that volcanic ash has potential as an adsorbent for the removal o thoprim by chemisorption.Table 7 displays the amount of minerals in volcanic ash after the adsorption o The comparison of mineral percentages in VADS before and after the adsorption Table 7 displays the amount of minerals in volcanic ash after the adsorption of TRM.The comparison of mineral percentages in VADS before and after the adsorption (Tables 3 and 7) reveals remarkable variations in the mineral composition, which is in line with XRD results.The mineral composition of VADS undergoes discernible changes in response to TRM adsorption, particularly in the percentages of forsterite and fayalite.Forsterite, which was 51.25% before adsorption, decreased significantly to 30.46% after TRM adsorption.This significant decrease suggests that forsterite is actively involved in TRM adsorption.This decrease may also result from increased silicon and magnesium leaching following adsorption.Fayalite contributes 27.81% of the mineral composition before adsorption, whereas this percentage increases significantly to 47.24% after TRM adsorption.This observed increase indicates an affinity between fayalite and TRM molecules during the adsorption process.These variations reflect the intricate interactions that occur during adsorption, with each mineral playing a unique role in impacting the overall efficacy of TRM removal.Further research into the precise roles of these minerals in TRM adsorption will help to a more comprehensive knowledge of the adsorption mechanism.The optimum parameters, which are C = 4.5 mg/L, t = 45.5 min, S = 747 rpm, and R = 0.04 g/mL, have demonstrated a high rapid adsorption rate of 75.88% in just 45.5 min.The unique properties of VADS, such as their composition, which produces an internal surface perfect for adsorption, may be the cause of this efficiency.The chemical composition of the VADS, interactions, and mass transfer all play a role in TRM adsorption.The mechanism of TRM adsorption into VADS can be through a series of chemical and physical interactions between the TRM molecule and the VADS [40,41].TRM adsorption on VADS is influenced by their chemical composition, especially the presence of metals such as aluminum and iron, as shown in the table of minerals in volcanic ash (Olivina (Mg, Fe) 2 SiO 4 and Augite (Si, Al) 2 O 6 ).These metal oxides can form complexes with the trimethoprim molecule, which increases its adsorption onto the VADS [42].According to the influence of the initial concentration, mass transfer plays a vital role during adsorption.Higher starting TRM concentrations result in decreased removal efficiency but increased adsorption capacity.The higher concentration functions as a driving factor to overcome the mass transfer resistance of TRM molecules between the aqueous phase and the adsorbent surface [40].The surface sorption interaction of TRM in the ash particle is important as both TRM and volcanic ash components contain functional groups able to form hydrogen bonds.Hydrogen bonding interactions between TRM and the volcanic ash surface can aid in adsorption by increasing TRM's surface stability by creating hydrogen bonds with its functional groups [43].TRM molecules have aromatic rings in their structure, the same as volcanic ash does.Therefore, weak interactions between aromatic rings, known as π-π interactions, could participate in the adsorption [44].Some volcanic ash components can be hydrophobic, and TRM is modestly hydrophobic (as demonstrated by log K ow = 0.91, which means a lipophilic/hydrophobic and nonpolar molecule [45]).These hydrophobic interactions between TRM and the volcanic ash surface could contribute to adsorption, particularly for non-polar portions of the molecule [45].

Conclusions
The purpose of this study was to provide a preliminary evaluation of the soils produced from volcanic ash viability as a sustainable adsorbent to remove pharmaceutical pollutants from water.Process analysis using RSM modeling allowed the evaluation of optimum adsorption conditions, under which more than 77% of the pollutant was removed.Furthermore, the influence of process variables, alone or in combination, was evaluated.Regarding the selection of these variables, it should be underlined that the pH was not included in the set of design factors as it was assumed that wastewater would be treated at its natural pH.However, the water pH could be easily included among the influential factors if one thinks of modifying the pH value in the treatment.Future research should be directed at investigating the removal capacity of this material for other pollutants and providing an in-depth understanding of the adsorption mechanisms.To this end, it is important to remember that RSM is a typical black-box approach, aimed at seeking simplified relationships to correlate a response variable with the most significant influencing factors, ignoring or circumventing any physical considerations.From this analysis, however, it is possible to obtain useful indications on the conditions in which to study the system of interest in more detail, for example through kinetic and/or thermodynamic modeling.

Figure 1 .
Figure 1.X-ray diffraction analysis of volcanic ash before adsorption.

Figure 1 .
Figure 1.X-ray diffraction analysis of volcanic ash before adsorption.

Figure 3 .
Figure 3. Pareto diagram for the model coefficients.

Figure 4 .
Figure 4. Perturbation plots for (a) initial TRM concentration; (b) contact time; (c) stirring speed; and (d) solid-to-liquid ratio.The levels of the other three elements were plotted at their central values for each diagram.

Figure 3 .
Figure 3. Pareto diagram for the model coefficients.

Figure 3 .
Figure 3. Pareto diagram for the model coefficients.

Figure 4 .
Figure 4. Perturbation plots for (a) initial TRM concentration; (b) contact time; (c) stirring speed; and (d) solid-to-liquid ratio.The levels of the other three elements were plotted at their central values for each diagram.

Figure 4 .Figure 5 .Figure 6 .
Figure 4. Perturbation plots for (a) initial TRM concentration; (b) contact time; (c) stirring speed; and (d) solid-to-liquid ratio.The levels of the other three elements were plotted at their central values for each diagram.For the initial antibiotic concentration and stirring speed, the sign and value of the slope of the corresponding lines provide a clear indication of their effects on the removal efficiency.Some representative response surface and contour plots are presented

Figure 5 .Figure 5 .Figure 6 .
Figure 5. Response surface plots of parameters effects on TRM removal (a) contact time (t) and solidto-liquid ratio (R); (b) contact time (t) and stirring speed (S).The levels of the remaining components were fixed at the central values for each plot (C = 6 mg/L; t = 35 min; S = 600 rpm; R = 0.03 g/mL).

Figure 6 .
Figure 6.Contour plots of the effects of the parameters on TRM removal (a) contact time (t) and solidto-liquid ratio (R); (b) contact time (t) and stirring speed (S).The levels of the remaining components were fixed at the central values for each plot (C = 6 mg/L; t = 35 min; S = 600 rpm; R = 0.03 g/mL).

Figure 7 .
Figure 7. X-ray diffraction analysis of volcanic ash after adsorption.

Figure 7 .
Figure 7. X-ray diffraction analysis of volcanic ash after adsorption.

Table 1 .
Actual and encoded values of factors in the Central Composite Design.

Table 3 .
Amount of minerals in volcanic ash before adsorption.

Table 4 .
Analysis of variance for the reduced quadratic model (DF: degrees of freedom; SS: sum of squares; MS: mean squares; F: F-value; p: p-value).

Table 5 .
Model coefficient estimates along with the corresponding 95% confidence intervals (CI) an standard errors (SE).

Table 6 .
Experimental (y exp ) and predicted (y calc ) TRM removal percentages at the optimum and at points inside and outside the factorial domain.

Table 6 .
Experimental (yexp)and predicted (ycalc) TRM removal percentages at the optimum points inside and outside the factorial domain.

Table 7 .
Amount of minerals in volcanic ash after adsorption.