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. 2022 Oct 10;7(41):36679–36688. doi: 10.1021/acsomega.2c04892

Mass-Transfer Simulation of Salicylic Acid on Weakly Polar Hyper-cross-linked Resin XDA-200 with Coadsorption of Sodium Ion

Pengfei Jiao 1,*, Jiamiao Liu 1, Zhaoqi Wang 1, Maripat Ali 1, Luying Gu 1, Shanshan Gao 1
PMCID: PMC9583085  PMID: 36278079

Abstract

graphic file with name ao2c04892_0009.jpg

The mass-transfer process of salicylic acid on hyper-cross-linked resin XDA-200 was experimentally and theoretically studied. Undissociated salicylic acid was found to be the favorable form for salicylic acid adsorption on the resin. A pH-dependent adsorption isotherm model established in this paper could well fit the adsorption isotherm data at different pH values. Surface diffusion is the main mass-transfer mode for salicylic acid in resin particles. The salicylate anions and Na+ coadsorbed on the resin. The modified surface diffusion model considering the coadsorption was proposed. The model could satisfactorily fit the concentration decay curves of salicylic acid at different pH values and feed concentrations. NaOH aqueous solution at pH 12 could elute salicylic acid in the fixed bed efficiently. A pH-dependent dynamic adsorption and elution process model considering axial diffusion, external mass transfer, surface diffusion, pH-dependent adsorption equilibrium, as well as coadsorption of salicylate anions and Na+ was established. The model could well predict the breakthrough and elution curves at different feed concentrations. The research carried out in this paper has reference significance for optimizing the separation process of salicylic acid and its analogues.

1. Introduction

The pollution of wastewater by drugs and their byproducts is an increasingly serious environmental problem.1−3 Salicylic acid is one of the simplest aromatic phenolic acids.4 It is a kind of analgesic, antipyretic drug and plays an important role in preventing platelet aggregation.5 It is also an irreplaceable synthetic raw material for some traditional medicines such as aspirin and glyburide as well as a synthetic raw material or intermediate for food preservatives, dyes, and pesticides.6 In recent years, salicylic acid has been identified as a water pollutant due to its chroma and high ecological toxicity.7 Salicylic acid can be detected in sewage and even drinking water. It can impair liver and kidney function, cause protein degeneration, and even cause mucosal bleeding. The presence of salicylic acid in wastewater and drinking water is a global challenge.8

Many methods have been used to remove salicylic acid from wastewater, including extraction,9 crystallization,10 ozonation,11 photocatalytic degradation,12 membrane separation,7 and adsorption.13−15 However, each method has some disadvantages such as introduction of byproducts, complexity of process, ineffectiveness for treating low concentration target compound, and expensive operation costs.16,17 Among the above methods, adsorption technology has become the most commonly used method for salicylic acid removal because of its advantages of convenient operation, simple equipment, high efficiency, low cost, and reusable adsorbents.18,19 A series of adsorbents including hyper-cross-linked resins,20−23 magnetic adsorption resin,24 metal nanocomposites,25 magnetic biochar,14 and magnetic magnesium–zinc ferrites26 have been prepared for the adsorption separation of salicylic acid. The adsorption thermodynamics and kinetics of salicylic acid have been studied in above studies. However, the simulation of mass-transfer process of salicylic acid in adsorbent particles and fixed bed has rarely been reported.

Mathematical modeling is a powerful tool for separation process design and optimization. Many mass-transfer models for adsorption separation process have been developed in the literature, such as solid-film linear-driving force model,27 transport-dispersive model,28 film–surface diffusion model,29 general rate model, and so forth. Salicylic acid is a weak acid, and its dissociation degree is affected by solution pH. Therefore, the adsorption of salicylic acid depends on the solution pH and the dissociation equilibrium of salicylic acid. The cooperative adsorption of salicylate anions and metal ions in the solution is probably non-negligible. However, the coadsorption and dissociation equilibrium of adsorbates were rarely considered simultaneously in the mass-transfer simulation in the literature.

Hyper-cross-linked resins have many advantages such as large specific surface area, high adsorption capacity, high mechanical strength, and long service life.30 Resins are the most commonly used adsorbents for salicylic acid adsorption separation. Therefore, this work focused on the simulation of mass-transfer process of salicylic acid in hyper-cross-linked adsorption resin particles and fixed bed. First, the adsorption performances of salicylic acid on different types of resins were compared, and the resin with better performance was screened. Second, the rate-limiting step for mass transfer in the resin particles was studied by the intraparticle diffusion model, and the mass-transfer process in the particles was simulated considering the coadsorption of Na+ and salicylate anions. Finally, the dynamic adsorption and desorption process of salicylic acid in the fixed bed were simulated. The studies carried out in this paper could provide a significant reference for optimizing the separation process of salicylic acid and its analogues.

2. Results and Discussion

2.1. Screening the Resin for Salicylic Acid Adsorption

The adsorption capacities of salicylic acid on different types of hyper-cross-linked adsorption resins are shown in Figure 1a. The physicochemical properties of the resins are listed in Table 1. The adsorption capacities of XDA-200 and XDA-1 resins are higher than those of other resins (see Figure 1a). The result is probably due to the high specific surface area of above two resins. The specific surface area of resin XDA-200 is lower than those of resins LX-3020 and LX-68M. The high adsorption amount of resin XDA-200 may result from the fact that the carboxyl groups on the resin form hydrogen bond with salicylic acid molecules. High adsorption capacity is beneficial to improve the treatment capacity of feed solution and separation efficiency. However, resin XDA-1 is a nonpolar resin. The hydration of the resin is energetically unfavorable. Therefore, the resin is not suitable for aqueous adsorption systems. The adsorption capacity of resin XDA-200 to salicylic acid gradually decreases with increasing pH (see Figure 1b). When the pH values are relatively low, salicylic acid molecules mainly exist in an unionized form. As pH increases, the concentration ratio of salicylate anion increases. The solubility of the salicylate anion in water is greater than that of unionized salicylic acid, which leads to reduction of the adsorption capacity. When pH is higher than 5.0, the adsorption capacity of salicylic acid is close to 0, indicating that salicylic acid can be probably eluted from the resin efficiently when the pH of eluant is higher than 5.0. In conclusion, the XDA-200 resin was selected as the adsorbent for subsequent experiments.

Figure 1.

Figure 1

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(a) Adsorption amounts of salicylic acid on different types of resins; (b) influence of pH on the adsorption capacity of XDA-200 resin.

Table 1. Physicochemical Properties of Resins Used in This Work.

resin matrix SBET(m2/g) polarity functional group
XDA-200 PS-DVBa 1018.1 weakly polar carbonyl
XDA-1 PS-DVB 1336.9 nonpolar none
XDA-6 PS-DVB 673.5 nonpolar none
LX-T81 PS-DVB 877.1 weakly polar carbonyl
LX-3020 PS-DVB 1139 strongly polar acylamide, ester group
LX-68M PS-DVB 1082.1 weakly polar ester group
LX-60 PS-DVB 845.1 weakly polar ester group
LSC-100 PS-DVB b strongly polar acylamide
LSA-12 PS-DVB 647 weakly polar aldehyde group, carbonyl
D101 PS-DVB 728.8 weakly polar carbonyl
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a

PS-DVB is the abbreviation of poly(styrene divinylbenzene).

b

The resin LSC-100 is a gel-type resin with a very low specific surface area.

The distribution coefficient of salicylic acid between solid and liquid phases under different pH conditions is shown in Figure 2. The values of the distribution coefficient decrease gradually with increasing pH, which is close to the change trend of the concentration ratio of nonionic salicylic acid in the solution. The results showed that nonionic salicylic acid was a favorable form for salicylic acid adsorption. The data in Figure 2 were fitted with the following empirical equation.31

2.1. 1

where K is the distribution coefficient of salicylic acid, S represents salicylic acid in different forms including nonionic salicylic acid and salicylate anion, and αS represents the concentration ratio of salicylic acid in different forms.

Figure 2.

Figure 2

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Influence of pH on the distribution coefficient of salicylic acid between solid and liquid phases.

The distribution coefficients of salicylic acid and salicylate anions obtained by fitting curves were 194.30 and 13.96, respectively. The distribution coefficient of nonionic salicylic acid was significantly higher than that of salicylate anion, indicating that the affinity between nonionic salicylic acid and resin was stronger than that between the salicylate anion and the resin.

2.2. Adsorption Equilibrium Behaviors of Salicylic Acid

Adsorption isotherms of salicylic acid on XDA-200 resin under different pH conditions are shown in Figure 3. Langmuir, Freundlich, Toth, and Sips adsorption isotherm models were used to fit the adsorption isotherm data. The model parameters obtained by fitting curves are shown in Table 2. The values of correlation coefficient R2 for Langmuir, Toth, and Sips models were close to each other. Moreover, the values of R2 for the above three models were greater than or close to that of the Freundlich model. In order to simplify the model equation and calculation, Langmuir model was selected to describe the adsorption equilibrium behaviors of salicylic acid. All adsorption isotherms at different pH values are convex indicating that the adsorption of salicylic acid on the resin is favorable. All values of kL are positive and decrease with increasing pH in the studies pH range. The kL value is related to the adsorption strength. With the increase of pH, the affinity between salicylic acid and resin becomes weak, so kL generally decreases with increasing pH. As can be seen from Figure 2, when the solution pH is higher than 5.0, the distribution coefficient barely changes. Therefore, the adsorption isotherms at pH values higher than 5.0 were considered the same as that at pH 5.0.

Figure 3.

Figure 3

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Experimental adsorption isotherms of salicylic acid and fitting results by (a) Langmuir model, (b) Freundlich model, (c) Toth model, and (d) Sips model.

Table 2. Adsorption Isotherm Model Parameters at Different pH Values.

 
 pH
model parameters 2.0 3.0 3.5 4.0 5.0
Langmuir model qm(mmol/g) 1.49 1.32 1.02 0.72 0.29
  kL(L/mol) 470.89 413.90 410.97 389.47 256.07
  R2 0.985 0.988 0.993 0.985 0.976
Freundlich model kf(L/mol) 17.40 12.70 10.98 6.09 3.74
  n 1.87 1.97 1.85 2.01 1.68
  R2 0.934 0.958 0.961 0.984 0.956
Toth model KT(L/mol) 580.64 473.77 402.24 391.42 65.70
  αT(L/mol) 107.32 157.50 313.18 1705.05 1.94 × 10–5
  τ 0.43 0.61 0.88 1.54 1.40 × 10–7
  R2 0.989 0.988 0.992 0.989 0.980
Sips model qm(mmol/g) 1.25 1.26 0.89 1.01 0.22
  Ks(L/mol) 714.51 461.08 585.87 154.15 432.34
  ns 1.25 1.06 1.19 0.75 1.32
  R2 0.989 0.985 0.994 0.987 0.975
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The changing curves of qm and kL with pH are shown in Figure 4a,b, respectively. The curves were fitted by several mathematical functions using nonlinear curve fitting in Origin 9.1. It was found that the following equation could well fit the curves.

2.2. 2
2.2. 3

Figure 4.

Figure 4

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Variation curves of (a) qm and (b) kL values with solution pH.

The fitting curves are shown in Figure 4a,b. The values of correlation coefficients of eqs 2 and 3 for fitting curves are 0.999 and 0.998, respectively. In conclusion, the pH-dependent adsorption isotherm model equation for salicylic acid is as follows

2.2. 4

Ultimately, the adsorption equilibrium relationship of salicylic acid at different pH values can be predicted by above pH-dependent adsorption isotherm model.

2.3. Mass-Transfer Process of Salicylic Acid in Resin Particles

The adsorption kinetic curves for salicylic acid under different initial solution pH and concentration conditions are shown in Figure 5. As can be seen from Figure 5a, the adsorption amount at pH 5.0 is significantly lower than that at pH 2.0 and 3.0. The phenomenon can be explained by the fact that the concentration ratio of salicylate anion at pH 5.0 is higher than that at pH 2.0 and 3.0. The adsorption amount increases with increasing initial feed concentration (see Figure 5b). The result is consistent with that shown in Figure 3. The adsorption kinetics experimental data were fitted by the intraparticle diffusion model, and the fitting results are shown in Figure 6. The fitting results under different operating conditions show a similar phenomenon, that is, each curve has two linear segments. In the first segment, the fitting lines all pass through the origin, indicating that intraparticle diffusion is the only rate-limiting step in the adsorption process of salicylic acid from the aqueous phase to the adsorption sites on the resin. A similar phenomenon was found in the adsorption process of rhodamine B on N-vinylimidazole-modified hyper-cross-linked resins.32

Figure 5.

Figure 5

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(a) Adsorption kinetics curves under different pH conditions; (b) adsorption kinetics curves under different initial concentrations.

Figure 6.

Figure 6

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Intraparticle diffusion model fitting for the adsorption kinetics data of salicylic acid under different operating conditions: (a) Different initial pH; (b) different initial concentrations.

Sodium ions do not adsorb on the XDA-200 resin. However, coadsorption exists between Na+ and salicylate anions due to electrostatic attraction. The change of Na+ concentration in solution will lead to the change of solution pH, thus affecting the adsorption of salicylic acid. In order to verify the existence of coadsorption, both the modified surface diffusion model with coadsorption and that without coadsorption were used to fit the adsorption kinetics data under different pH conditions. The fitting results are shown in Figures 5a and S1. As can be seen from Figures 5a and S1, when the solution pH is ∼2 and 5, the fitting results of the two models are not significantly different. However, there is a significant difference between the simulated curve in Figure S1 and the experimental data when the solution pH is ∼3. At pH 2, there is no Na+ in the solution. Therefore, coadsorption does not exist. When pH is ∼5, the concentration of Na+ in the solution is relatively high, while the adsorption capacity of salicylic acid is relatively low. Therefore, the amount of Na+ adsorbed on the resin via coadsorption with salicylate anions is small relative to the amount of Na+ in the solution, which has no significant influence on the solution pH and the adsorption amount of salicylic acid. When the solution pH is ∼3, the concentration of Na+ in the solution is relatively low, and the amount of Na+ adsorbed on the resin is relatively large, resulting in a significant change in solution pH. Therefore, the fitting results of the model without considering the coadsorption of Na+ differ greatly from the experimental results. In sum, the coadsorption of Na+ with salicylate anions is negligible at about pH 3.0.

The modified surface diffusion model with coadsorption of Na+ and salicylate anions was used to fit the adsorption kinetic curves of salicylic acid under different pH and concentration conditions, and the fitting curves are shown in Figure 5. The values of model parameters obtained by fitting are listed in Table 3. The values of ARD % are all lower than 8.0%, indicating that the model can provide a general prediction to the adsorption kinetics data. The results show that the mass-transfer process of salicylic acid in XDA-200 resin particles can be well simulated by the modified surface diffusion model. For microporous adsorbents, surface diffusion is the main mass-transfer mode for adsorbates in adsorbent pores. Therefore, the model is suitable for salicylic acid adsorption in XDA-200 resin with a pronounced micropore system.

Table 3. Kinetic Adsorption Model Parameters for Salicylic Acid.

  pH
 initial concentration (mol/L)
parameter 2 3 5 3.71 × 10–3 7.28 × 10–3 1.12 × 10–2
Ds(cm2/min) 5.0 × 10–7 5.5 × 10–7 5.3 × 10–7 5.0 × 10–7 5.0 × 10–7 6.5 × 10–7
ARD % 7.48 7.77 6.53 4.19 6.35 7.78
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2.4. Dynamic Adsorption and Elution of Salicylic Acid

The adsorption breakthrough and elution curves of salicylic acid are shown in Figure 7a,b, respectively. As can be seen from Figure 7a, the stoichiometric time (ct = 0.5cfe) of salicylic acid decreases with increasing initial concentration of the feed solution. This is because the adsorption isotherms of salicylic acid are convex. For convex isotherms, the retention time of adsorbates decreases with increasing concentration.33 The elution yields of salicylic acid were all higher than 99%. When the initial concentrations of the feed solution were 3.62 × 10–2 and 1.09 × 10–2 mol/L, deionized water was used as the eluant. The elution curves tailed severely. Nearly 3000 min was needed to elute salicylic acid completely (see Figure 7b). When the initial concentration was 7.49 × 10–2 mol/L, the salicylic acid could be eluted quickly with NaOH aqueous solution at pH 12 used as the eluant (eluting time was less than 500 min). The rapid elution of salicylic acid was due to the rapid increase of pH of the mobile phase in the chromatographic column, which leads to the fact that salicylic acid mainly exists in the form of anions. The weak affinity between salicylate anions and resin results in the rapid outflow of salicylic acid from the chromatographic column. The breakthrough and elution curves of salicylic acid predicted by the pH-dependent dynamic separation process model proposed in this paper are shown in Figure 7. The values of model parameters are shown in Table S1. As can be seen from Figure 7, the model can well predict the breakthrough and elution curves of salicylic acid at different initial concentrations of the feed solution. The results indicate that the model proposed in this paper can be used to simulate the mass-transfer process of salicylic acid and further optimize the separation process.

Figure 7.

Figure 7

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(a) Adsorption breakthrough curves of salicylic acid; (b) elution curves of salicylic acid.

3. Conclusions

The mass-transfer process of salicylic acid on weakly polar hyper-cross-linked resin XDA-200 was experimentally and theoretically studied. The pH-dependent adsorption isotherm model proposed in this paper can well fit the adsorption isotherms of salicylic acid under different pH conditions. Surface diffusion is the main mass-transfer mode of salicylic acid in XDA-200 resin particles. The coadsorption of Na+ and salicylate anions exists in the adsorption system. The modified surface diffusion model considering the coadsorption can well fit the adsorption kinetics curves of salicylic acid under different pHs and initial solution concentrations. The dynamic separation process model considering the dissociation equilibrium of salicylic acid and coadsorption of Na+ and salicylate anions was established in this paper. The model can well predict the mass-transfer process of salicylic acid in fixed -bed with various feed concentrations and pH values. The research carried out in this paper has a certain reference significance for the efficient separation of salicylic acid and its analogues.

4. Materials and Methods

4.1. Resins

The hyper-cross-linked resins used in this paper were purchased from Sunresin New Materials Co., Ltd., Xi’An (Xi’An, China). The pretreatment methods of the resins can be found in our previous paper.34

4.2. Chemicals

Salicylic acid and hydrochloric acid were purchased from Tianjin Hengxing Chemical Reagent Manufacturing Co., Ltd. (Tianjin, China). Sodium hydroxide and anhydrous ethanol were provided by Tianjin Fengchuan Chemical Reagent Technology Co., Ltd. (Tianjin, China) and Wuxi Yatai United Chemical Co., Ltd. (Wuxi, China), respectively. All above reagents were of analytical grade and used without further purification. Deionized water was prepared by a laboratory pure water machine (WP-UP-YJ-40, Sichuan Wortel Water Treatment Equipment Co., Ltd., Chengdu, China).

4.3. Screening Resin for Salicylic Acid Adsorption and Determination of Adsorption Isotherms of Salicylic Acid

An aqueous solution of salicylic acid (∼3.62 × 10–3 mol/L) was prepared from which 25 mL was taken out and put into several 50 mL triangular bottles. Then XDA-200 resin (1 g) was added to each triangle flask. The adsorption equilibrium was achieved by shaking the flasks at 150 rpm and 298 ± 1 K in a shaker (HNY-200B, Tianjin Honour Instrument Co., Ltd., Tianjin, China) for more than 5 h. The concentration of salicylic acid was measured at 296 nm by an UV–vis spectrophotometer (BioSpectrometer, Eppendorf AG, Hamburg, Germany). The adsorption capacity of salicylic acid was calculated according to eq 5.

4.3. 5

where qe is the adsorption capacity of salicylic acid (mmol/g), c0 is the concentration of solution before adsorption (mol/L), ce is the concentration of solution at adsorption equilibrium (mol/L), V is the volume of solution (mL), and M is the mass of resin (g).

The adsorption capacities of other resins were determined by a procedure similar to that of XDA-200 resin. The adsorption capacities of the resins were compared to select the adsorbent for subsequent experiments.

An aqueous solution of salicylic acid (∼3.62 × 10–3 mol/L) was prepared. 50 mL of the solution was taken out and placed in several 100 mL triangle flasks. The solutions were adjusted to different pH values (1.5, 2.0, 2.5, 8.0, 9.0, 11.0, and 12.0). Then, the wet resin XDA-200 (0.5 g) was added to the flasks. The flasks were shaken at 150 rpm and 298 ± 1 K in a shaker for more than 5 h to achieve adsorption equilibrium. The pH values of the solutions were determined by a pH meter (FE28, Mettler-Toledo, LLC, Zurich, Switzerland), and the concentration of salicylic acid was measured. The adsorption capacity of salicylic acid was calculated according to eq 5.

Several aqueous solutions of salicylic acid at different concentrations were prepared. 25 mL of the solutions was taken and placed in several 50 mL triangulated bottles. Then, the wet resin XDA-200 (2 g) was added to each bottle. The pH of the solutions was adjusted to 2.0. The adsorption equilibrium was achieved using the same procedures as above. The adsorption capacity at different initial concentrations was determined. The changing curve of adsorption capacity with equilibrium concentration was the adsorption isotherm at pH 2.0. The adsorption isotherms under other pH conditions were determined by similar procedures.

4.4. Adsorption Kinetics Curves at Different Initial pH Values and Concentrations

The aqueous solution of salicylic acid (250 mL) at a concentration of ∼7.24 × 10–3 mol/L was prepared and placed in a 500 mL round-bottom flask. The solution pH was adjusted to ∼2.0. Then, the wet resin XDA-200 (10 g) was added into the flask. The mixture was stirred vigorously, and several samples were taken at different time intervals to determine the concentration of salicylic acid. Equation 5 was used to calculate the adsorption capacity of salicylic acid at different moments. The adsorption kinetics curve at pH 2.0 was prepared with time as abscissa and adsorption capacity at different moments as the ordinate. Then, the adsorption kinetics curves at pH 3 and 5 and those at different initial concentrations were measured by the same method.

4.5. Dynamic Adsorption and Elution Curves of Salicylic Acid

Hydrochloric acid solution at pH 2.0 was passed into a glass chromatographic column of 1.15 cm inner diameter from the upper end of the column. The column was filled with resin XDA-200 (3 g). A pH meter was used to measure the pH values of the effluent at the exit of the column until the pH value approaches 2.0. Then, the salicylic acid aqueous solution (∼7.24 × 10–3 mol/L) was prepared, and the pH value was adjusted to 2.0. The solution was passed into the chromatographic column through the upper end. A peristaltic pump (BT100-1L, Hebei, China) was used to control the flow rate at 0.5 mL/min. A partial collector was used to collect samples at the exit of the column at regular intervals and to determine the concentration of the samples. The injection was finished until the solution concentration at the exit of the column was close to the concentration of the feed solution. The curve of the solution concentration at the exit of the column over time was the breakthrough curve of salicylic acid. After the injection was finished, the column was eluted with NaOH solution at pH 12 at a flow rate of 0.5 mL/min until the solution concentration approached 0. The elution curve of salicylic acid was the changing curve of the solution concentration at the outlet of the column with time. The breakthrough and elution curves at other initial concentrations of feed solution were determined using the same operation method except that deionized water was used as the eluant.

All experiments in this paper were carried out at least 3 times with an experimental error of less than 6%. The data listed in this paper are the average values of three groups of experimental data.

5. Theory

5.1. Adsorption Isotherm Models

5.1.1. Langmuir Adsorption Isotherm Model

5.1.1. 6

where qm is the maximum monolayer adsorption capacity (mmol/g) and kL is Langmuir constant (L/mol).

5.1.2. Freundlich Adsorption Isotherm Model

5.1.2. 7

where kf and n are Freundlich constants.

5.1.3. Toth Isotherm Model35

5.1.3. 8

where KT (L/mol), αT (L/mol), and τ are constants of the Toth isotherm model.

5.1.4. Sips Adsorption Isotherm Model

5.1.4. 9

where Ks presents the adsorption energy (L/mol) and ns is the heterogeneity factor.

5.2. Kinetic Adsorption Models

5.2.1. Intraparticle Diffusion Model

Intraparticle diffusion model proposed by Weber and Morris can be described by the following equation36

5.2.1. 10

where qt is the adsorption amount at time t (mmol/g), kp is the diffusion rate parameter [(mmol/g)/(min)1/2], and t is the time (min).

5.2.2. Modified Surface Diffusion Model

In order to simplify the model, the following model assumptions were made. The temperature of the adsorption system remained constant during the adsorption process. The adsorbent was spherical particles of uniform size. The radial solute concentration distribution in the column was uniform.

Modified surface diffusion model contains the following equations.

The mass conservation equations of salicylic acid and Na+ between solid and liquid phases are as follows

5.2.2. 11
5.2.2. 12

where cSA,b is the concentration of salicylic acid in the bulk solution (mol/L). R is the radius of resin particles (cm). r is the radial position within resin particles (cm). cNa+ and cH+ are the concentrations of Na+ and H+ in the bulk solution (mol/L).

The mass conservation equation of salicylic acid in the resin particle element is as follows

5.2.2. 13

where Ds is the surface diffusion coefficient (cm2/min).

In the aqueous solution, the dissociation degree of salicylic acid depends on the solution pH. The dissociation process of salicylic acid is shown as follows

5.2.2. 14

where Ke is the dissociation equilibrium constant of salicylic acid and its value is 1.05 × 10–3.37 The second dissociation equilibrium constant of salicylic acid (2.19 × 10–14) was neglected in this paper. SA represents unionized salicylic acid. SA– represents the anionic form of salicylic acid. The calculation equations of the concentration of salicylic acid in different forms are as follows

5.2.2. 15
5.2.2. 16

where cSA and cSA– are the concentrations of unionized salicylic acid and salicylate anion, respectively (mol/L).

The electroneutral condition in the solution is as follows

5.2.2. 17

where cCl– and cOH– are the concentrations of Cl– and OH–, respectively (mol/L).

The values of cH+ and cOH– can be related by the following equation

5.2.2. 18

The pH values can be calculated using the following equation

5.2.2. 19

The initial and boundary conditions are shown below

5.2.2. 20
5.2.2. 21
5.2.2. 22

where cSA,fe is the concentration of salicylic acid in the feed solution (mol/L).

The concentration history in bulk solution and the concentration profiles in resin particles can be obtained by solving the above equations using MATLAB2010a. The partial differential equations were discretized into ordinary differential equations by the orthogonal configuration finite element method. Then, the ordinary differential equations were solved by ODE23. The relative and absolute tolerances are 10–5. The values of Ds are solved by minimizing the following objective function

5.2.2. 23

where N is the number of experimental data points. cj,exp and cj,pred are the experimentally measured and predicted concentrations of salicylic acid, respectively (mol/L).

The average relative deviation between the experimentally measured and predicted adsorption kinetics data can be expressed by the following equation

5.2.2. 24

5.3. Dynamic Separation Process Model in the Chromatographic Column

Axial diffusion and liquid film mass transfer were considered in this model.

The mass conservation equation of salicylic acid in the axial mobile phase of fixed bed is as follows

5.3. 25

where v is the interstitial velocity (cm/min), ci and ci,s are the concentration of solute i in the mobile phase and near the surface of the resin particles, respectively (mol/L), x is the axial position in the fixed bed (cm), εb is the bed voidage, ki,film is the diffusion coefficient in the liquid film outside of the resin particles (cm/min), and Dax are axial diffusion coefficients (cm2/min).

The mass conservation equations of Na+ and Cl– in the axial mobile phase of fixed bed are as follows

5.3. 26
5.3. 27

ρp is the apparent wet density of the resin (g/mL).

The mass-transfer process of salicylic acid in resin particles is expressed by eq 13.

The boundary conditions of fixed bed and resin particles are as follows

5.3. 28
5.3. 29
5.3. 30
5.3. 31

The initial conditions during adsorption are as follows

5.3. 32

The concentration and adsorption capacity of adsorbates in the column at the end of the adsorption stage are the initial conditions during desorption.

The adsorption equilibrium of salicylic acid molecules on the surface of resin particles is reached instantaneously. The adsorption equilibrium equation is expressed as follows

5.3. 33

Equations 14–17 were used to calculate the concentrations of salicylic acid in different dissociation states in the mobile phase and express the electric neutral conditions.

The solving method of the above model equations is similar to that of the modified surface diffusion model.

Di,ax and ki,film were calculated using the following equations38

5.3. 34
5.3. 35

where U is the superficial velocity of the mobile phase (cm/min), dp is the diameter of the resin particles (cm), and Di,m is the molecular diffusivity of solute i (cm2/min). The values of DNa+,m and DCl–,m are 7.8 × 10–4 and 1.79 × 10–3 cm2/min, respectively.39,40 The value of DSA,m was calculated by Wilke–Chang correlation as follows.41

5.3. 36

where φ is the association parameter, MB is the molecular weight of water, T is the operating temperature (K), ηB is the viscosity of the solution (mPa·s), and Vi,A is molar volume of adsorbate i at its normal boiling point [mL/(g·mol)].

Acknowledgments

This research was supported by the Scientific and Technological Project of Henan Province (grant no. 202102110285) and School-Level Research Project of Nanyang Normal University (grant no. 2018ZX009).

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.2c04892.

  • Adsorption kinetics curves of salicylic acid on XDA-200 resin predicted by the modified surface diffusion model without coadsorption of Na+ and operating and model parameters for salicylic acid (PDF)

The authors declare no competing financial interest.

Supplementary Material

ao2c04892_si_001.pdf (161.1KB, pdf)

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