# Three-Dimensional Mass Transfer Modeling of Hydroquinone Adsorption on Phragmites australis Biochar

^{1}

^{2}

^{*}

## Abstract

**:**

_{s}is 2.5 × 10

^{−10}–1.74 × 10

^{−9}cm

^{2}/s, and the contribution rate of surface diffusion SDCP% is close to 100%, which is much larger than pore volume diffusion, revealing that regardless of the contact time and position, surface diffusion occupies the main position in intraparticle diffusion.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Preparation

#### 2.3. Characterization

_{p}(cm

^{3}/g) denotes the pore volume of PAC; ρ

_{p}(kg/m

^{3}) denotes the particle density of PAC; ρ

_{s}(kg/m

^{3}) denotes the solid density of PAC; and ε

_{p}denotes the void ratio of PAC.

#### 2.4. Adsorption Experiment

_{t}of PAC at arbitrary time t and equilibrium time, and q

_{e}(mg/g) were calculated as shown in Equations (3)–(5):

_{A}

_{0}and C

_{A}(mg/L) represent the initial concentration of hydroquinone and the concentration at any time t, respectively; C

_{e}(mg/L) represents the concentration of hydroquinone at adsorption equilibrium; q

_{t}(mg/g) represents the amount of P. australis biomass material adsorbed at any time t; q

_{e}(mg/g) represents the amount of P. australis biomass material adsorbed at adsorption equilibrium; V (mL) represents the volume of hydroquinone; and m (g) represents the mass of the P. australis biomass material.

## 3. Mathematical Modeling

#### 3.1. Isotherm Models

_{m}(mg/g) indicates the maximum adsorption of the hydroquinone by the P. australis biomass material as calculated by the Langmuir isotherm model; k

_{L}(L/mg) indicates the adsorption constant; k

_{F}(mg/g (L/mg) 1/n) indicates the adsorption constant; and 1/n indicates the strength of the adsorption effect and the evaluation of the heterogeneity of the adsorbent when n < 1, indicating favourable in the range of adsorption concentrations, and when n > 1, indicating favourable only in the high concentration range [27].

#### 3.2. 3D Mass Transfer Model

_{A}and C

_{Ap}(mg/L) denote the concentration of the adsorbate in solution and inside the PAC, respectively; q (mg/g) denotes the adsorption volume of PAC; k

_{L}(cm/s) denotes the external mass transfer coefficient; D

_{ep}and D

_{s}denote the diffusion coefficients for pore volume diffusion and surface diffusion, respectively; and C

_{Ap}

_{|r=R}denotes the solute concentration within the particle calculated at the boundary; in addition, assuming that the adsorption rate of the adsorbate at the active site is instantaneous, the relationship between q and C

_{AP}can be evaluated by the adsorption isotherm model.

_{L}, D

_{s}and D

_{ep}, must be obtained. Where the k

_{L}values can be obtained by using the theory proposed by Furusawa and Smith [29,30] in 1973, as shown in Equation (12):

_{A}/C

_{A}

_{0}; S (cm

^{2}/g) denotes the specific surface area per unit mass of adsorbent; and the right half of Equation (12), in parentheses, indicates the slope of the concentration decay at t = 0, which can be estimated from the slopes at the two time points t = 0 and t = 5.

_{ep}can be calculated from Equation (13) [29]:

_{AB}denotes the diffusivity of the adsorbent molecules in aqueous solution and can be calculated from Equation (14) [7,31]:

_{B}(g/mol) denote the water association parameter of 2.60 and the molar mass of 18.02, respectively; T denotes the ambient temperature of 303.15 K; the viscosity of water η

_{B}= 0.904 cp; and V

_{A}(cm

^{3}/mol) denotes the molar volume of the adsorbate, which can be calculated by the Le Bas method [32].

_{s}was estimated from the diffusion model data with experimental data by the least squares optimization method and was calculated as shown in Equation (15) [29]:

_{Aexp}and C

_{Acal}(mg/L) denote the concentration of the sorbent obtained by the diffusion model and experimentally calculated at different times, respectively. The mass transfer process of the sorbent inside the PAC was simulated by using the finite element method, COMSOL Multiphysics 5.4 and other mapping software.

## 4. Results and Discussion

#### 4.1. Characterisation of Solid Density

^{3}, the particle density is 0.52 kg/m

^{3}, and the void fraction is 0.68. From the results, it can be seen that PAC has a large internal pore space, which is conducive to the adsorption process.

#### 4.2. Adsorption Isotherm

^{2}value of the Freundlich isotherm model (0.9901–0.9972) is higher than that of the Langmuir model, and the n value greater than 1 is the dominant adsorption. The results indicate that the Freundlich isotherm model can better describe the adsorption behavior of hydroquinone on PAC, which has a heterogeneous surface, and the adsorption of hydroquinone on the surface of PAC is heterogeneous and belongs to the adsorption process of the multi-molecular layer. In addition, the calculated results from the Langmuir isotherm model show that the maximum adsorption capacity of hydroquinone on PAC is 158.73 mg/g for a single layer, which possesses a strong adsorption capacity.

#### 4.3. Simulation of Intraparticle Adsorption and Mass Transfer Processes

#### 4.3.1. Concentration Decay Curve for Hydroquinone

#### 4.3.2. Concentration Decay Curve for Hydroquinone

_{s}= 0. According to the set of model equations (Equations (8)–(11)), the values of the external mass transfer coefficient k

_{L}and the effective pore volume diffusion coefficient D

_{ep}need to be obtained, as shown by Equations (12) and (13), respectively. The values of k

_{L}were calculated to obtain a range of 0.5 × 10

^{−2}to 1.4 × 10

^{−2}cm/s, and the estimated value of D

_{ep}was 1.54 × 10

^{−10}cm

^{2}/s. Figure 2a–d represents the values of k

_{L}using pore-volume-diffusion-model-predicted and experimentally obtained concentration decay curves. It can be seen from the results that the use of the pore volume dispersion model does not adequately explain the experimental data obtained; the pore volume dispersion model overestimates the experimental data, and the difference becomes more pronounced as the initial concentration increases.

#### 4.3.3. Simulation Applications of Pore Volume and Surface Diffusion Models

_{L}and D

_{ep}, values for D

_{s}are also obtained in the pore volume and surface diffusion models. By analyzing the data fitted to the model with the experimental data, the values of D

_{s}obtained using Equation (15) range from 2.5 × 10

^{−10}to 1.74 × 10

^{−9}cm

^{2}/s. As shown in Figure 2a–c,e, the values of D

_{s}obtained using the pore volume and concentration decay curves of hydroquinone within the PAC adsorption system were obtained by fitting the surface diffusion model. As shown in Figure 2e, the experimental data for the adsorption of hydroquinone on PAC can be well fitted using the pore volume and surface diffusion models.

_{AP}and the corresponding surface diffusion N

_{AS}. The estimating equations shown in Equations (16) and (17) [28]:

_{AP}and surface diffusion N

_{AS}under different time conditions is represented in Figure 4 and Figure 5. The direction of the flux (black arrows) converges towards the interior of the PAC particles, indicating that the lowest concentration of hydroquinone can be reached in the interior. In the Figures, the red color represents the maximum values of N

_{AP}and N

_{AS}, and the blue color represents the minimum. It is clear from these data that both mass transport mechanisms occur simultaneously, but their magnitudes are a function of time and position within the PAC particles, which is consistent with Frhlich’s findings [15,28]. The maximum values of N

_{AP}and N

_{AS}are obtained near the outer surface of the PAC particle during the initial time period; thereafter, they continue to increase near the center of the particle over a long time. Furthermore, the difference between the magnitudes of N

_{AP}and N

_{AS}can be seen from Figure 4 and Figure 5, when the time is 60 min, the maximum N

_{AP}is 8.58 × 10

^{−10}mg/cm

^{2}/min, and the maximum N

_{AS}is 3.25 × 10

^{−8}mg/cm

^{2}/min, the N

_{AS}value is two orders of magnitude higher than the N

_{AP}value. This indicates that surface diffusion flux is more important than pore volume diffusion [29]. From the characterization results of PAC (SEM, FTIR, XPS, XRD), it was found that the PAC surface is rich in adsorption active sites, which may be the reason for the surface diffusion flux being larger than the pore volume diffusion [2,5].

_{AP}and N

_{AS}to the intraparticle diffusion drive using the following equation (Equation (18)) [28]:

## 5. Conclusions

^{−10}to 1.74 × 10

^{−9}cm

^{2}/s, verifying that a faster adsorption rate will be generated as the concentration increases. Moreover, the contribution of surface diffusion was close to 100% regardless of the contact time and location, confirming the dominance of surface diffusion in intraparticle diffusion in this study. The development of a three-dimensional mass transfer model will help to more accurately model and explain the adsorption and mass transfer of adsorbate within the adsorbent.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Sun, Y. Anodic Enhancement by Advanced Oxidation and Coupled Biological Treatment of Refractory Organic Wastewater. Ph.D. Thesis, Zhejiang University, Hangzhou, China, 2020. [Google Scholar]
- Shi, S.; Lv, J.; Liu, Q.; Nan, F.; Feng, J.; Xie, S. Optimized preparation of Phragmites australis activated carbon using the Box–Behnken method and desirability function to remove hydroquinone. Ecotoxicol. Environ. Saf.
**2018**, 165, 411–422. [Google Scholar] - Li, G.; Pang, S.; Wu, Y.; Ouyang, J. Enhanced removal of hydroquinone by graphene aerogel-Zr-MOF with immobilized laccase. Chem. Eng. Commun.
**2018**, 205, 698–705. [Google Scholar] [CrossRef] - Shi, S. Removal Potential and Mechanism of Phenolic Pollutants by Phragmites australis Biomass Functionalised Materials. Ph.D. Thesis, Shanxi University, Taiyuan, China, 2021. [Google Scholar]
- Díaz-Blancas, V.; Ocampo-Pérez, R.; Leyva-Ramos, R.; Alonso-Dávila, P.A.; Moral-Rodríguez, A.I. 3D Modeling of the overall adsorption rate of metronidazole on granular activated carbon at low and high concentrations in aqueous solution. Chem. Eng. J.
**2018**, 349, 82–91. [Google Scholar] [CrossRef] - Wang, J.; Guo, X. Adsorption kinetic models: Physical meanings, applications, and solving methods. J. Hazard. Mater.
**2020**, 390, 122156. [Google Scholar] [CrossRef] - Souza, P.R.; Dotto, G.L.; Salau, N.P.G. Detailed numerical solution of pore volume and surface diffusion model in adsorption systems. Chem. Eng. Res. Des.
**2017**, 122, 298–307. [Google Scholar] [CrossRef] - Ocampo-Pérez, R.; Rivera-Utrilla, J.; Gómez-Pacheco, C.; Sánchez-Polo, M.; López-Peñalver, J.J. Kinetic study of tetracycline adsorption on sludge–derived adsorbents in aqueous phase. Chem. Eng. J.
**2012**, 213, 88–96. [Google Scholar] [CrossRef] - Ocampo-Pérez, R.; Daiem, M.M.A.; Rivera-Utrilla, J.; Méndez-Díaz, J.D.; Sánchez-Polo, M. Modeling adsorption rate of organic micropollutants present in landfill leachates onto granular activated carbon. J. Colloid Interface Sci.
**2012**, 385, 174–182. [Google Scholar] [CrossRef] - Largitte, L.; Pasquier, R. A review of the kinetics adsorption models and their application to the adsorption of lead by an activated carbon. Chem. Eng. Res. Des.
**2016**, 109, 495–504. [Google Scholar] [CrossRef] - Qiu, H.; Lv, L.; Pan, B.-C.; Zhang, Q.-J.; Zhang, W.-M.; Zhang, Q.-X. Critical review in adsorption kinetic models. J. Zhejiang Univ.–Sci. A
**2009**, 10, 716–724. [Google Scholar] [CrossRef] - Knust, K.N.; Foley, M.P.; Mubarak, M.S.; Skljarevski, S.; Raghavachari, K.; Peters, D.G. Electrochemical reduction of 5–chloro–2–(2,4–dichlorophenoxy) phenol (triclosan) in dimethylformamide. J. Electroanal. Chem.
**2010**, 638, 100–108. [Google Scholar] [CrossRef] - Xu, R.; Xie, Y.; Tian, J.; Chen, L. Adsorbable organic halogens in contaminated water environment: A review of sources and removal technologies. J. Clean. Prod.
**2021**, 283, 124645. [Google Scholar] [CrossRef] - De Gisi, S.; Lofrano, G.; Grassi, M.; Notarnicola, M. Characteristics and adsorption capacities of low-cost sorbents for wastewater treatment: A review. Sustain. Mater. Technol.
**2016**, 9, 10–40. [Google Scholar] [CrossRef] [Green Version] - Ocampo-Perez, R.; Leyva-Ramos, R.; Alonso-Davila, P.; Rivera-Utrilla, J.; Sanchez-Polo, M. Modeling adsorption rate of pyridine onto granular activated carbon. Chem. Eng. J.
**2010**, 165, 133–141. [Google Scholar] [CrossRef] - Leyva-Ramos, R.; Geankoplis, C.J. Model simulation and analysis of surface diffusion of liquids in porous solids. Chem. Eng. Sci.
**1985**, 40, 799–807. [Google Scholar] [CrossRef] - Comerton, A.M.; Andrews, R.C.; Bagley, D.M.; Yang, P. Membrane adsorption of endocrine disrupting compounds and pharmaceutically active compounds. J. Membr. Sci.
**2007**, 303, 267–277. [Google Scholar] [CrossRef] - Yüksel, S.; Kabay, N.; Yüksel, M. Removal of bisphenol A (BPA) from water by various nanofiltration (NF) and reverse osmosis (RO) membranes. J. Hazard. Mater.
**2013**, 263, 307–310. [Google Scholar] [CrossRef] - Sun, Y.Y. Preparation, Characterization and Adsorption Performance of Reed Bamboo Activated Carbon. Ph.D. Thesis, Shandong University, Jinan, China, 2014. [Google Scholar]
- Wu, J.; Yu, H. Biosorption of 2,4–dichlorophenol from aqueous solution by Phanerochaete chrysosporium biomass: Isotherms, kinetics and thermodynamics. J. Hazard. Mater.
**2006**, 137, 498–508. [Google Scholar] [CrossRef] - Hu, X.; Jia, L.; Cheng, J.; Sun, Z. Magnetic ordered mesoporous carbon materials for adsorption of minocycline from aqueous solution: Preparation, characterization and adsorption mechanism. J. Hazard. Mater.
**2019**, 362, 1–8. [Google Scholar] [CrossRef] - Fu, J.; Zhu, J.; Wang, Z.; Wang, Y.; Wang, S.; Yan, R.; Xu, Q. Highly–efficient and selective adsorption of anionic dyes onto hollow polymer microcapsules having a high surface–density of amino groups: Isotherms, kinetics, thermodynamics and mechanism. J. Colloid Interface Sci.
**2019**, 542, 123–135. [Google Scholar] [CrossRef] - Freundlich, H.M.F. Uber die adsorption in lusungen. J. Phys. Chem.
**1985**, 57, 387–470. [Google Scholar] - Freundlich, H.M.F. Over the adsorption in solution. J. Phys. Chem.
**1906**, 57, 385–471. [Google Scholar] - Arshadi, M.; Mousavinia, F.; Amiri, M.J.; Faraji, A.R. Adsorption of methyl orange and salicylic acid on a nano–transition metal composite: Kinetics, thermodynamic and electrochemical studies. J. Colloid Interface Sci.
**2016**, 483, 118–131. [Google Scholar] [CrossRef] - Qu, J.; Akindolie, M.S.; Feng, Y.; Jiang, Z.; Zhang, G.; Jiang, Q.; Deng, F.; Cao, B.; Zhang, Y. One–pot hydrothermal synthesis of NaLa(CO
_{3})_{2}decorated magnetic biochar for efficient phosphate removal from water: Kinetics, isotherms, thermodynamics, mechanisms and reusability exploration. Chem. Eng. J.**2020**, 394, 124915. [Google Scholar] [CrossRef] - Xu, P.; Zeng, G.M.; Huang, D.L.; Lai, C.; Zhao, M.H.; Wei, Z.; Li, N.J.; Huang, C.; Xie, G.X. Adsorption of Pb(II) by iron oxide nanoparticles immobilized Phanerochaete chrysosporium: Equilibrium, kinetic, thermodynamic and mechanisms analysis. Chem. Eng. J.
**2012**, 203, 423–431. [Google Scholar] [CrossRef] - Frhlich, A.C.; Ocampo-Pérez, R.; Diaz-Blancas, V.; Salau NP, G.; Dotto, G.L. Three–dimensional mass transfer modeling of ibuprofen adsorption on activated carbon prepared by sonication. Chem. Eng. J.
**2018**, 341, 65–74. [Google Scholar] [CrossRef] - Ocampo-Perez, R.; Aguilar-Madera, C.G.; Díaz-Blancas, V. 3D modeling of overall adsorption rate of acetaminophen on activated carbon pellets. Chem. Eng. J.
**2017**, 321, 510–520. [Google Scholar] [CrossRef] - Furusawa, T.; Smith, J.M. Fluid-particle and intraparticle mass transport rates in slurries. Ind. Eng. Chem. Fundam.
**1973**, 12, 197–203. [Google Scholar] [CrossRef] - Wilke, C.R.; Chang, P. Correlation of diffusion coefficients in dilute solutions. AIChE J.
**1955**, 1, 264–270. [Google Scholar] [CrossRef] - Poling, B.E.; Prausnitz, J.M.; O’Connell, J.P. The Properties of Gases and Liquids; McGraw–Hill: New York, NY, USA, 1977; pp. 401–452. [Google Scholar]

**Figure 2.**Concentration decay curves of hydroquinone on PAC: (

**a**) 25 mg/L; (

**b**) 50 mg/L; and (

**c**) 100 mg/L hydroquinone fitted by pore volume and surface diffusion model, surface diffusion model, and pore volume diffusion model; 25, 50, and 100 mg/L hydroquinone fitted by (

**d**) pore volume and surface diffusion model, (

**e**) pore volume diffusion model, and (

**f**) surface diffusion model.

**Figure 4.**(

**a**–

**h**) Evolution of magnitude and direction of N

_{AP}during the adsorption of hydroquinone in PAC.

**Figure 5.**(

**a**–

**h**) Evolution of magnitude and direction of N

_{AS}during the adsorption of hydroquinone in PAC.

**Figure 6.**(

**a**–

**h**) Evolution of SDCP% for hydroquinone transport inside PAC as a function of contact time.

Project | Value |
---|---|

ρ_{s} (kg/m^{3}) | 1.63 |

ρ_{p} (kg/m^{3}) | 0.52 |

ε_{p} | 0.68 |

**Table 2.**Related parameters of adsorption isotherm models at 20, 30 and 40 °C of hydroquinone on PAC.

Isotherm Models | Hydroquinone | |||
---|---|---|---|---|

20 °C | 30 °C | 40 °C | ||

Langmuir | q_{m} (mg/g) | 147.06 | 156.25 | 158.73 |

k_{L} (L/mg) | 0.3063 | 0.3170 | 0.3535 | |

Adj R^{2} | 0.9647 | 0.9624 | 0.9943 | |

Freundlich | k_{F} (mg/g(L/mg)^{1/n}) | 50.32 | 40.65 | 39.05 |

n | 3.71 | 2.68 | 2.67 | |

Adj R^{2} | 0.9972 | 0.9969 | 0.9901 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Shi, S.; Luo, A.; Hao, J.; Xie, S.; Feng, J.
Three-Dimensional Mass Transfer Modeling of Hydroquinone Adsorption on *Phragmites australis* Biochar. *Toxics* **2023**, *11*, 639.
https://doi.org/10.3390/toxics11070639

**AMA Style**

Shi S, Luo A, Hao J, Xie S, Feng J.
Three-Dimensional Mass Transfer Modeling of Hydroquinone Adsorption on *Phragmites australis* Biochar. *Toxics*. 2023; 11(7):639.
https://doi.org/10.3390/toxics11070639

**Chicago/Turabian Style**

Shi, Shengli, Aiguo Luo, Jianwei Hao, Shulian Xie, and Jia Feng.
2023. "Three-Dimensional Mass Transfer Modeling of Hydroquinone Adsorption on *Phragmites australis* Biochar" *Toxics* 11, no. 7: 639.
https://doi.org/10.3390/toxics11070639