# The Effect of Reverse Sorption on an Extraction Kinetics Melanin Case

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

_{2})

_{3}CNH

_{2}) for maintaining a constant pH was used as a solvent in the entire experimental series.

#### 2.2. Mechanical Treatment

#### 2.3. Studying the Extraction Kinetics

#### 2.4. Mathematical Models

_{0}is the equilibrium concentration at t → ∞ (mg/mL); r is the characteristic diffusion length (in this case, it is equal to the particle radius), µm; and t is time, min [20,21].

_{t}is the amount of substance released at instant t, mg; M

_{∞}is the amount of substance released after an infinite time, mg; D

_{m}is the diffusion coefficient, µm

^{2}/min; C

_{ms}is the solubility of the substance in the matrix, mg/mL; r

_{0}is the radius of the spherical matrix, µm; C

_{Init}is the initial substance concentration in the matrix, mg/mL; and t is time, min [22].

_{1}is the amount of substance released; M

_{∞}is the amount of substance in the equilibrium state; M

_{t}is the amount of substance released at instant t; K is the constant taking into account structural modifications and geometric characteristics of the system (also being regarded as the desorption rate constant); and n is the power exponent of release (associated with the mechanism of substance release) as a function of time t.

_{i}is the amount of substance released, mg; M

_{∞}is the amount of substance in the equilibrium state, mg; M

_{i}is the amount of substance released at instant t, mg; K is the constant taking into account structural modifications and geometric characteristics of the system depending on time t, min

^{−1}; and t is time, min.

_{Init}is the initial solid-phase concentration, mg/mL; C is the concentration in the solid state (in the substance) at instant t, mg/mL; C

_{1}is the concentration in the solution at instant t, mg/mL; B

_{i}is the constant form factor of a particle (a dimensionless unit); D is the effective diffusion coefficient in the solid-phase pores, µm

^{2}/min; R is the size of solid particles (µm); µ

_{i}is the characteristic root (a dimensionless unit); and t is time, min [24].

#### 2.5. Structure and Morphology Analysis

_{200}is the intensity of reflection (200); and I

_{min}is the minimum between reflections (110) and (200).

## 3. Results and Discussion

#### 3.1. Analysis of the Effect of Temperature on Extraction

_{∞}.

#### 3.2. Calculation of the Diffusion Coefficient Using the Baker–Lonsdale Model

^{2}).

#### 3.3. Calculation of the Diffusion Coefficient Using the Akselrud’s Model

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Changes in melanin sorption capacity of the plant biomass compared to that for the equilibrium concentration of melanin in the solution at different temperatures: curve 1—dependence at 40 °C; curve 2—dependence at 50 °C; and curve 3—dependence at 60 °C.

**Figure 2.**The Langmuir isotherms of melanin adsorption on buckwheat hulls: 1—dependence at 40 °C; 2—dependence at 50 °C; and 3—dependence at 60 °C.

**Figure 3.**The Freundlich isotherms of melanin adsorption on buckwheat hulls: 1—dependence at 40 °C; 2—dependence at 50 °C; and 3—dependence at 60 °C.

**Figure 4.**The plot showing comparison of D according to the Baker–Lonsdale model before and after applying the correction coefficient: 1—before applying the correction coefficient; 2—after applying the correction coefficient.

**Figure 5.**The plot showing comparison of D according to Akselrud’s model before and after applying the correction coefficient: 1—before applying the correction coefficient; 2—after applying the correction coefficient.

**Table 1.**Changes in melanin concentration in the solution with respect to the equilibrium concentration.

Weight of the Sample of Buckwheat Hulls for Melanin Extraction, g | Ultimate Equilibrium Concentration of Melanin in the Solution, µg/mL | Changes in Melanin Concentration in the Solution after the Equilibrium Was Attained, µg/mL | ||
---|---|---|---|---|

Temperature: 40 °C | Temperature: 50 °C | Temperature: 60 °C | ||

0.5 | 39 ± 1.95 | 1.7 ± 1.2 | 3.0 ± 1.2 | 0.1 ± 0.9 |

1.0 | 70.3 ± 3.52 | 9.0 ± 0.7 | 6.8 ± 1.0 | 8.2 ± 0.9 |

1.5 | 119.6 ± 5.98 | 15.1 ± 0.8 | 13.7 ± 0.8 | 26.8 ± 0.6 |

2.0 | 142.1 ± 7.10 | 22.4 ± 1.3 | 15.3 ± 1.0 | 40.5 ± 0.8 |

3.0 | 172.6 ± 8.63 | 27.7 ± 1.0 | 33.7 ± 1.4 | 35.7 ± 1.2 |

3.5 | 211.4 ± 10.57 | 29.4 ± 1.0 | 46.8 ± 1.5 | 51.8 ± 2.1 |

7.0 | 384.2 ± 19.21 | 31.2 ± 2.2 | 45.9 ± 2.7 | 40.4 ± 1.7 |

14.0 | 598.7 ± 29.93 | 37.6 ± 1.0 | 45.2 ± 1.3 | 42.4 ± 3.4 |

20.0 | 705.5 ± 35.28 | 42.8 ± 3.1 | 44.4 ± 1.0 | 43.1 ± 2.1 |

**Table 2.**The coefficients of Freundlich and Langmuir equations for the isotherms of melanin adsorption on buckwheat hulls at 40, 50, and 60 °C.

Equation Form | Temperature, °C | Correlation | Sorption Parameters | |
---|---|---|---|---|

Freundlich equation | $A=a\xb7{C}^{\frac{1}{n}}$ or $lgA=lga+\frac{1}{n}\xb7lgC$ | 40 | R^{2} = 0.8309 | a = 0.067 ± 0.021, 1/n = 0.60 ± 0.11 |

50 | R^{2} = 0.9846 | a = 4.1 ± 1.4, 1/n = 1.9 ± 0.10 | ||

60 | R^{2} = 0.9334 | a = 1494 ± 13 1/n = 4.0 ± 0.9 | ||

Langmuir equation | $\frac{c}{A}=\frac{1}{{A}_{\infty}\xb7k}+\frac{c}{{A}_{\infty}}$ | 40 | R^{2} = 0.9037 | A_{∞} = 0.012 ± 0.002 mmol/g *,k = 10.9 ± 1.8 |

50 | R^{2} = 0.9858 | A_{∞} = 0.008 ± 0.001 mmol/g *,k = 102 ± 1 | ||

60 | R^{2} = 0.9799 | A_{∞} = 0.007 ± 0.001 mmol/g *,k = 925 ± 1 |

**Table 3.**The results of calculating the diffusion coefficient without and with allowance for correction.

No. | Crystallinity Index, % | Average Particle size, µm | D Baker–Lonsdale · ${10}^{3}$$,{\mathbf{\mu}\mathbf{m}}^{2}$/min. Before Applying the Correction Coefficient | ${\mathit{R}}^{2}$ | D Baker–Lonsdale · ${10}^{3}$$,{\mathbf{\mu}\mathbf{m}}^{2}$/min. After Applying the Correction Coefficient | ${\mathit{R}}^{2}$ |
---|---|---|---|---|---|---|

Buckwheat Hulls | ||||||

3 | 64 ± 2 | 262 | 98 | 0.907 | 56 | 0.906 |

2 | 56 ± 3 | 300 | 328 | 0.964 | 219 | 0.964 |

1 | 51 ± 4 | 529 | 1113 | 0.910 | 1115 | 0.901 |

5 | 45 ± 3 | 398 | 352 | 0.912 | 277 | 0.911 |

4 | 27 ± 4 | 35 | 19 | 0.814 | 8 | 0.815 |

No. | Crystallinity Index, % | Average Particle Size, µm | D Akselrud · ${10}^{4}$$,{\mathbf{c}\mathbf{m}}^{2}$/s Before Applying the Correction Coefficient | ${\mathit{R}}^{2}$ | D Akselrud · ${10}^{4}$$,{\mathbf{c}\mathbf{m}}^{2}$/s After Applying the Correction Coefficient | ${\mathit{R}}^{2}$ |
---|---|---|---|---|---|---|

Buckwheat Hulls | ||||||

3 | 64 ± 2 | 262 | 10.0 | 0.936 | 1.51 | 0.945 |

2 | 56 ± 3 | 300 | 14.7 | 0.925 | 2.12 | 0.928 |

1 | 51 ± 4 | 529 | 55.4 | 0.941 | 49.5 | 0.952 |

5 | 45 ± 3 | 398 | 22.2 | 0.931 | 4.32 | 0.923 |

4 | 27 ± 4 | 34 | 1.8 | 0.920 | 0.09 | 0.918 |

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**MDPI and ACS Style**

Lomovskiy, I.; Kiryanov, A.; Skripkina, T.
The Effect of Reverse Sorption on an Extraction Kinetics Melanin Case. *Processes* **2023**, *11*, 3192.
https://doi.org/10.3390/pr11113192

**AMA Style**

Lomovskiy I, Kiryanov A, Skripkina T.
The Effect of Reverse Sorption on an Extraction Kinetics Melanin Case. *Processes*. 2023; 11(11):3192.
https://doi.org/10.3390/pr11113192

**Chicago/Turabian Style**

Lomovskiy, Igor, Aleksey Kiryanov, and Tatiana Skripkina.
2023. "The Effect of Reverse Sorption on an Extraction Kinetics Melanin Case" *Processes* 11, no. 11: 3192.
https://doi.org/10.3390/pr11113192