Properties and Kinetics of Selective Zinc Leaching with Choline Chloride and Urea

Abstract

A choline chloride-urea (ChCl-urea) deep eutectic solvent (DES) was used to experimentally investigate the secondary recovery of zinc from zinc-bearing dust sludge via a leaching process. The effects of varying the liquid–solid ratio, leaching temperature, stirring speed, and leaching time on the zinc leaching efficiency were determined, and the optimum values of these parameters were found to be 15:1, 90 °C, 400 rpm, and 600 min, respectively, at which a leaching efficiency of 86.87% was achieved. XRF and EDS analyses confirmed that the zinc content in the sludge decreased noticeably after leaching, while those of other elements did not, indicating the selective and efficient leaching of zinc. A study of the leaching kinetics showed that the reaction conforms to the nuclear shrinkage model without solid product layer formation, and the calculated apparent activation energy is 22.16 kJ/mol.

1. Introduction

Zinc is an important raw material for the national economy of China. Over the past two decades, the country’s demand for this material has continued to grow. The proportion of zinc consumed by China in relation to global zinc consumption increased from 15.18% in the year 2000 to over 50% by 2020, and the total amount of zinc consumed by the country stands at 6.42 million metric tons [1,2,3,4]. Although China is a large zinc producer, the poor endowment of primary zinc mineral resources and the resource exhaustion resulting from many years of mining have resulted in its dependence on imported zinc exceeding 35%, which affects the country’s strategic resource security [5,6,7]. To maximize resources, the recovery of zinc from zinc-bearing waste is becoming increasingly important; however, such waste is difficult to recycle due to the wide range of sources of varying quality and the increased potential for secondary pollution. Hence, it is important for the zinc recycling industry to be developed in a green and efficient way.

There are many ways to use zinc-bearing dust sludge, including the extraction of valuable metals or direct materialization. Yang [8] prepared α-Fe₂O₃/ZnFe₂O₄ using blast furnace dust as a raw material. The product showed good photocatalytic degradation activity for the methylene blue group and realized the resource utilization of zinc-bearing dust sludge. Gong [9] used a zinc volatilization roasting–magnetic separation process to recycle the zinc in high zinc-bearing dust sludge. However, a large amount of both zinc oxide and iron oxide were reduced simultaneously during roasting, resulting in high carbon consumption, while the volatilization of zinc in the high-temperature environment resulted in a large amount of energy wastage. Additionally, traditional acid leaching or alkali leaching methods can be used to extract zinc, although both these approaches suffer from drawbacks. Specifically, acid leaching will tend to dissolve not only zinc but also other metallic substances present in the zinc-containing dust sludge, such as iron and calcium. Alternatively, when alkali leaching is used, a high zinc leaching efficiency cannot be obtained as the alkaline solution can only dissolve the zinc oxide present in the sludge and not the zinc ferrite [10,11,12]. However, in both types of processes, the corrosive nature of the solutions can lead to equipment damage and environmental pollution.

Compared to traditional zinc extraction processes, the use of deep eutectic solvents (DESs) offers significant advantages due to their excellent physical and chemical properties [13]. In recent years, research into the application of such solvents in the separation of mixtures has gradually increased, and their use in fields such as the dissolution of metal minerals and sewage treatment has become increasingly widespread [14,15,16]. ChCl-urea DESs, in particular, have been shown to possess a unique selective dissolution ability for ZnO. During the leaching process, these solutions undergo a complexation reaction with ZnO to form [ZnOCl(NH₂CONH₂)₂]⁻ [17], thereby enabling the extraction of metallic zinc. Against this backdrop, the present study uses an experimental approach to investigate the leaching of zinc oxide from zinc-bearing dust sludge using a ChCl-urea DES with a ChCl:urea molar ratio of 1:2. To optimize the process, the effects of varying the key parameters such as the liquid–solid ratio, leaching temperature, leaching time, and stirring speed are investigated. In addition, the kinetics of the leaching reaction is studied based on the nuclear shrinkage model. The goal is to develop a simple method for the recovery of zinc from zinc-bearing dust sludge. The process effectively avoids the corrosion of strong acid and alkali, and a high-temperature environment with high energy consumption which will significantly reduce the cost of utilizing or recycling zinc-bearing dust sludge.

2. Materials and Methods

2.1. Properties of Zinc-Bearing Dust Sludge

The zinc-bearing dust sludge used in the experiments was obtained from a steel plant in Antai, Shanxi, China. Its chemical element analysis (

Table 1. Chemical multielement analysis of zinc-bearing dust sludge (wt.%).

Element	TFe	ZnO	SiO2	Cl	Al2O3	CaO	PbO	MgO	K2O
wt. %	35.11	12.98	6.08	5.76	3.86	3.70	2.13	2.04	1.30
Standard deviation	0.01	0.02	0.01	0.01	0.03	0.01	0.02	0.01	0.01

) reveals that the chemical composition of the sample is complex, with the main elements present being Fe, Zn, and Si. In terms of compounds present, the proportions of ZnO and Fe₂O₃ were 12.98% and 35.11%, respectively. It is also worth noting that the chlorine content of the sludge was 5.76%. When chlorine is present, it will undergo chlorination reactions with water to produce corrosion-causing acid, while simultaneously undergoing replacement reactions with Fe₂O₃, ZnO, and other metal oxides in the sludge, thereby accelerating the corrosion of the metal oxide surface.

Laser particle size analysis was carried out on the zinc-bearing dust sludge (Figure 1), which revealed that the volume-weighted average particle size of the sludge sample was 76.80 µm. X-ray diffraction (XRD) analysis results are shown in Figure 2, whence it can be seen that the main zinc-bearing minerals present were simonkolleite (Zn₅(OH)₈Cl₂), zincite (ZnO), sphalerite (ZnS), and franklinite (ZnFe₂O₄). In addition, the main iron-bearing minerals present were magnetite and hematite, and small amounts of gypsum and quartz were also present. The type of X-ray used in XRD is Cu Kα radiation with a wavelength of 0.154056 nm.

2.2. Main Reagents and Instruments Used

The main reagents used in this study were choline chloride (HOC₂H₄N(CH₃)₃Cl) and urea (NH₂CONH₂). The main instruments used were a vacuum drying oven (DZF-6020, Shanghai Jinghong Laboratory Instrument Co., Ltd., Shanghai, China), and an X-ray fluorescence spectrometer (XRF) (RIGAKU ZSX Priums, PANalytical, Tokyo, Japan).

2.3. Preparation of Deep Eutectic Solvent

To prepare the ChCl-urea DES, some choline chloride and urea were placed in a vacuum drying oven for 840 min under a temperature and pressure of 80 °C and −0.05 MPa, respectively, before being mixed thoroughly in a molar ratio of 1:2, placed into a 1 L beaker, and heated in an oil bath at 80 °C to obtain a uniform transparent solution which was sealed for later use [18]. The prepared ChCl-urea DES is shown in Figure 3. It can be seen from the figure that this ChCl-urea DES is a colorless and transparent liquid with a viscosity greater than water. At 80 °C, the viscosity of the DES was 20 mPa·s.

2.4. Experimental Method

In each experiment, 10,000 g of a sludge sample was added to the prepared ChCl-urea DES in a 300 mL conical flask at a given ratio of liquid at 5:1,10:1,15:1, or 20:1 volume to solid mass (liquid–solid ratio). A magnetic rotor was added to the prepared conical flask, it was placed on the magnetic stirrer and heated in a water bath at 60, 70, 80, 90, and 100 °C. The leaching temperature and stirring speed were controlled using the six-link asynchronous electric magnetic stirrer. The experiment ended after a certain reaction time, the filter residue and filtrate were separated using the vacuum filter extractor and the filter residue was dried and weighed, and the volume of the filtrate was measured and ascertained the zinc contention the filtrate via atomic absorption. Each single factor experiment was repeated three times, and if the experimental data was normal, the final leaching efficiency was obtained by taking the average of the three results, which made the experimental data more reliable. The zinc leaching efficiency, ε, was calculated as follows:

$$\mathsf{\epsilon }=\frac{{\mathrm{V}}_1{ \times \mathrm{c}}_1}{{\mathrm{m}}_0{ \times \mathrm{x}}_0} \times 100\%$$

(1)

where m₀ is the mass of the zinc-bearing sludge dust sample (g), x₀ is zinc content of the zinc-bearing dust sludge sample (%), V₁ is the volume of leachate (L), and c₁ is the concentration of zinc in the leachate (g/L).

3. Results and Discussion

3.1. Effect of Different Conditions on the Zinc Leaching Efficiency

3.1.1. Liquid–Solid Ratio

The liquid–solid ratio was varied at different leaching times while keeping the leaching temperature and stirring speed constant at 70 °C and 400 rpm, respectively (Figure 3). The results show that for leaching times < 600 min, the zinc leaching efficiency is greatly affected by the liquid–solid ratio, whereas for leaching times > 600 min, the leaching efficiency increases slowly with time before plateauing at 600 min. The main reason for this is that increasing the liquid–solid ratio leads to a reduction in the concentration of zinc-bearing dust sludge in DESs and in the concentration of [ZnOCl(NH₂CONH₂)₂]⁻, which increases the rate of mass transfer [19] between the sludge and the DES, thereby increasing the leaching efficiency. With continuous leaching, the zinc content in the sludge gradually decreases, and the solid–liquid reaction rate tends towards equilibrium. At a leaching time of 600 min, the leaching efficiency increased by only 0.82% (from 74.30% to 75.12%) when the liquid–solid ratio was increased from 15:1 to 20:1. Because of the relatively high viscosity of this DES, a large liquid–solid ratio will cause certain difficulties for subsequent liquid–solid separation, and at the same time, considering the cost of the experiment, therefore, the liquid–solid ratio in subsequent experiments was fixed at 15:1.

3.1.2. Leaching Temperature

The leaching temperature was varied at different leaching times while keeping the liquid–solid ratio and stirring speed constant at 15:1 and 400 rpm, respectively (Figure 4). The results show that the zinc leaching effect is heavily temperature-dependent, as increasing the temperature can reduce the viscosity of the ChCl-urea DES and increase the reaction rate. However, as the temperature continues to increase, the leaching efficiency plateaus. Figure 4 shows that, at a leaching time of 600 min, the zinc extraction efficiencies at 90 °C and 100 °C (which represents the maximum possible temperature of the water bath used) were 86.87% and 87.84%, respectively. Considering that the zinc leaching efficiency was not very different under the two temperature conditions, the leaching temperature in subsequent experiments was fixed at 90 °C.

3.1.3. Stirring Speed

Under certain conditions, increasing the stirring speed of the mixture can increase the reaction efficiency of the leaching agent by increasing the solid–liquid contact area and reducing the thickness of the diffusion layer. However, under leaching temperature and time conditions of 90 °C and 600 min, respectively, Figure 5 shows that the stirring speed had a relatively small effect on the leaching efficiency. Above 400 rpm, however, the zinc leaching efficiency hardly changed. Given that excessively fast stirring can cause the leaching liquid to splash, which is undesirable, 400 rpm was chosen as the optimum stirring speed.

3.1.4. Leaching Time

As zinc leaching is an equilibrium process, increasing the leaching time will only improve the leaching efficiency as long as equilibrium has not yet been reached. In this study, the leaching time was varied from 120–840 min. Figure 3, Figure 4 and Figure 5 show that, once the leaching time increases to 600 min, the zinc leaching efficiency does not change significantly thereafter, indicating that this time corresponds to diffusion equilibrium. Hence, the optimum leaching time was selected as 600 min.

3.2. Response Surface Model of Zinc Oxide Leaching in Zinc-Bearing Dust Sludge

The orthogonal experiment was designed so that the liquid–solid ratio, leaching temperature, leaching time, and stirring speed were used as independent variables, and zinc leaching efficiency was used as the evaluation index, and the factor values and level codes were obtained (

Table 2. Experimental factor values and level coding.

Factor	Code	Level Coding
		−1	0	1
Liquid-solid ratio (mL/g)	X1	10:1	15:1	20:1
Time (min)	X2	80	90	100
Temperature (°C)	X3	480	600	720
Stirring speed (rpm)	X4	300	400	500

). The Stat-Ease Design-Expert 12.0 software package was used to design 29 sets of leaching experiments, in which the zinc leaching efficiencies obtained under different conditions are shown in

Table 3. Experimental design and results.

Number	Factor				Zinc Leaching Efficiency
	X1 (mL/g)	X2 (min)	X3 (°C)	X4 (rpm)	Y (%)
1	0	0	−1	1	82.50
2	0	−1	0	1	81.51
3	0	1	0	1	87.31
4	0	1	−1	0	82.65
5	−1	0	0	1	83.44
6	1	0	0	−1	86.50
7	1	0	1	0	87.58
8	0	0	0	0	86.87
9	1	0	−1	0	83.85
10	−1	−1	0	0	78.34
11	0	−1	−1	0	77.37
12	−1	1	0	0	84.12
13	1	0	0	1	87.20
14	0	0	0	0	87.47
15	0	0	−1	−1	81.02
16	0	0	1	1	87.30
17	1	−1	0	0	82.17
18	0	0	0	0	85.90
19	0	0	1	−1	86.00
20	0	−1	0	−1	80.13
21	−1	0	−1	0	80.30
22	−1	0	0	−1	82.26
23	0	1	0	−1	86.54
24	0	1	1	0	88.26
25	1	1	0	0	87.80
26	0	−1	1	0	85.57
27	0	0	0	0	86.32
28	0	0	0	0	86.47
29	−1	0	1	0	83.53

.

The Stat-Ease Design-Expert 12.0 software package was used to analyze the sample data and the repeatedly binomial regression model of zinc leaching efficiency was obtained (Equation (2)).

Y = 86.61 + 1.93A + 2.63B + 2.55C + 0.5675D − 0.0375AB + 0.1250AC − 0.1200AD − 0.6475BC −
0.1525BD − 0.0450CD − 1.30A2 − 1.97B2 − 1.45C2 − 0.7247D2

(2)

where A is the liquid–solid ratio, B is the leaching time, C is the leaching temperature, and D is the stirring speed.

Equation (2) was used in the analysis of the variance of the zinc leaching efficiency model. In the analysis results (

Table 4. Variance analysis of zinc leaching efficiency model.

Source	Sum of Squares	df	Mean Square	F-Value	p-Value
Model	248.10	14	17.72	22.47	<0.0001
A-Liquid-solid ratio	44.51	1	44.51	56.44	<0.0001
B-Time	83.16	1	83.16	105.45	<0.0001
C-Temperature	77.78	1	77.78	98.62	<0.0001
D-Stirring speed	3.86	1	3.86	4.90	0.0440
AB	0.0056	1	0.0056	0.0071	0.9339
AC	0.0625	1	0.0625	0.0793	0.7824
AD	0.0576	1	0.0576	0.0730	0.7909
BC	1.68	1	1.68	2.13	0.1668
BD	0.0930	1	0.0930	0.1180	0.7364
CD	0.0081	1	0.0081	0.0103	0.9207
A²	11.00	1	11.00	13.95	0.0022
B²	25.10	1	25.10	31.83	<0.0001
C²	13.58	1	13.58	17.23	0.0010
D²	3.41	1	3.41	4.32	0.0566
Residual	11.04	14	0.7886
Lack of Fit	9.63	10	0.9625	2.72	0.1735
Pure Error	1.41	4	0.3537

), if p < 0.0001, the effect was highly significant, if p ≤ 0.0500, it was significant, and if p > 0.1000, it was not significant. The F-value of the model (Table 4) was 22.47, p < 0.0001, indicating that this regression equation was highly significant, and there was a non-linear relationship between each factor and the leaching efficiency of the response value. The lack of fit was 2.72 and its p-value was 0.1735, which was not significant, indicating that the regression equation fitted well. From the p-value and the coefficients of Equation (2), it can be judged that the order of the significant influence of the factors on zinc leaching efficiency was leaching time> leaching temperature> liquid-solid ratio> stirring speed.

Response surface of the influence of various factors on zinc leaching efficiency were shown in Figure 6.

To verify the accuracy of the model, three sets of experiments were carried out under different experimental conditions. The comparison between the zinc leaching efficiency values and the values calculated by the multiple regression fitting is shown in

Table 5. Comparison of mental values and calculated values.

Liquid-Solid Ratio (mL/g)	Time (min)	Temperature (°C)	Stirring Speed (rpm)	Experimental Value (%)	Calculated Values (%)
10:1	720	80	500	82.12	82.48
20:1	480	100	300	85.25	85.04
15:1	480	100	300	83.96	84.13

. Under different conditions, the deviation between the experimental value and the calculated value of multiple regression fitting was less than 0.50%. Therefore, the model can truly reflect the effects of various factors on zinc leaching efficiency.

3.3. Characterization of Zinc-Bearing Dust Sludge before and after Leaching

To study the changes in the morphology and surface composition of the raw material and leaching residue, the samples were analyzed by a scanning electron microscope (SEM) before and after leaching. The results are shown in Figure 7a–c, whence it can be seen that the surface of the sludge before leaching was rough and irregular, with many relatively dense and bright colored flocs and strips present; however, after leaching, many holes and obvious gullies appeared, which is likely due to the dissolution of zinc oxide.

The point scanning results of the X-ray spectrum analysis (Figure 7) show that the zinc content in the dense flocks and striped parts of the sample was higher before leaching (Figure 7b, point A), while the darker parts of the sample surface consist of carbon and oxygen (Figure 7b, point B). The large reduction in flocs and strips after leaching also serves as an indicator that zinc has been leached. The XRD pattern after leaching (Figure 7d) showed that the main minerals present in the leaching residue were hematite, marcasite, and zoisite, and that the diffraction intensity of zinc-containing minerals cannot be detected. The type of X-ray used in XRD was Cu Kα radiation with a wavelength of 0.154056 nm.

Table 6. XRF analysis of leaching residue (%).

TFe	ZnO	SiO2	Cl	Al2O3	CaO	PbO	MgO	K2O
27.22	1.86	10.18	2.28	6.17	3.54	1.50	1.51	0.16

shows the XRF analysis results for the leaching residue under optimal leaching conditions, whence it can be seen that the ZnO content of the samples before and after leaching decreased from 12.98% to 1.86%, while that of Fe₂O₃ decreased from 35.11% to 27.22%. Furthermore, the leaching efficiency was 20.01%, and the content of other oxides did not change significantly. These results indicate that the ChCl-urea DES indeed possesses excellent ZnO-dissolving properties.

3.4. Reaction Mechanism

The formation of the ChCl-urea DES with a molar ratio of 1:2 is as follows [20]:

HOC₂H₄N(CH₃)₃Cl (aq) + 2(NH₂CONH₂) (aq) = [HOC₂H₄N(CH₃)₃]⁺ (aq) + (NH₂CONH₂)₂[Cl]⁻ (aq)

(3)

In this process, the choline chloride and urea molecules act as hydrogen bond acceptors and hydrogen bond donors, respectively, interacting to generate hydrogen bond forces, which destroys the lattice structure of ChCl and urea, and reduces the lattice energy, thereby lowering the melting point of ChCl and urea, and forming a liquid mixture [21]. The BIOVIA Materials Studio software package was used to simulate the microstructure of the ChCl-urea DES (Figure 8), in which one HOC₂H₄N(CH₃)₃⁺, one Cl⁻, and two NH₂CONH₂ molecules are combined with each other through hydrogen bonds, with the Cl^– forming a hydrogen bond with the −NH in NH₂CONH₂, and the O in urea forming a hydrogen bond with the −CH in HOC₂H₄N(CH₃)₃⁺.

In the leaching process, the ChCl-urea DES dissolved the ZnO in the zinc-bearing dust sludge to form the complex [ZnOCl(NH₂CONH₂)₂]⁻, as follows:

ZnO (s) + 2(NH₂CONH₂) (aq) + [Cl]^– (aq) = [ZnOCl(NH₂CONH₂)₂]^– (aq)

(4)

The Materials Studio-simulated microstructure of the [ZnOCl(NH₂CONH₂)₂]^– is shown in Figure 9, shows that ChCl-urea decomposed in the process of interacting with ZnO, during which the choline cations formed multiple hydrogen bonds with the oxygen atoms on the surface of ZnO, while the Cl^– and urea formed chemical bonds with the Zn atoms.

3.5. Leaching Kinetic Analysis

To determine the mechanism of the leaching reaction and maximize the efficiency of the leaching process, the reaction kinetics was modeled. The reaction of ZnO with the ChCl-urea DES is a heterogeneous (solid–liquid reaction), and the reactants (powder particles) were regarded as uniform spheres; hence, the most used type of model for such systems, the nuclear shrinkage model, was adopted. During the leaching process, the free urea reacts with Cl^– and zinc oxide in the zinc-bearing dust sludge, and the product [ZnOCl(NH₂CONH₂)₂]⁻ dissolved in the leaching agent. Therefore, the leaching process is produced without a solid product layer reaction. Due to the high concentration of ChCl-urea DES, the consumption of urea and Cl⁻ during the reaction can be ignored, and the concentration of the extractant can be regarded as unchanged. Therefore, the integrated rate equation is shown below [22]:

$${1 - (1 - \mathrm{x})}^{\frac{1}{3}}=\frac{\mathrm{b}{\mathrm{k}}^{\prime }{\mathrm{C}}_0}{\mathrm{a}\mathsf{\rho }{\mathrm{r}}_0}\mathrm{t}=\mathrm{kt}$$

(5)

where x is the leaching efficiency of ZnO in the dust sludge at time t; k^’ is the apparent rate constant (min⁻¹), t is the reaction time (min), and C₀ and ρ are the initial concentration and molar density (both in mol/L) of the ChCl-urea DES, respectively, r₀ is the initial radius of the reaction particles of the zinc-bearing dust sludge sample (m); k is the kinetic constant calculated (m/min), and a and b are the stoichiometric coefficients of ZnO and (NH₂CONH)₂[Cl]⁻, respectively.

3.5.1. Determination of the Kinetic Model

Using the data from Section 3.1, the kinetic constant k and correlation coefficient of the leaching reaction were calculated using Equation (5), with the results shown in

Table 7. Kinetic constants and correlation coefficients of reaction kinetic models under different conditions.

Parameter	Leaching Reaction Kinetic Model
	${1 - (1 - \mathrm{x})}^{\frac{1}{3}}=\frac{\mathrm{b}{\mathrm{k}}^{\prime }{\mathrm{C}}_0}{\mathrm{a}\mathsf{\rho }{\mathrm{r}}_0}\mathrm{t}=\mathrm{kt}$
	x	k′(m/min)	k(min−1)	R2
Liquid–solid ratio/(mL/g)
5:1	54.49%	1.61 × 10−8	4.18 × 10−4	0.9924
10:1	68.03%	2.39 × 10−8	4.97 × 10−4	0.9856
15:1	74.30%	2.78 × 10−8	4.98 × 10−4	0.9909
20:1	75.12%	3.63 × 10−8	4.36 × 10−4	0.9882
T/°C
60	62.83%	1.21 × 10−6	1.57 × 10−2	0.9788
70	74.30%	1.64 × 10−6	2.13 × 10−2	0.9784
80	81.37%	2.03 × 10−6	2.45 × 10−2	0.9802
90	86.87%	2.30 × 10−6	2.99 × 10−2	0.9957
Stirring speed/rpm
100	82.96%	2.00 × 10−6	4.53 × 10−4	0.9967
200	84.18%	3.48 × 10−6	4.46 × 10−4	0.9934
300	85.04%	3.54 × 10−6	4.79 × 10−4	0.9952
400	86.87%	3.56 × 10−6	4.82 × 10−4	0.9947
500	87.21%	3.73 × 10−6	4.97 × 10−4	0.9956

.

The values calculated using the leaching kinetic model at different values of the liquid–solid ratio, leaching temperature, and stirring speed are shown in Figure 10, which confirms that, according to Equation (5), the zinc leaching efficiency is linearly correlated with all three variables, further indicating the validity of this model.

3.5.2. Determination of Apparent Activation Energy and Pre-Exponential Factor

The reaction rate constant was modeled using the Arrhenius equation, as follows:

$${\mathrm{k}=\mathrm{Ae}}^{{-\mathrm{E}}_{\mathrm{a}}/\mathrm{RT}}$$

(6)

$${\mathrm{lnk}=\mathrm{lnA} - \mathrm{E}}_{\mathrm{a}}/\mathrm{R}$$

(7)

where A is the pre-exponential factor, R is the universal gas constant (=8.314 J mol⁻¹K⁻¹), T is the absolute temperature, and E_a is the apparent activation energy of the reaction. Drawing from Equation (7), Figure 11 was obtained. The activation energy of the leaching reaction is 21.66 kJ/mol.

3.5.3. Leaching Kinetic Equation

To quantitatively describe the influence of the liquid–solid ratio and leaching temperature on the kinetics of zinc leaching, a semi-empirical equation was proposed, as follows [23,24]:

$$1 - {\left(1 - \mathrm{x}\right)}^{\frac{1}{3}}=\mathrm{kt}=\left[{\mathrm{k}}_{\mathrm{c}}·{\mathrm{N}}^{\mathsf{\alpha }}·{\mathrm{C}}^{\mathsf{\beta }}·{\mathrm{e}}^{ -\frac{\mathrm{Ea}}{\mathrm{RT}}}\right]\mathrm{t}$$

(8)

where k_c is the pre-exponential factor, and N, C, and T are the liquid–solid ratio, stirring speed, and leaching temperature, respectively. If C and T are constant, then N is the only variable, and Equation (8) may be simplified as:

$$1 - {\left(1 - \mathrm{x}\right)}^{\frac{1}{3}}{=\mathrm{kt}=\mathrm{k}}_{\mathrm{c}}·{\mathrm{N}}^{\mathsf{\alpha }}·\mathrm{t}$$

(9)

$$\frac{\mathrm{d}\left[1 - {\left(1 - \mathrm{x}\right)}^{\frac{1}{3}}\right]}{\mathrm{dt}}{=\mathrm{k}=\mathrm{k}}_{\mathrm{c}}·{\mathrm{N}}^{\mathsf{\alpha }}$$

(10)

$$\ln \left[\frac{\mathrm{d}\left[1 - {\left(1 - \mathrm{x}\right)}^{\frac{1}{3}}\right]}{\mathrm{dt}}\right]=\mathrm{lnk}=\mathsf{\alpha }\mathrm{lnN}+\ln {\mathrm{k}}_{\mathrm{c}}$$

(11)

For Equation (11), if the values of lnK and lnN under different liquid–solid ratios are known, then lnk-α, which was $\ln \left[\frac{\mathrm{d}\left[1 - {\left(1 - \mathrm{x}\right)}^{\frac{1}{3}}\right]}{\mathrm{dt}}\right]-\mathrm{LnN}$ correlation drawing, can be performed, as shown in Figure 12a. Linear fitting on the scatter points was performed to get the equation in the Figure 12a, where α = 0.55744, lnk_c = −9.37142. In the same way, it can be calculated as β = 0.0551, lnk_c = −7.95112 in Equation (10), and Figure 12b was obtained. From Figure 12, we can see that E_a/R = −2604.8451, lnk_c = 3.705, and k_c = −4.53918 can be calculated by the average method. Hence, the kinetic equation of zinc leaching becomes:

$$1- {\left(1 - \mathrm{x}\right)}^{\frac{1}{3}}=\left[-4.53918·{\mathrm{N}}^{0.55744}·{\mathrm{C}}^{0.0551}·{\mathrm{e}}^{- \frac{2604.8451}{\mathrm{T}}}\right]\mathrm{t}$$

(12)

4. Conclusions

(1)

Based on the single-factor experimental results, the optimum process conditions for zinc leaching were determined to be a liquid–solid ratio of 15:1, a stirring speed of 400 rpm, a leaching temperature of 90 °C, and a leaching time of 600 min, resulting in a leaching efficiency of 86.87%.

(2)

The leaching reaction involved the complexation of Zn with the ChCl-urea DES with ZnO to form [ZnOCl(NH₂CONH₂)₂]⁻.

(3)

SEM analysis showed that the surface morphology of the zinc-bearing dust sludge samples changed noticeably before and after leaching, with the samples becoming darker and a large number of holes appearing on the surface. EDS and XRF analyses confirmed that the metallic zinc content was indeed reduced after leaching, while that of other elements did not change significantly.

(4)

The kinetics of the leaching process was found to be consistent without solid product layer formation with the nuclear shrinkage model. Using this model, the activation energy was calculated to be 22.16 kJ/mol, and an empirical correlation was obtained to quantify the dependence of the leaching efficiency on the liquid–solid ratio, stirring speed, and leaching temperature.