Effect of Solid Concentration on Particle Size Distribution and Grinding Kinetics in Stirred Mills
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe article is written on a rather relevant topic - the study of the influence of various factors on the grinding of raw materials to obtain a certain size class.
The article is well structured, but there are some questions and comments.
1. The purpose of the study should be more clearly stated.
2. The scientific novelty of the study is not quite clear, as similar work has been done before, which is noted in the introduction. The scientific novelty should be emphasized.
3. Materials and methods: What is the initial size of quartz before crushing? The initial mass of the sample?
4. What coarsenesses are taken as coarse size, desired size and overgrinding size?
5. Why particle size was measured by a r Mastersizer. With an initial sample of 512 g, taking a representative sample for analysis (a few grams) is quite difficult. Why wasn't sieve analysis with analysis on a laser diffractometer of fine class used?
6. As a recommendation: it would be interesting to analyze the specific surface area of the newly formed classes as a function of grinding time and solid concentration, as well as to look under a microscope at the shape of the resulting particles.
Author Response
The article is written on a rather relevant topic - the study of the influence of various factors on the grinding of raw materials to obtain a certain size class.
The article is well structured, but there are some questions and comments.
Comment 1. The purpose of the study should be more clearly stated.
Response 1: We thank the reviewer for this comment. The purpose of the study has been added in Section 1. Revisions according to this comment were highlighted in red in the revised manuscript.
Comment 2. The scientific novelty of the study is not quite clear, as similar work has been done before, which is noted in the introduction. The scientific novelty should be emphasized.
Response 2: We thank the reviewer for this comment. The scientific novelty has been added in Section 1. Revisions according to this comment were highlighted in red in the revised manuscript.
Comment 3. Materials and methods: What is the initial size of quartz before crushing? The initial mass of the sample?
Response 3: We thank the reviewer for this comment. Before the quartz was crushed, the d80 was about 5 mm. The initial mass was about 100 kg.
Comment 4. What coarsenesses are taken as coarse size, desired size and overgrinding size?
Response 4: We thank the reviewer for this comment. The material is divided into three size intervals: coarse size (+45 μm), desired size (-45+10 μm) and overgrinding size (-10 μm). Revisions according to this comment were highlighted in red in the revised manuscript.
Comment 5. Why particle size was measured by a r Mastersizer. With an initial sample of 512 g, taking a representative sample for analysis (a few grams) is quite difficult. Why wasn't sieve analysis with analysis on a laser diffractometer of fine class used?
Response 5: We thank the reviewer for this comment. Mastersize-2000 uses laser diffraction to measure the particle size and the particle size distribution of materials. Mastersizer-2000 was produced by Malvern Panalytical Ltd, United Kingdom. To achieve the purpose of analysis, the powder sample was initially dispersed in water and then was underwent ultrasonic treatment for 60 seconds. The sample utilized for the particle size analysis was extracted from the ground material. Each test was repeated three times to obtain an average value.
Comment 6. As a recommendation: it would be interesting to analyze the specific surface area of the newly formed classes as a function of grinding time and solid concentration, as well as to look under a microscope at the shape of the resulting particles.
Response 6: We thank the reviewer for this comment. In this manuscript, we wanted to study the effect of the solid concentration on the particle size distribution and grinding kinetics. We agree that it is helpful for us to further study the relationship between the specific surface area of the newly formed classes as a function of grinding time and solid concentration since the specific surface area of the newly formed classes is an important parameter for grinding products. Therefore, in the future research, we will systematically study the specific surface area of the newly formed classes as a function of grinding time and solid concentration, as well as the shape of the resulting particles.
Reviewer 2 Report
Comments and Suggestions for AuthorsThe manuscript entitled " Effect of solid concentration on particle size distribution and grinding kinetics in stirred mills" was to examine the effect of grinding condition on the grinding performance of the stirred mill. It is crucial for grinding processing to produce maximum fraction of the desired size in grinding products and improve grinding efficiency. The experimental data was simulated by the PBM. Data from those simulations were analyzed using AR method. Therefore, this topic is of great importance. I have a few comments that should be addressed:
1) The second "Table 2" should be "Table 3", and "Table 3" should be "Table 4" in the manuscript.
2) In Page 6: it is recommended that the legend in Figure 3 and Figure 6 use graph with different shapes.
3) Page 5: In section 3.2, it is recommended that the author provide the definition of the solid concentration.
4) You mention in the manuscript that the desired size is the -45+10 μm fraction. Is there a specific reason for choosing this size fraction?
5) “It demonstrates that to produce the maximum fraction of the desired size grinding products, the residence time of the material in the mill should be shortened and the solid concentration should be increased.” The reviewer does not quite understand, please explain.
Comments on the Quality of English LanguageThe English language expression is still acceptable.
Author Response
The manuscript entitled " Effect of solid concentration on particle size distribution and grinding kinetics in stirred mills" was to examine the effect of grinding condition on the grinding performance of the stirred mill. It is crucial for grinding processing to produce maximum fraction of the desired size in grinding products and improve grinding efficiency. The experimental data was simulated by the PBM. Data from those simulations were analyzed using AR method. Therefore, this topic is of great importance. I have a few comments that should be addressed:
Comment 1. The second "Table 2" should be "Table 3", and "Table 3" should be "Table 4" in the manuscript.
Response 1: We thank the reviewer for this comment. We are very sorry for these errors. Revisions according to this comment were highlighted in red in the revised manuscript.
Comment 2. In Page 6: it is recommended that the legend in Figure 3 and Figure 6 use graph with different shapes.
Response 2: We thank the reviewer for this comment. We are very sorry for this error. Revisions according to this comment were highlighted in red in the revised manuscript.
Comment 3. Page 5: In section 3.2, it is recommended that the author provide the definition of the solid concentration.
Response 3: We thank the reviewer for this comment. The definition of the solid concentration has been added in Section 3.2. Revisions according to this comment were highlighted in red in the revised manuscript.
Comment 4. You mention in the manuscript that the desired size is the -45+10 μm fraction. Is there a specific reason for choosing this size fraction?
Response 4: We thank the reviewer for this comment. Stirred media mills are increasingly used for secondary or tertiary grinding in the mineral industry where P80 (P80 is the particle size of the material when the undersize distribution is 80% in grinding products) of less than 100 µm is required. In addition, many researchers agree that fine particles have a lower separation efficiency when the particle size is smaller than 10 μm, especially for the flotation process and the gravity separation process. Stirred mills are more efficient for the particle size range typical of regrind circuits with a particle size down to a P80 value of around 20-40 μm. Furthermore, the feed has a median particle size x50 of 63 µm and a x90 of 194 µm. Based on these analyses, we chose the size interval of -45+10 μm as the desired size interval.
Comment 5. “It demonstrates that to produce the maximum fraction of the desired size grinding products, the residence time of the material in the mill should be shortened and the solid concentration should be increased.” The reviewer does not quite understand, please explain.
Response 5: We thank the reviewer for this comment. We apologize for the confusion. We have rewritten this sentence in the revised manuscript. Revisions according to this comment were highlighted in red in the revised manuscript.
Reviewer 3 Report
Comments and Suggestions for AuthorsComments for author File: 
Comments.pdf
Author Response
The authors have studied the effect of solid concentration on particle size distribution and grinding kinetics in stirred mills considering Quartz as the material of interest. After some minor revisions, the manuscript can be accepted for publication.
Comment 1. How many times each experiment corresponding to a particular solid concentration have been repeated. If possible, show the error bar in the figure showing the experimental results.
Response 1: We thank the reviewer for this comment. The sample utilized for the particle size analysis was extracted from the grinding experiment. Because it will cost a large amount of experimental work if all grinding experiments are repeated, very few published works chose to repeat the grinding experiment [1] [2] [3]. Therefore, we only chose to repeat some grinding experiments and found that their experimental error was relatively small. Although we didn’t repeat all the grinding experiment, the particle size distribution of the sample from each grinding experiment was analyzed three times to obtain an average value. We added the error bar for the repeated analysis of the particle size distribution of each sample Figs.8 10 and 11 in the revised manuscript.
Reference:
[1] M. Hasan, S. Palaniandy, M. Hilden, M. Powell, Calculating breakage parameters of a batch vertical stirred mill, Miner. Eng. 111 (2017) 229-237.
[2] S.L.A. Hennart, W.J. Wildeboer, P. van Hee, G.M.H. Meesters, Identification of the grinding mechanisms and their origin in a stirred ball mill using population balances, Chem. Eng. Sci. 64 (2009) 4123-4130.
[3] M. Noske, K. Li, K. Bruning, S. Breitungfaes, A. Kwade, Impact of stress conditions on stirred media milling of a two component mixture, Miner. Eng. 146 (2020) 106100.
Comment 2. How the authors have differentiated the size class for the coarse, desired, and overgrinding particles? What is the size range for coarse, desired, and overgrinding particles? Please mention it in the manuscript.
Response 2: We thank the reviewer for this comment. In mineral processing, the definition of the coarse size, the desired size and the overgrinding size is as follows:
- the coarse size refers to particles in the material that need to be ground and liberated;
- the desired size refers to particles in the material that have reached the required particle size range;
- the overgrinding size refers to particles in the material that have relatively intensive extent of breakage.
In this manuscript, the particle size range of the three intervals is as follows: +45 μm, -45+10 μm, -10 μm. Revisions according to this comment were highlighted in red in the revised manuscript.
Comment 3. The breakage rate (for the coarse size) increases with increase in solid concentration, although some deviations were observed at 50 % solid concentration. Is it because of some experimental error. Have you tried to repeat this set of experiment?
Response 3: We thank the reviewer for this comment. The value of the S1,ini at a 50 % solid concentration is smaller than that at 45% and 55% solid concentrations. However, that the value of the S1,ini(1+at) at a 50 % solid concentration is higher than that at 45% and 55% solid concentrations. We performed repeated tests and found that the error was very small.
Comment 4. The acceleration parameter for the coarse size in the non-first order model first increases, then decreases, and after that remains constant. Is there any reason for this trend. Can you cite some literature in support of this finding.
Response 4: We thank the reviewer for this comment. The reason is that the solid concentration affects the acceleration parameter through the following aspects: the buoyancy and the resistance of the slurry in the grinding chamber affect the collision frequency and the friction strength between the grinding media. When the solid concentration is relatively low, the slurry possesses high powder flowabilities. Particles are easily pushed out of the active grinding zone between the approaching grinding media. As the solid concentration is increased, a coating layer can be formed on the surface of the grinding media, particles are easily captured between the approaching grinding media, thus increasing the acceleration parameter. A further increase in the solid concentration increases the viscosity of the slurry while decreases the impact of the grinding media, which prevents the direct contact between grinding media and lining plates, thus decreasing the acceleration parameter or remains constant [1].
As we know, there are very few studies focused on the effect of grinding conditions on the acceleration parameter.
Reference:
[1] Chen B, Theory of grinding. Metallurgical Industry Press, Beijing, (1989) pp 116–120.
Comment 5. Also please explain the effect on φ with increase in solid concentration.
Response 5: We thank the reviewer for this comment. As shown in Table 1, the value of S1,A, and S1,B is almost equal. This result indicates that there is no strong correlation between the solid concentration and the value of φ.
Comment 6. Have you not considered two component model for the desired size range.
Response 6: We thank the reviewer for this comment. The assessment result indicates that both the first order model and the non-first order model have a superior fitting performance over the two component model. Therefore, for the desired size range, we didn't consider the two component model.
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe authors answered the questions. But I would like to clarify:
- Was the research conducted using an experimental design? This information should be clarified.
The article can be published.
Author Response
Comment 1. Was the research conducted using an experimental design? This information should be clarified.
Response 1: Yes, the research was conducted using an experimental design that was based on a single-factor variation approach. In this design, the independent variable was manipulated systematically to observe its effect on the dependent variable, while all other potential confounding variables were held constant. This approach allowed for a clear and isolated examination of the relationship between the manipulated factor and the observed outcome, enhancing the validity and reliability of the research findings.
