Effect of Drying Conditions on Kinetics, Modeling, and Thermodynamic Behavior of Marjoram Leaves in an IoT-Controlled Vacuum Dryer

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

please see the attachment.

Comments for author File: Comments.pdf

Author Response

Dear Reviewer 1

 

The paper gives a detailed study on drying marjoram leaves. The research is new. It tries to fill a gap by studying how drying temperature and pressure together affect drying results. It focuses on saving costs and keeping quality. The method is clear. It uses different math models and cost tools to check how well the drying works. The results show that the Modified Midilli (I) model works best. It also finds that the best cost and quality come at -10 kPa and 60℃. These points give useful help for improving postharvest methods. Still, the paper needs to fix some parts. It should improve how it explains things, make the method more solid, and clean up how it shows the work.

 

Comment 1: The preparation of marjoram leaves mentions washing and wiping but lacks details on leaf size, uniformity, or drying tray material, which could affect drying kinetics.

Response-: The authors are extremely thankful to the reviewer for this thoughtful point. It was added to subheading 2.1., kindly check the updated paper.

 

Comment 2: The reported drying rate (0.034 g water/g dry matter∙min, line 487, page 26) gives no error range and shows no repeat tests. Adding the standard deviation or a confidence interval would show how accurate the value is.

Response-: The authors are extremely thankful to the reviewer for this thoughtful point. Each experiment was conducted in triplicate to ensure the reliability and reproducibility of the results. The average moisture content from the three replicates was used in all subsequent calculations, graphical representations, and mathematical modeling to minimize visual clutter in the figures caused by the large number of variables under investigation. This approach allowed for clearer interpretation and presentation of the data trends. To evaluate and fit the drying behavior, non-linear regression analysis was performed using Microsoft Excel (version 2016). This analysis was employed to estimate the parameters of the selected drying models as well as to compute key statistical indicators, including the root mean square error (RMSE), the coefficient of determination (R²), and the adjusted coefficient of determination (R²ₐdⱼ), as defined in Equations 19–21. The best-fitting model was identified based on the criteria of minimizing RMSE and maximizing R² and R²ₐdⱼ, which reflect the model’s predictive accuracy and goodness of fit, kindly check the updated paper (Subheading 2.1 & 2.3.5.).

 

Comment 3: Table 3 on page 9 shows economic parameters like a 3% interest rate, a 2.5% inflation rate, and 350 drying days each year. The paper does not explain why these values were chosen or give sources based on Libya’s economy. Libya has economic instability, so these numbers may not reflect real conditions. The paper should cite credible sources for these values or run sensitivity tests.

Response-: The authors are extremely thankful to the reviewer for this thoughtful point. We fully agree with your observation. To ensure that the data presented in this study can be accurately reproduced and independently evaluated, especially in the context of differing national economies, we provided fixed numerical values based on official data from the National Bank of Libya available at the time of the study. This approach was intentionally adopted to allow for a transparent and locally relevant economic assessment. Moreover, by grounding our analysis in nationally recognized financial data, we aimed to facilitate the re-calculation and adjustment of results by other researchers or stakeholders using their own country’s economic indicators. This not only enhances the transparency and reproducibility of the study but also improves its applicability and reliability across different economic contexts.

 

Comment 4: The paper uses different symbols for the same variable. For example, it uses ? for moisture content in Equation 1 on page 5 and M for moisture content in Equation 14 on page 7. This can confuse readers. The paper should use the same symbol for each variable throughout. It should also use the same term, such as using either “moisture content” or “MC” in all sections.

Response-: The authors are extremely thankful to the reviewer for this thoughtful point. they were adjusted, kindly check the updated paper.

 

Comment 5: The thermodynamic analysis calculates ∆?, ∆?, and ∆?. However, the paper only gives a short explanation of what these values mean. For example, it mentions that entropy values are negative but does not explain what this means for the drying process. The paper should give a clear explanation of how these values affect drying efficiency.

Response-: The authors are extremely thankful to the reviewer for this thoughtful point. It was adjusted, kindly check the updated paper (subheading 3.7.).

 

Comment 6: The drying experiments report precise values, such as moisture content at 825.93% d.b. The paper does not mention how many times each measurement was taken. It also does not report any measurement uncertainties or standard deviations. This makes it hard to know how reliable the results are. The authors should include error bars or standard deviations for key values like drying rate and moisture diffusivity.

Response-: The authors are extremely thankful to the reviewer for this thoughtful point. Each experiment was conducted in triplicate to ensure the reliability and reproducibility of the results. The average moisture content from the three replicates was used in all subsequent calculations, graphical representations, and mathematical modeling to minimize visual clutter in the figures caused by the large number of variables under investigation. This approach allowed for clearer interpretation and presentation of the data trends.

The measurement uncertainties were added to subheading 2.4., kindly check the updated paper.

 

Comment 7: The DVD description shows a 200-liter round chamber and a 600-watt heater. It leaves out details on insulation and airflow control. These points matter for saving energy. Adding them would make the technical description stronger.

Response-: The authors are extremely thankful to the reviewer for this thoughtful point. they were added to subheading 2.2, kindly check the updated paper.

Reviewer 1

 

The paper gives a detailed study on drying marjoram leaves. The research is new. It tries to fill a gap by studying how drying temperature and pressure together affect drying results. It focuses on saving costs and keeping quality. The method is clear. It uses different math models and cost tools to check how well the drying works. The results show that the Modified Midilli (I) model works best. It also finds that the best cost and quality come at -10 kPa and 60℃. These points give useful help for improving postharvest methods. Still, the paper needs to fix some parts. It should improve how it explains things, make the method more solid, and clean up how it shows the work.

 

Comment 1: The preparation of marjoram leaves mentions washing and wiping but lacks details on leaf size, uniformity, or drying tray material, which could affect drying kinetics.

Response-: The authors are extremely thankful to the reviewer for this thoughtful point. It was added to subheading 2.1., kindly check the updated paper.

 

Comment 2: The reported drying rate (0.034 g water/g dry matter∙min, line 487, page 26) gives no error range and shows no repeat tests. Adding the standard deviation or a confidence interval would show how accurate the value is.

Response-: The authors are extremely thankful to the reviewer for this thoughtful point. Each experiment was conducted in triplicate to ensure the reliability and reproducibility of the results. The average moisture content from the three replicates was used in all subsequent calculations, graphical representations, and mathematical modeling to minimize visual clutter in the figures caused by the large number of variables under investigation. This approach allowed for clearer interpretation and presentation of the data trends. To evaluate and fit the drying behavior, non-linear regression analysis was performed using Microsoft Excel (version 2016). This analysis was employed to estimate the parameters of the selected drying models as well as to compute key statistical indicators, including the root mean square error (RMSE), the coefficient of determination (R²), and the adjusted coefficient of determination (R²ₐdⱼ), as defined in Equations 19–21. The best-fitting model was identified based on the criteria of minimizing RMSE and maximizing R² and R²ₐdⱼ, which reflect the model’s predictive accuracy and goodness of fit, kindly check the updated paper (Subheading 2.1 & 2.3.5.).

 

Comment 3: Table 3 on page 9 shows economic parameters like a 3% interest rate, a 2.5% inflation rate, and 350 drying days each year. The paper does not explain why these values were chosen or give sources based on Libya’s economy. Libya has economic instability, so these numbers may not reflect real conditions. The paper should cite credible sources for these values or run sensitivity tests.

Response-: The authors are extremely thankful to the reviewer for this thoughtful point. We fully agree with your observation. To ensure that the data presented in this study can be accurately reproduced and independently evaluated, especially in the context of differing national economies, we provided fixed numerical values based on official data from the National Bank of Libya available at the time of the study. This approach was intentionally adopted to allow for a transparent and locally relevant economic assessment. Moreover, by grounding our analysis in nationally recognized financial data, we aimed to facilitate the re-calculation and adjustment of results by other researchers or stakeholders using their own country’s economic indicators. This not only enhances the transparency and reproducibility of the study but also improves its applicability and reliability across different economic contexts.

 

Comment 4: The paper uses different symbols for the same variable. For example, it uses ? for moisture content in Equation 1 on page 5 and M for moisture content in Equation 14 on page 7. This can confuse readers. The paper should use the same symbol for each variable throughout. It should also use the same term, such as using either “moisture content” or “MC” in all sections.

Response-: The authors are extremely thankful to the reviewer for this thoughtful point. they were adjusted, kindly check the updated paper.

 

Comment 5: The thermodynamic analysis calculates ∆?, ∆?, and ∆?. However, the paper only gives a short explanation of what these values mean. For example, it mentions that entropy values are negative but does not explain what this means for the drying process. The paper should give a clear explanation of how these values affect drying efficiency.

Response-: The authors are extremely thankful to the reviewer for this thoughtful point. It was adjusted, kindly check the updated paper (subheading 3.7.).

 

Comment 6: The drying experiments report precise values, such as moisture content at 825.93% d.b. The paper does not mention how many times each measurement was taken. It also does not report any measurement uncertainties or standard deviations. This makes it hard to know how reliable the results are. The authors should include error bars or standard deviations for key values like drying rate and moisture diffusivity.

Response-: The authors are extremely thankful to the reviewer for this thoughtful point. Each experiment was conducted in triplicate to ensure the reliability and reproducibility of the results. The average moisture content from the three replicates was used in all subsequent calculations, graphical representations, and mathematical modeling to minimize visual clutter in the figures caused by the large number of variables under investigation. This approach allowed for clearer interpretation and presentation of the data trends.

The measurement uncertainties were added to subheading 2.4., kindly check the updated paper.

 

Comment 7: The DVD description shows a 200-liter round chamber and a 600-watt heater. It leaves out details on insulation and airflow control. These points matter for saving energy. Adding them would make the technical description stronger.

Response-: The authors are extremely thankful to the reviewer for this thoughtful point. they were added to subheading 2.2, kindly check the updated paper.

Kind regards

The authors

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The article is devoted to the study of the vacuum drying process of marjoram leaves at different temperatures and pressures. The authors developed an experimental drying unit with temperature and humidity control.
Comments on this work:
- The introduction contains many repetitions; for example, the advantages of vacuum drying are described 2–3 times in different words.
- The variety, age, origin of the raw material, and storage conditions are not specified.
- Was a comparison made with control drying, for example, using conventional convection?
- It is not specified whether the experiments were repeated. How was the statistical reliability of the results assessed? Standard deviations, measurement errors, or confidence intervals are also not provided.
- There is no discussion of the limitations of the study.
- The work is presented as technological, but there is no data on the content of essential oils and other substances before and after drying, which could confirm that the drying is indeed “gentle.”
- Excessively detailed explanations of the meanings of “moisture,” “drying curve,” and “enthalpy” are acceptable for a textbook, but not for a scientific article.

Author Response

Dear reviewer 2.

The article is devoted to the study of the vacuum drying process of marjoram leaves at different temperatures and pressures. The authors developed an experimental drying unit with temperature and humidity control. Comments on this work:

Comment 1: The introduction contains many repetitions; for example, the advantages of vacuum drying are described 2–3 times in different words.

Response-: The authors are extremely thankful to the reviewer for this thoughtful point. Duplicate was removed, kindly check the updated paper.

Comment 2: The variety, age, origin of the raw material, and storage conditions are not specified.

Response-: The authors are extremely thankful to the reviewer for this thoughtful point.  It was added to subheading 2.1, kindly check the updated paper.

Comment 3: Was a comparison made with control drying, for example, using conventional convection?

Response-: The authors are extremely thankful to the reviewer for this thoughtful point. Yes, of course. In this study, three drying temperatures (40°C, 50°C, and 60°C) and three operating pressure conditions—ambient pressure (natural air drying without vacuum), –5 kPa, and –10 kPa—were employed to evaluate their effects on the drying process, kindly check the updated paper (26-27).

Comment 4: It is not specified whether the experiments were repeated. How was the statistical reliability of the results assessed? Standard deviations, measurement errors, or confidence intervals are also not provided.

Response-: The authors are extremely thankful to the reviewer for this thoughtful point. Each experiment was conducted in triplicate to ensure the reliability and reproducibility of the results. The average moisture content from the three replicates was used in all subsequent calculations, graphical representations, and mathematical modeling to minimize visual clutter in the figures caused by the large number of variables under investigation. This approach allowed for clearer interpretation and presentation of the data trends. To evaluate and fit the drying behavior, non-linear regression analysis was performed using Microsoft Excel (version 2016). This analysis was employed to estimate the parameters of the selected drying models as well as to compute key statistical indicators, including the root mean square error (RMSE), the coefficient of determination (R²), and the adjusted coefficient of determination (R²ₐdⱼ), as defined in Equations 19–21. The best-fitting model was identified based on the criteria of minimizing RMSE and maximizing R² and R²ₐdⱼ, which reflect the model’s predictive accuracy and goodness of fit, kindly check the updated paper (Subheading 2.1 & 2.3.5.).

Comment 5: There is no discussion of the limitations of the study.

Response-: The authors are extremely thankful to the reviewer for this thoughtful point. It was added after the conclusion section, kindly check the updated paper.

Comment 6: The work is presented as technological, but there is no data on the content of essential oils and other substances before and after drying, which could confirm that the drying is indeed “gentle.”

Response-: The authors are extremely thankful to the reviewer for this thoughtful point.  The present study constitutes the initial phase of a broader, ongoing research project focused on optimizing the post-harvest processing of marjoram (Origanum majorana L.). In parallel, a separate but related study is currently under review in another peer-reviewed journal. That study specifically investigates the combined effects of operating pressures and drying temperatures on the quality attributes, essential oil yield, and the physical and chemical composition of marjoram leaves. To ensure scientific clarity, avoid redundancy, and prevent any potential overlap in data presentation or interpretation, each study has been intentionally designed and submitted as an independent research work. This separation allows for a more detailed and focused analysis within each manuscript while maintaining the overall integrity and coherence of the research project, kindly check the future work of the developed paper.

Comment 7: Excessively detailed explanations of the meanings of “moisture,” “drying curve,” and “enthalpy” are acceptable for a textbook, but not for a scientific article.

Response-: The authors are extremely thankful to the reviewer for this thoughtful point. We fully appreciate your perspective; however, the other reviewers have requested a more detailed explanation of the underlying theories and fundamental principles to ensure the clarity and comprehensibility of the work for all readers. We kindly ask for your understanding regarding the current requirements.

kind regards

The authors

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

"Mathematical modeling, drying kinetics, and thermodynamic properties for cost-effectively drying marjoram leaves under different levels of pressure and temperature based on the IoT concept” is a well-structured research paper that includes sections on introduction, materials and methods, results, discussion, and conclusion. The article presents interesting findings, but there are areas for improvement.

1. In line 116, you state that the average initial moisture content of marjoran leaves was 82.59% on a dry basis, which is a very high percentage. Could you please provide a formula for estimating this data?
2. Check the label 2 in Figure 1 for any errors.
3. Lines 166-170, 187-88, these statements are not part of the materials and methods section. They should be moved to the results or discussion section. Also, could you remove these parts (lines 167-70 and 188-9) and explain how you measure this parameter or calculate it?
4. Line 184, I suppose It’s not Me, but μe. Also, please add the index abbreviation meaning.
5. Line 320 and table 4: Please add a unit of measurement for the k values.
6. Line 414: You obtained 2.68 kJ/mol of EA, which is too small. It's an explosive reaction. Could you please double-check this data? How long does it take to carry out these processes?
7. Figure 10: Why do you use the D coefficient for calculating AE? Classical Arrhenius calculations use k for this.
8. Pages 18-23: This date is too large. Please keep only the main findings and put other information in supplementary materials. Why is the constant rate negative?
9. Abstract: Line 37: Incorrect units for EA.

This research is interesting, and the manuscript has potential for publication after revisions.

Comments for author File: Comments.pdf

Author Response

Dear Reviewer 3.

"Mathematical modeling, drying kinetics, and thermodynamic properties for cost-effectively drying marjoram leaves under different levels of pressure and temperature based on the IoT concept” is a well-structured research paper that includes sections on introduction, materials and methods, results, discussion, and conclusion. The article presents interesting findings, but there are areas for improvement.

Comment 1: In line 116, you state that the average initial moisture content of marjoram leaves was 82.59% on a dry basis, which is a very high percentage. Could you please provide a formula for estimating this data?

Response-: The authors are extremely thankful to the reviewer for this thoughtful point. It was about 825.93% on a dry basis (d.b.) and about 89.2% on a wet basis, and AlJuhaimi et al. stated that the initial moisture content of fresh marjoram leaves was about 88.61% on a wet basis, kindly check the following paper.

AlJuhaimi, F., Mohamed Ahmed, I. A., Özcan, M. M., Uslu, N., & Karrar, E. (2024). Effect of Drying Methods on the Antioxidant Capacity and Bioactive and Phenolic Constituents in the Aerial Parts of Marjoram (Origanum majorana L.) Grown Naturally in the Taurus Mountains in the Mediterranean Region. Processes, 12(9), 2016.

 

Comment 2: Check the label 2 in Figure 1 for any errors.

Response-: The authors are extremely thankful to the reviewer for this thoughtful point. All labels were correct, kindly check the updated paper.

 

Comment 3: Lines 166-170, 187-88, these statements are not part of the materials and methods section. They should be moved to the results or discussion section. Also, could you remove these parts (lines 167-70 and 188-9) and explain how you measure this parameter or calculate it?

Response-: The authors are extremely thankful to the reviewer for this thoughtful point.  They were removed, kindly check the updated paper.

 

Comment 4: Line 184, I suppose It’s not Me, but μe. Also, please add the index abbreviation meaning.

Response-: The authors are extremely thankful to the reviewer for this thoughtful point.  It was adjusted, kindly check the updated paper.

 

Comment 5: Line 320 and table 4: Please add a unit of measurement for the k values.

Response-: The authors are extremely thankful to the reviewer for this thoughtful point. It was added, kindly check the updated paper.

 

Comment 6: Line 414: You obtained 2.68 kJ/mol of EA, which is too small. It's an explosive reaction. Could you please double-check this data? How long does it take to carry out these processes?

Response-: The authors sincerely thank the reviewer for this valuable observation. In response, the data have been carefully reviewed and verified for accuracy. The revised manuscript reflects these updates. As shown in the updated Table 6, previous studies reported an activation energy of approximately 1.055 kJ/mol, which is now clearly presented and discussed in the current version of the paper, kindly check the following paper.

Jebri, M., Desmorieux, H., Maaloul, A., Saadaoui, E. & Romdhane, M. Drying of Salvia officinalis L. by hot air and microwaves: dynamic desorption isotherms, drying kinetics and biochemical quality. Heat and Mass Transfer 55, 1143–1153 (2019).

 

Comment 7: Figure 10: Why do you use the D coefficient for calculating AE? Classical Arrhenius calculations use k for this.

Response-: Excellent question and you're absolutely right to note the classical Arrhenius equation typically uses a rate constant (k):

 

 

But in drying processes, we often use a modified Arrhenius-type relationship where the effective moisture diffusivity (D_eff) plays the role similar to the rate constant (k). Here's why:

1. Drying is a Diffusion-Controlled Process

• In many agricultural or food drying systems (especially during the falling-rate period), the rate-limiting step is internal moisture diffusion.
• Therefore, the effective moisture diffusivity reflects how easily moisture moves within the material — it's the controlling mechanism, not just a reaction rate.

2. Fick’s Second Law Governs Drying

For many drying experiments, moisture movement is modeled by Fick’s second law:

 

• From this, we extract D_eff ​ by fitting experimental moisture ratio data.
• To understand how D_eff ​ changes with temperature, we use an Arrhenius-type equation:

 

Where:

• ​: pre-exponential factor
• ​: activation energy for diffusion
• R: universal gas constant
• T: absolute temperature

3. Physical Meaning of Activation Energy in Drying

In this context, ​ quantifies the energy barrier for moisture movement inside the product.

• It’s not the energy required to initiate a chemical reaction, but rather to overcome resistance to moisture diffusion — such as:

• Capillary action
• Cell wall permeability
• Structural changes during drying

Summary:

We use D_eff ​ in an Arrhenius-type equation for drying because:

• Drying is typically diffusion-driven.
• D_eff​ reflects the internal moisture movement rate.
• This approach allows us to estimate how temperature affects drying performance, and quantify the activation energy for moisture diffusion, not for a chemical reaction.

 

Comment 8: Pages 18-23: This date is too large. Please keep only the main findings and put other information in supplementary materials. Why is the constant rate negative?

Response: The authors are extremely thankful to the reviewer for this thoughtful point. During the current study, ten mathematical models were used to describe the drying kinetics of marjoram leaves under different levels of pressure and temperature. And the experimental data from each drying process was analyzed using eleven drying models and tabulated in Table 7. Subsequently, non-linear regression analysis was conducted utilizing Microsoft Excel (version 2016) to estimate the coefficients of the provided models and statistical measures listed in Equations 19-21. The optimal model was identified based on the criterion of minimal root mean squared error (RMSE) values and maximal coefficient of determination (R²) and adjusted coefficient of determination ( ). Then, the ten models for both drying systems at different levels of pressure and temperature were listed in Table 7, and the relation between observed and predicted moisture ratio at different drying time for the best models for both drying systems at different layer thicknesses was plotted in Figure 12. From our perspective, presenting the data directly enables readers to make immediate and accurate comparisons without the need to consult additional sources. This approach enhances the transparency and integrity of the research for both the readers and the authors. Therefore, we kindly request your understanding and support in retaining Table 7 as an integral part of the study.

Additionally, Negative constants in non-rate terms (like constant rate) are often fitting artifacts, used to improve curve fitting—they are valid as long as:

• The overall moisture ratio stays between 0 and 1.
• The curve behaves physically (i.e., moisture ratio decreases over time).
• Use visual inspection and statistical metrics (R², RMSE, χ²) to confirm model suitability.

 

Comment 9: Abstract: Line 37: Incorrect units for EA.

Response-: The authors are extremely thankful to the reviewer for this thoughtful point.  It was adjusted, kindly check the updated paper.

 

This research is interesting, and the manuscript has potential for publication after revisions.

 

The authors once again thank the learned Editors and Reviewers for their valuable comments for improving the quality of the manuscript.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Authors have done a great job. This paper is ready for publication

Reviewer 2 Report

Comments and Suggestions for Authors

- Shorten the abstract slightly, emphasizing the results and conclusions.
- Make the caption for Figure 12 more informative.
- In section “3.7,” negative entropy is interpreted as “chemical adsorption,” but this requires a more detailed explanation. What structural changes occur exactly?