Multidimensional Separation by Magnetic Seeded Filtration: Theoretical Study

Round 1

Reviewer 1 Report

In the manuscript entitled "Multidimensional Separation by Magnetic Seeded Filtration: Theoretical Study", I do see good work and good presentation. I recommend the publication of the manuscript after minor revisions.

The general pattern of the abstract has to be [problem definition] -> [concept] -> [action] -> [results] -> [significance]. This is a good structure, enticing the readers and getting citations.

Minor editing of the English language is required.

Author Response

The general pattern of the abstract has to be [problem definition] -> [concept] -> [action] -> [results] -> [significance]. This is a good structure, enticing the readers and getting citations.

The authors feel that the current version of the abstract already fits the reviewer’s suggestion pretty well. However, some slight modifications were made based on the comment. Please note that the word limit is already exhausted.

[Problem definition]: MSF and multidimensional separation in general, plus experimental challenges require theoretical investigations. This was slightly extended.

[Concept]: Theoretical Study with Monte Carlo model (no changes).

[Action]: Description of 11-material system and synthetic kernels (no changes).

[Results]: Results are summarized at length (no changes).

[Significance]: Raising questions on the general definition of 2D grade efficiency functions with respect to agglomeration-based processes and showing the importance of a simulation tool like the developed MC model (no changes).

Reviewer 2 Report

Manuscript describes the separation of particle by assembled magnetite. This agglomeration is much interesting for separation. These phenomena are related to the structure. The following are comments. please consider the revision version.

1) magnetite position is controlled by magnetic field. PBE analysis is related to the power of magnetization?

2) shear on the particle is in this study considered. can you add the flow in this analysis?

Author Response

magnetite position is controlled by magnetic field. PBE analysis is related to the power of magnetization?

If understood correctly, the question is whether or not the magnetization of magnetite is relevant for the process and how it is reflected in the PBE? This is a valid point and was clarified in sections 2.1. and 2.3.

During agglomeration, no magnetic field is present, so the magnetization does not influence agglomeration behavior and is not considered in the PBE. However, magnetic separation is influenced by magnetization, as a higher value leads to an “easier” separation. All of the relevant parameters are summarized in C_mag when applying the simple model equation (7) and are discussed at length in the cited reference [14]. 

shear on the particle is in this study considered. can you add the flow in this analysis?

As discussed in equation (4), the mean shear rate is calibrated with experiments and therefore not investigated in detail. However, multiscale modeling (with CFD-DEM and PBE coupling) can be applied to gain more information. This was added below Eq. (4) in section 2.1.

Reviewer 3 Report

The authors introduce Magnetic Seeded Filtration (MSF) as a promising method for solid-liquid separation, capable of fractionating multi-material suspensions based on particle size and surface properties. The process relies on selective hetero-agglomeration between non-magnetic target and magnetic seed particles, followed by magnetic separation. However, due to experimental challenges in analyzing such suspensions, the authors develop and validate a Monte Carlo (MC) model for simulating hetero-agglomeration processes, comparing it to a discrete population balance model.

The numerical investigation conducted by the authors focuses on charge-based and hydrophobicity-based separations in an 11-material system. Utilizing synthetic agglomeration kernels derived from real-world observations, the study yields results consistent with prior experimental findings. The authors demonstrate that while multidimensional separation is possible, unwanted hetero-agglomeration between target particles diminishes selectivity, especially when separation criteria are dissimilar. They emphasize the advantages of hydrophobicity-based systems in mitigating this effect. Moreover, the authors present 2D-grade efficiency functions T(φ, d) for MSF, providing valuable insights into the process. However, they highlight a significant dependency of these functions on the initial state of the suspension, raising doubts about their general applicability for agglomeration-based processes. This underscores the necessity of simulation tools like the developed MC model.

One suggestion for improvement would be the inclusion of a section titled "Conclusions" to summarize the obtained results succinctly. Such a section would enhance the article's clarity and facilitate easier understanding for readers.

In conclusion, this article contributes significantly to the understanding of hetero-agglomeration processes in MSF, offering valuable insights through numerical simulations. In my opinion, the article needs minor revision (add Conclusions to the work).

Author Response

One suggestion for improvement would be the inclusion of a section titled "Conclusions" to summarize the obtained results succinctly. Such a section would enhance the article's clarity and facilitate easier understanding for readers.

Thank you for your feedback and comment. The authors discussed this before submitting the manuscript and decided that adding a separate Conclusions section would distract from the fundamental points raised in the previous section (Discussion). In addition, we feel that a separate section would be more of a repetition of what has already been said in the Discussion, since the Conclusions are intertwined with the summarizing discussion. Therefore, we actively decided against having a separate Conclusions section in the first version, especially since the Author's Guide states that it is not mandatory.

A simple solution to this is to simply rename the section to "Discussion and Conclusions", since both are currently included, but should not be forcibly separated (modified in the revised version). Of course, if the editor also feels that a separate Conclusions section should be added and/or the reviewer feels that this is a critical point for publication, we will be happy to include it in the next iteration.