Assessment of the Total Volume Membrane Charge Density through Mathematical Modeling for Separation of Succinic Acid Aqueous Solutions on Ceramic Nanofiltration Membrane

Round 1

Reviewer 1 Report

The manuscript is focused on the modeling of the nanofiltration process. Authors presented relations between the predicted total volume membrane charge densities, ionic strength, component concentration, also those introduced by the pH regulator, and viscosities of solutions on the performance of the ceramic membrane.

IF the model is limited only to the ceramic membranes, please mention this in the title of the work. 

Fig 3,4,5 – if possible, please add the error bars.

Fig. 5 – in the case of MS2 there is a big difference between the estimated and experimental values. Moreover, for this solution the amount of added compound which regulated pH (NaCl) was huge. Did the authors consider the sodium error in this case?

Please remove the parts from the template, e.g. line1, line 649 – “1” is appearing.

Although the work is interesting, the authors did not mention what is going on with the membrane. This part is missing and at the same time, it is very important. Please work a little bit on this point.

The conclusion section is slightly too long and it looks like the report somehow. Please cut this section.

Please organize the literature in a careful way. For instance references nr 20 and 21 only the year is appearing. Please add full bibliographic information about the membrane, according to the style for MDPI.

 

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

The manuscript is investigating an applicability of some mathematical modeling for nano filtration process with using experimental data of filtration of succinic acid with some pH regulator agents. Though the content is interesting, the manuscript has some unclear explanations that must be revised. My questions are as follows:

L254

The authors are required to explain the validation of usage of the Hagen-Poiseuille equation in the current system, which seems to be in turbulent condition (Re=19293), because the equation is derived under a laminar flow condition. Otherwise, the authors should describe the critical Reynolds number of the current system. This matter could be related to the discrepancy between the calculated volume flux and experimental one (Section 4.2).

L359-361

The difference between the value of X_d for the steady state process conditions and the fixed membrane charge should be explained more clearly. Owing to the lack of the definition of the X_d for the steady state process condition, I’m not able to understand the reason why the authors claim they “should not” be confused.

L362-364

Although the authors claim the presence of strong electrostatic repulsion between succinate anions and membrane surface functional group, we can generally say that an electrostatic repulsion in aqueous solution at high ionic strength is screened and weakened. If the authors intend to claim the presence of strong electrostatic repulsion at the ionic strength of 0.12 (MS1), the same repulsion should be appearing at the ionic strength of 0.21 (MS3), which is similar to the case of MS1.

L386-387

If the authors assume a mechanism of ion binding by pore wall, especially Na⁺ binding for the case of MS2, they must detect a decrease of concentration of these ions in solution. I believe the authors are able to show the results of Na concentration measured by the MIP-OES. In addition, the authors are required to explain why such binding occur only in the case of MS2 from a viewpoint of physico-chemical sense.

L411

Replace XD by Xd.

L439

The second statement might be misleading. Although the retention ratio (R) for MS2 was smaller than the one for MS1, the amount of retention for MS2 was larger than the one for MS1.

Author Response

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Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The authors took into account all of the comments and suggestions. The manuscript has been corrected and improved. The work is ready to be published.

Author Response

I would like to express many thanks to Reviewer for a very detailed review, which allow us to improve the manuscript significantly.

Reviewer 2 Report

Though my questions are mostly solved, there are several things that need to be confirmed in the part newly added.

L333-334: Is this sentence correct? I think it may be “MS1” or “MS1 and MS3” instead of “MS1 and MS2”.

L426-427: According to the Fig4 that newly added, there is no significant difference between the concentration of magnesium at 15 min and that at 240 min in the case of MS3. Therefore, this original sentence (which suggests the selective adsorption…) might contradict the results newly added. Do the authors advocate that the selective adsorption of magnesium occurr below the detection limit?

Author Response

Please see the attachment.

Author Response File: Author Response.docx