Accurate Determination of Electrical Potential on Ion Exchange Membranes in Reverse Electrodialysis

Round 1

Reviewer 1 Report

This manuscript focuses on the electrical potential in IEMs, which was estimated by a boundary updating scheme proposed in previous paper. The numerical method was introduced as if it was proposed in this manuscript, but most of the formulas in this manuscript were described in the previous paper, which may be suspected as self-plagiarism. The authors should refer to the references appropriately and describe what is new. Furthermore, some corrections are needed in the manuscript. Therefore, the manuscript needs some major changes, the publication of this manuscript has to be determined after clarification of remarks I attached below.

 

1. The authors need to refer to the papers including your previous study appropriately and describe what is new.
2. At Eqs. (8) and (9): The authors need to explain why the net charges in transition layers were estimated by a simple accumulation.
3. In the validity check for numerical method, the concentrations at the boundaries of membrane were given, but under these calculation conditions, it may be natural that the numerical solution agrees with the analytical solution. The authors need to carefully explain your validity check.
4. Is the time t real time or virtual time to find a steady-state solution?
5. Abstract and conclusions need to be modified more appropriately.
6. Is Fig. 1 drawn properly based on Eqs. (10) to (13)?
7. At Eq. (11): The authors would find your mistake.
8. The authors need to adopt appropriate subscripts of variables. Subscripts 0 and L indicate the position in the membrane, so that 0 and L should not be used for bulk concentrations.

Author Response

Attached

Author Response File: Author Response.pdf

Reviewer 2 Report

The review reports for separations-1366168

 

This work investigated the accurate determination of the potentials developed on the ion exchange membranes. A rigorous numerical method was developed for this purpose by solving the Nernst-Planck-Poisson (NPP) equations. The results indicate the identical values of Donnan potential obtained with the well-established analytical methods verifying the validity of this numerical method. In general, the manuscript is well constructed; the results and models are appropriately discussed. It is publishable in separations after minor revision. Several minor problems are listed below for the author’s consideration.

1. The electro-convention part was missing in Eq. 1, which should be described precisely and why it was neglected.
2. Page 8, line 236-237, “It clearly demonstrates that the ion flux through the membrane is largely determined by the concentration difference across the membrane with relatively minor impact of charge density on the membrane.” Please discuss in detail why the concentration difference dominantly determines the ion flux.
3. Page 8, line 242-243, “In this example, cations are the limiting factor for ion transport because they have smaller mobility than the anions.” The description here should be discussed in detail with appropriate reference.
4. 21, 22, 23 should be moved to section 2 for better reading.

 

Author Response

Attached

Author Response File: Author Response.pdf

Reviewer 3 Report

In this manuscript the authors claim to accurately determinate electrical potential of IEMs for reverse electrodialysis by solving Nernst-Planck-Poisson equations. Although the topic of the manuscript is interesting for the scientific community, the manuscript present serious scientific flaws based on the following comments:

1. Introduction section: It is not true that much less studies have been carried out on RED with respect to PRO, these is a plenty of literature on RED. Please, cite this literature
2. Figure 1: Concentration profiles along transition layers are not linear at all
3. Table 1: the authors do not motivate the parameters chosen for their study or cite the literature. On this regard: i) concentrations are not of pratical interest, with these concentrations too low membrane potential is generated for practical applications. A study by changing bulk concentrations is needed. ii) the concentration of fixed charge is definitely too low, usually it is considered at least 1000 times higher. iii) membrane thickness is too low, a membrane with a thickness of 50 nm does not make sense, therefore the whole study is not reliable at all. iv) this value of dielectric constant look too low (and dielectric constant does not have unit of measure)
4. The results of this study need to be compared with experimental results to be considered as reliable. If the results are comparable with those obtainable with eq. 21, why should we use your method and not simply eq. 21?
5. Unit of measure of potential is mV and not mv

Author Response

Attached

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The author appropriately revised the manuscript according to the comments from the reviewer. 

Author Response

Thank you very much for your reconfirmation of our revision.

Reviewer 3 Report

1.Please, cite more recent studies on RED. For instance:

i) Correlations between Properties of Pore-Filling Ion Exchange Membranes and Performance of a Reverse Electrodialysis Stack for High Power Density, Membranes 2021, 11(8), 609; ii) Developments and future prospects of reverse electrodialysis for salinity gradient power generation: Influence of ion exchange membranes and electrodes, Desalination Volume 491, 1 October 2020, 114540;iii) Energy Harvesting by Waste Acid/Base Neutralization via Bipolar Membrane Reverse Electrodialysis, Energies 2020, 13(20), 5510;

2. Please, change concentration profiles in Figure 1. Since they are not linear, and we agree on that, please do not sketch as linear.

3. Permittivity and dielectric constant are the same and they are dimensionless. I do not understand this too low permittivity value. How did you choose this number? Please, explain it in the manuscript text.

Author Response

Attached

Author Response File: Author Response.pdf

Round 3

Reviewer 3 Report

The manuscript has been changed following my suggestions