Review Reports

Round 1

Reviewer 1 Report

The authors have submitted a very interesting manuscript, in which they describe a systematic study on MRV of viscous flow through a porous sample. The reconstruction of experimental MRV data has been performed with different spatial resolution and the results have been compared to CFD simulations leading to the conclusion that, if one aims at volume-averaged properties such as the mean flow rate of the mean velocity, a voxel size of about 20% of the pore size is sufficient.

This topic and the main findings are certainly of great interest as there is increasing interest in cross-validation studies using MRV and CFD simulations. Therefore, I should like to support the publication of this carefully prepared manuscript in MDPI-physics. However, before publication the authors may consider the following critique points in a minor revision:

1. p.2, #62: “… because of hardware limits or restricted measurement time.”. I propose to add a remark on other aspects that limit the spatial resolution in MRI/MRV, in particular the SNR issue.
2. p.2., #78: This statement is not correct, because the "meaning" of the NMR signal intensity depends on the pulse sequence used. The signal magnitude will be proportional to the number of spins in the voxel, but only under certain conditions the signal intensity is mainly determined by the spin density. Other contrast mechanism such as relaxation (T1, T2, T2*), diffusion, temperature etc. may influence the signal intensity (magnitude) as well. To avoid any misunderstanding for those readers who are not familiar with NMR/MRI, please, improve this part.
3. p.3, #95: Is not "simulation" a better expression than "theoretical measurement"?
4. p.5, #185: Please, add "in"?: “highlighted in Figure 3”.
5. p.6, Fig.3: Please, add a and b to the subfigures because "Fig. 3a" is used in the text.
6. 6, #203: should not "glycerol-water" be used instead of "glycerine-water" (as in the text before)?
7. p.6, #213: Please, delete the space before the comma.
8. p.6, #213: Please, check for consistency: "GREEN faces" in Fig. 3b?
9. p.10, #297: "Figure 8"? Please, check figure number, probably this statement refers to Fig. 7.
10. p.12, references: ref. 16: pages or article number is missing. ref. 18: Some details of this proceeding paper seem to be missing.

Author Response

Please see the attachment."

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper addresses the use of magnetic resonance imaging with phase-contrast velocimetry to directly study flows in porous media.  The authors acquired a high resolution data set for a porous medium with a triply periodic pore structure.  They then down sampled to raw MRI data to see the effect of acquiring MRV data with a range of spatial resolutions, finding that a resolution of 0.2 pore scales was sufficient to provide accurate estimates of the mean velocity.  They showed some deviation between the highest resolution MRV and CFD simulations, but the agreement was generally quite good.   I felt that the work has practical value, that the results shown justify the conclusions, and that the paper was well written. In particular, the fact that a relatively coarse resolution  is adequate to calculate the average velocity seems to me to be a very significant result. I think some additional analysis of the results would add significantly to the paper without excessive additional effort.  My suggestions are below.

 

1. Quantitative integral measures of the disagreement between CFD and MRV would be a useful addition.  For example, the mean square deviation (perhaps excluding partial volume voxels) would be interesting and would provide a benchmark for future work.

 

2. An important function of porous media in some applications is to promote mixing. Mixing rates can be assessed by tracking streamlines through the computed/measured velocity field as was done by Onstad.  I think it would be really interesting to see how such a mixing calculation is affected by changing the measurement resolution.  The results presented show that extreme spatial resolution is not required for accurate mean velocity measurements.  Is the same true for dispersion through the medium.  That would be a very significant conclusion if it held.

Author Response

Please see the attachment."

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

In the revised manuscript, the authors have considered all of my critique points. Additionally, the authors have extended the manuscript and added some figures, perhaps in response to critique points of other reviewers or the editor.

Therefore, I would like to recommend to accept this manuscript for publication in MDPI Physics.

I have only noticed in Fig.s 6+7 that a space should be added between “0.02” and “mm”.

Reviewer 2 Report

The authors have responded appropriately to my suggestions and that the manuscript is improved.  I believe that the work should be published in its present form.