Sedimentation of Two Side-by-Side Heavy Particles of Different Density in a Shear-Thinning Fluid with Viscoelastic Properties

Round 1

Reviewer 1 Report

There are a number of comments to the article.

1. Indicate the shape of the particles. How close is it to spherical?
2. The spatial scale is not indicated in Figure 4.
3. Table 2 includes density data already given in the text of this section. In this case, the calculation of alpha is trivial and there is no need to put it in a separate table.
   4. In line 187 viscous resistance proposed to be ignored. In line 191 viscous resistance expressed as a formula. Looks a little bit controversial.
   5. In line 217 "Vx in x-z plane, Vy in x-z plane" doubles. Is this a misprint?
   6. In line 160 stated that 4-10 experiments were done, but later, for example, S line on fig. 8 supposed to be for single experiment, not averaged. To be correct it is worth to mention all data are averaged or instantaneous.
   7. Fig 8 in legend "x-z" -> "S*"
   8. In line 240 "t=2s" is a mistake?
   9. Line 270. What is DKT?
   10. Fig. 12 Should axis label be Vxl (Vxh on the right figure)?
   11. Conclusion expected to be meaningful. Particles typical trajectories should be described. It is better not to use nomenclature like alpha or L*. Use "density ratio" instead. I think that links like "Fig.12" or "section 3.3" should be avoided also. Nice discussion was done about viscoelastic effects in sections 3.3 and 3.4. I think that they should be repeated in conclusion section. Abstract also can be used partially in a conclusion section.

Author Response

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Reviewer 2 Report

Below I submit my review of "Sedimentation of two side-by-side heavy particles of different density in a shear-thinning fluid with viscoelastic properties" by Sensen Yang Chengxu Tu, Minglu Dai, Xianfu Ge, Rongjun Xu, Xiaoyan Gao and Fubing Bao.

The manuscript presents an experimental piece of investigation of the sedimentation phenomena of heavy particles in a non-Newtonian, shear-thinning and viscoelastic carrier fluid.  Two same sized particles with different densities are used in the investigation. The effect of the initial distance between the particles (7 different distances used) and the density difference (3 different values) are examined. In conclusion, three different regimes for two particles settling side-by-side are proposed by the authors. The main argumentation for these is based in the existence of the negative wake that follows the denser particle settling and the corresponding corridor of reduced viscosity.

In general, the manuscript is structured in logical sections and argumentation is built in a well understood manner. Presentation is neat, but some figures need extra polishing to reach a high-level publication standard. The experimental methods described follow the general good scientific practice. The language is good but there are various grammar errors and various typos, that, nevertheless, do not hinder the reader in understanding the scientific content. They should be taken care of meticulously during the revision process though.

The manuscript nicely presents a novel side of a two-particle settling problem which is not widely covered by previous studies and seems to be of interest in the respective community. I am positive that it fits well in the scope of applied sciences and would be interesting for its general readership.

Thus, I am supportive of publication in applied sciences provided that the authors make adequate revisions to address my following concerns and comments:

Major points:

1. There needs to be further argumentation on the PIV data presented by the authors. Details on the experimental protocol for the PIV measurements should be included in the manuscript. Fig. 4 should include a scale bar for comparison, and it should be noted whether this is a time-averaged profile or an instantaneous one. The authors claim that just by the existence of the negative wake observed in Fig. 4, the viscoelastic and shear-thinning properties of the PAAm are validated (l.131-132). These properties are sufficiently proven to be true by the rheological measurements the authors present in Figs. 2 and 3. The flow conditions downstream the settling sphere might be indicative of such rheological properties of the PAAm, but they could also be affected by the high Re number (>10⁴) as the authors state. I would expect the authors to address this explicitly and reinforce their argument with preexisting literature.
2. In l. 187 the authors state that Re number is greater than 10⁴. How was this value calculated? What value was used for the PAAm viscosity? In the same sense, a Figure where the viscosity of PAAm is compared to the shear rate (γ) would be really appreciated as an addition to Fig. 2.
3. In l. 189, the authors state that the drag coefficient tends to a value of 0.44. It should be stated if this is the case for shear-thinning & viscoelastic fluids, or this is found for rheologically distinct fluids but the authors make this assumption.
4. In Fig. 8c and if Fig. 9, it is clearly visible that the terminal velocity of the Si₃N₄ sphere in water is higher than that in the PAAm solution, whereas the contrary seems to be the case with the other two materials used. The authors themselves appear to acknowledge a different behaviour in earlier stages as well (l. 240) but there are no further comments on this. How do the authors explain this? This discrepancy should be clearly discussed in the revised manuscript.
5. What is the meaning of the error bars in Fig. 9. The authors should present a more comprehensive error estimation analysis in the revised manuscript. Some error sources that should be discussed include: deviations on the spheres size (in l. 146 the authors state that the size of the particles is just similar, an error on the diameter should be included here), effect on the result by any asynchronous release of the two spheres (how well was this controlled?), in l. 160 it is stated that 4-10 repetitions were performed for each experiment, this should be discussed more (i.e. how sensitive is the system on initial conditions?)
6. The author’s proposal for three different settling regimes should be reconsidered. It seems that types (i) and (ii) are in fact the same settling regime which in the case of type (ii) it lacks the time and space to completely evolve. This is implicitly discussed by the authors as well ( in l.331). Fig. 12a and Fig.12b suggest this fact as well, as the trajectories seem quite similar, but it seems that not enough time is left for the Fig12b experiment. The authors should reconsider their classification and should provide a better argumentation on this, otherwise the settling types (i) and (ii) ought to be merged in one single settling type.
7. The authors should discuss more one of the core findings of their research which is the fact that the PAAm solution stabilizes the settling path for single spheres. In l. 391 this is stated again but no concrete mechanism is proposed. Maybe the inclusion of relevant literature can elucidate this point.
   
   Minor points:
8. To suit the special issue’s scope, some application literature in the field of microfluidics should be cited in the introduction, to comply with readership’s expectations.
9. In l. 41 citations should be provided for the industrial and natural processes stated.
10. Do the author’s have any data on the surface smoothness of the spheres? A comment should be added that this might affect the conditions near the sphere wall, especially in shear-thinning fluids.
11. Fig. 4: The caption has a typo: “negative” should be the case instead of “navigate”.
12. In l. 147-148, maybe Fig. 4 should read Fig. 5?
13. Fig.7 should be enhanced. It should be bigger, and a scale bar would be appreciated.
14. Fig.8 should be enhanced to allow the reader to get more information. The y-axis should be enlarged (as in Fig. 9) and the three subfigures could be centered and aligned.
15. In l. 240, do the authors mean t = 0.2 s? If yes, this should be revised.
16. Abbreviations such as DKT and PIV should be explained before their first use as standard publishing practice dictates.
17. A comment should be added in the claim in l. 312 about the reason on why no collision is observed in the studied system. Maybe this could happen when a different density difference spheres couple is studied?
18. In Fig. 12, it should be noted which figure corresponds to the light or heavy particle. The y axis label should be amended as well as it does not only correspond to the v_x

Comments for author File: Comments.pdf

Author Response

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Reviewer 3 Report

The article deals with the sedimentation of particles side by side with different densities, but with the same size, in a shear-thinning liquid with viscoelasticity. The authors compare their results with the results for the sedimentation of only one particle and also with the sedimentation in water. They conclude that there is a deviation on the terminal velocity of the particle, when comparing to the water. This behavior is attributed to the shear thinning behavior of the PAAm. They also studied the effect of the dimensionless distance between the particles and and the density difference between the particles in the sedimentation. 

The study is well conducted but I advice some minor modifications.

line 105: 1000mm  change to 1000 mm

line 115: The rheological properties of the PAAm solution examined at 20 ℃ by a rheometer. I think it should be: The rheological properties of the PAAm solution were examined at 20 ℃ by a rheometer

line 119-121: the authors explain that for a low shear rate, the PAAm solution  presents high viscosity, and the viscosity decreases with the value of the shear rate. However, they only present a graph of the shear stress in function of the shear rate - Fig. 2. It was useful for the reader that in addition to this graph, was also presented the graph of the viscosity in function of the shear rate.

line 129: Fig. 3 instead of Fig 3

line 157, 178, 182, 189, 194 and all the subscripts in the article: ρ_l instead of ρl (this is only an example, in the article they are not in subscript) C_D instead of CD

line 172: Fig. 6 instead of Fig.6

line 212: 19 ms instead of 19ms

line 219 Fig. 8 instead of Fig.8

line 237: 0.4 s instead of 0.4s

line 240: 2 s instead of 2s

line 243: Fig. 9 instead of Fig.9

Fig. 9 Attention to the axis, in this figure the representation of the units are different:  u / ms^-1 and t (s), you should use / or ( ) in all the graphics

From line 279 to 291: I think it would be better to talk about the three types of trajectory first, and then talk about  Fig. 11. Something like this:

Compared to the trajectory of heavy particles, the particle-particle interaction has a stronger impact on the light particle.  There are three basic types of the trajectory of the light particle in the x-z plane as the light particle tracing the heavy one:

• Type (i) in the horizontal direction (x), the light particle first is strongly attracted and then is repelled by the rectilinear path of the heavy one (for L*=1.2 and α=1.92, 2.79 and 4.71);
• Type (ii) the light particle approaches to the heavy one in the x direction, and then travel a certain distance within the path of the heavy one (for L*=2.0 and α=1.92 and 2.79) without bounce from the wake of the heavy particle in our limited field of the view of the camera;
• Type (iii) the light particle is slightly away from the path of heavy one at first in the horizontal direction, and then the light particle moves back to its original position in x direction (for L*=3 and α=1.92, 2.79 and 4.71)

Fig. 11 presents these basic types of the trajectory of the trajectory. The line connects between the particles illustrated the instantaneous position of this pair of particles at a certain moment.

Fig. 11 The images of the graphics are not aligned with (a), (b) and (c) captions. And the legends should be (a) Type (i); (b) Type (ii); and (c) Type (iii) (just include the spaces between the words).

line 348: Fig. 11 instead of Fig.11

line 342: type (i)

line 353: t = 0.0422 s

line 375: type (iii) instead of type(iii), and the same for the Fig. 12 captions

Author Response

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Round 2

Reviewer 2 Report

After carefully studying the authors’ answers, I can confirm that most of them have satisfied my initial concerns. The manuscript is now adequately amended according to the author’s replies. I can recommend publication provided that some minor points are furtherly addressed by the authors.

1. The authors should make a comment and discuss clearly in their text the discrepancy between the settling velocities discussed in the previous revision round (Point iv). In Lines 323-326 a very studied assumption is made for the initial fluctuation, but the authors still ignore in their discussion the fact that in only one of the three cases studied (Si3N4) the settling velocity is higher in PAAm than in water. Even if this is not the focus of the paper, it is a fact that is clearly visible in the Figs. 10 & 11 and it should be explicitly discussed.
2. In Fig. 4 the term “dynamical viscosity” should be changed to “dynamic viscosity” as standard terminology requires.
3. In Line 474 should read “decrease”?

Author Response

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