Time-Dependent Viscous Flow Behavior of a Hydrophobic Fumed Silica Suspension

Round 1

Reviewer 1 Report

This paper presents a rheological study on the time-dependent flow behaviour of hydrophobic silica suspension in polypropylene glycol. The study is very thorough and it is clear that the authors are highly knowledgeable in the area (as also indicated by their high number of publication on the topic, particularly on hydrophobic fumed silica suspensions). I only recommend that several figures be improved in clarity, e.g. the scaling of Figures 2 and 3. The results of the steady apparent viscosity (shown in Figure 4) should also be shown in Figures 7 and 8. Finally, considerable revision needs to be applied to the grammar and phrasing of the manuscript. Many sentences are very awkward to read, e.g. lines 277-278, 302-305, etc.

I recommend this manuscript be accepted for publication.

Author Response

Answer to Reviewer 1 comments (in blue)

This paper presents a rheological study on the time-dependent flow behaviour of hydrophobic silica suspension in polypropylene glycol. The study is very thorough, and it is clear that the authors are highly knowledgeable in the area (as also indicated by their high number of publications on the topic, particularly on hydrophobic fumed silica suspensions).

Thanks a lot for your comments. We have warmly considered them being sure they will improve our manuscript.

I only recommend that several figures be improved in clarity, e.g. the scaling of Figures 2 and 3.

Figure scales have been modified to use the same in Figures 2 and 3.

The results of the steady apparent viscosity (shown in Figure 4) should also be shown in Figures 7 and 8.

Experimental results shown in Figures 4, 7, and 8 have been revised (and repeated in some cases). Compatible results (with the experimental error) have been found and finally shown.

Finally, considerable revision needs to be applied to the grammar and phrasing of the manuscript. Many sentences are very awkward to read, e.g. lines 277-278, 302-305, etc.

English grammar has been revised by a native speaker.

I recommend this manuscript be accepted for publication.

Reviewer 2 Report

1. On Page 2, Line 51, the authors mention hydrodynamic interactions between particles. In the discussion of their experimental results, there is nothing regarding hydrodynamic interactions. Please add a comment on the role of hydrodynamic interactions. In particular, what is the role of inter-particle hydrodynamic interaction on the Brownian motion of the particles and thus the erosion of an aggregate?
2. On Page 2, Line 72, the authors point out that the confirmation of reversibility condition is important to the identification of different shear behaviors. Later, the discussion of reversibility condition does not stand out from the rest of the presentation. Please improve on this point. 
3. The authors use “equilibrium structure” to describe the morphology of particles after sufficiently long resting time. Is it possible that the structure is not at equilibrium but is a kinetically frozen structure? 
4. While the authors have related the apparent shear viscosity to the existence of aggregates (hydroclusters) in the suspension at rest, can the authors provide a more quantitative description of the relation? For instance, how would one expect the shear viscosity depend on the size and concentration of the aggregates?
5. In Figure 4, the same apparent viscosity may correspond to two different stress values? This is an interesting result. Please consider explaining it using the mechanism described in the manuscript. 
    

Author Response

Answer to Reviewer 2 comments (in blue)

Thanks a lot for your comments. We have warmly considered them being sure they will improve our manuscript.

1. On Page 2, Line 51, the authors mention hydrodynamic interactions between particles. In the discussion of their experimental results, there is nothing regarding hydrodynamic interactions. Please add a comment on the role of hydrodynamic interactions. In particular, what is the role of inter-particle hydrodynamic interaction on the Brownian motion of the particles and thus the erosion of an aggregate?

We have used the following hypothesis to explain the unexpected apparent thixotropic behavior with step-up tests in the shear-thickening region. Hydrodynamic forces are bigger in magnitude when the shear stress value is bigger. They cause the initial “instantaneous” hydroclusters formation, whose size is larger when the shear stress value increases. This physical fact gives place to the high (and very fast achieved) initial viscosity value just after the application of a step-up. On the other hand, while hydrodynamic forces tend to maintain the initial size of hydroclusters, Brownian (or thermal agitation) erodes the hydroclusters and progressively diminishing its size. This comment has been rewritten for the new version of the manuscript.

2. On Page 2, Line 72, the authors point out that the confirmation of reversibility condition is important to the identification of different shear behaviors. Later, the discussion of reversibility condition does not stand out from the rest of the presentation. Please improve on this point. 

Reviewer is right in this worthy appreciation. The standard procedure should consist in to continue a step-up test with a step-down one and vice versa. Alternatively, a general limit of reversibility test can be used to confirm the reversibility of the material response for stepwise tests. This last option has been used in this work.

3. The authors use “equilibrium structure” to describe the morphology of particles after sufficiently long resting time. Is it possible that the structure is not at equilibrium but is a kinetically frozen structure? 

Honestly, the concept of “kinetically frozen structure” is new for us. After searching in the literature on the subject, we have concluded that this term could be used to describe structures without any relaxation process. We know that structures developed in the state-of-rest of our fluid show some relaxation time when a stress is applied to as was demonstrated elsewhere (ref 24) studying the viscoelastic response of the structure-at-rest developed in the same fluid as that here used. 

4. While the authors have related the apparent shear viscosity to the existence of aggregates (hydroclusters) in the suspension at rest,

Hydroclusters are not developed at rest. They are the consequence of the application of stresses higher than the value for the onset of the shear-thickening behavior.

can the authors provide a more quantitative description of the relation? For instance, how would one expect the shear viscosity depend on the size and concentration of the aggregates?

We have not looked for a quantitative relationship between hydroclusters size and number and the viscosity value. We think that to achieve this objective, it would be needed to complete this study with some in situ visualization (rheo-optical methods for example). Taking reviewer interesting suggestion into account, we have initiated the design of an experiment using the RheoScope modulus of our MARS III rheometer (Haake) with the objective to visualize hydroclusters formation and evolution during shear. The task does not seem easy and will be the subject of a future research.

5. In Figure 4, the same apparent viscosity may correspond to two different stress values? This is an interesting result. Please consider explaining it using the mechanism described in the manuscript. 

As the reviewer has pointed out this is a curious (although no new) result. From a mathematical point this is a mere coincidence because the viscosity is a calculus of the quotient between stress and shear rate. Then, it could be considered that it is a casual fact that the shear rates corresponding to the respective shear stresses give place to the same quotient stress/shear rate. However, other thing (and more interesting of course) is the possible physical explanation (if there exists) for these observations. For example, if we compare two stress values giving the same viscosity value, one of them corresponding to the first shear thinning region and the second one corresponding to the shear thickening region, microscopic distortions of the flow field, which gives place to the same macroscopic viscosity value, must be probably different. The same can be said when stresses of the shear thickening and the second shear thinning regions giving the same viscosity values are compared. We have not currently a satisfactory answer for this result and prefer to avoid non founded speculations. On the other hand, we thank reviewer for so suggestive comment.