Shear Thinning in the Prandtl Model and Its Relation to Generalized Newtonian Fluids

Round 1

Reviewer 1 Report

Review of manuscript  number 742509 entitled "Shear thinning in the Prandtl model and its relation to generalized Newtonian fluids" by Muser submitted for publication in Lubricants.

This is a very well written and complete discussion of the way in which the concepts proposed by Prandtl can be extended to studying fluid viscosity and shear thinning.  The work is very completely described and while it does take some work to go through the detailed  arguments, this it is in part because the manuscript does not shirk from squarely addressing some of the subtleties of the model.

It is not clear that the polemic in Section 1.1. adds anything substantial to the paper, and science abounds in discussions on the attribution of  ideas (the Leibniz–Newton calculus controversy, for example), so that slipping this into an otherwise extremely nice paper to not improve it. 

One of the central issues discussed in this work is the importance of low-order expansion of the stress dependence of viscosity in a isotropic medium. I am not aware of having seen discussions of the importance of symmetry in stress-induced phenomena previously. Section 2.1.3 of the manuscript is intended to illustrate this and a it would clarify the manuscript is an introductory paragraph were included to this section.

While the manuscript is very well written, there are a few typographical errors:

Page 2, Line 38: exponentially with pressure

Equation 6: The format need to be corrected to give the correct exponent.

Page 8, Line 229: from one minimum of the

Author Response

I thank the referee for the overall very positive endorsement of my manuscript.

The referee did not seem to appreciate Section 1.1. Since this work is meant to be scientific and not historic, I followed the advice and removed it. 

This invoked a small change of a sentence in the introduction (line 28 in original submission) from:

The Prandtl model --- while having been mistakenly attributed to Tomlinson, see Sect. 1.1 ---

to 

..., see the interesting summary by Popov and Gehrt [3] preceding their translation of Prandtl's original work ---

I also added one sentence in the Introduction that Coulomb never claimed friction to be independent of velocity with a reference to his work to not lose this comment entirely from Sect. 1.1 

However, I dropped historic comments on the Barus equation.

The typos, which the referee found, are corrected. However, there was one misunderstanding, regarding the last suggestion of the referee:

It was supposed to be "basin" rather than "bassin". Since the referee did not recognize that it was a typo, I added a footnote to the term "basin", in which its meaning is defined. I saw no possibility to add the definition without breaking the flow of ideas in the sentence/paagraph. 

Additional changes include three or four grammatical or typographical corrections.

Reviewer 2 Report

This research work is well constructed and the author follows very logical reasoning. The manuscript discusses the Prandtl model in shear thinning. There is a lot of interest in liquid lubricants and rheology, and the work here certainly will attract the interest of researchers working in this field.

Author Response

There are no comments to be addressed.

I thank the referee for the positive endorsement.