The Viscosity of Liquids in the Dual Model
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsSee attached file
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Reviewer 2 Report
Comments and Suggestions for AuthorsDear Editors,
In the paper "The Viscosity of Liquids in the Dual Model," Peluso employs a model (DLM) for liquids that he introduced in several preceding papers (40-44) to model the viscosity of liquids. The viscosity of liquids is an intriguing parameter, as it has thus far resisted direct calculation from fundamental principles although it shows similar behaviour if plotted against typical thermodynamical parameters for fluids of very different constituents. One objective of this study is to demonstrate that the viscosity values derived from the DML model exhibit Arrhenius-like behavior. Such behavior is indeed an important characteristic of a model of viscosity, and not all models undergo such a sanity check.
The paper is informative to read and recalls the historic foundations, explores the intricacies of viscosity, including its calculation and correlation with other thermodynamic parameters in the context of the DLM and other models. I find it a valuable resource. It should be published.
The paper contains some sections that are repetitive of material published by the author in previous works. It could therefore be considerably more concise. However, although repetitive, it supposedly helps the reader to quickly comprehend the paper, as the topics covered are extensive. Furthermore, in reporting the findings of existing literature, the text is frequently structured in a manner that closely resembles the wording of the original reference or that of previous publications by the same author.
The DML model put forward and employed in this as well as earlier contributions grounds on the same ideas as many other models describing the liquid as constituted by solid and “very-liquid” partitions.
Most assessments made in the paper are qualitative or on the order of magnitude. I don’t think it very important for the merits of this contribution if every one is rigorously correct or sometimes lacks rigorousness, correctness or justification. Since it is unlikely that the very model used is providing the answer on how to deduce the viscosity in liquids. This is probably also not the present aim of the DLM model. For this purpose, it lacks rigorousness in the definition of the physics of its inner working. For example:
- when can icebergs emit a wave-packet? When they are excited, it is said. Till we are at 0K they are always excited. So, what exactly is this excitation, necessary for the wave-packet. Can they always emit and cool down?
- of what character are this wave-packets? Are they longitudinal, transversal or both? Since they are short in time, they are composed of many frequencies. What is the dispersion of this wave packets? Can the wave-packets be reflected from icebergs or anything else like the boundary?
- I guess one of the important consequences of the wave packets is the transport of momentum without mass transport. But this is also possible by elastic means, I guess, like in Newton's cradle. So, my question is, if the icebergs would collide directly, due to dense packing, with icebergs is there a need for the wave-packets?
- if a wave-packet is emitted, e.g. towards layers of lower velocity as in figure 4, the liquid particle will take velocity components perpendicular to the straining direction and a mass transport perpendicular to x-axis starts. Is this something one should care about? Are velocity components mixing?
- it seems the icebergs are thought of crystals. Why is that, why isn’t it sufficient to be of amorphous solid? How is the size affecting the supported modes? How is the model dealing with entropy and enthalpy if the number and size of the icebergs is changing? Are icebergs breaking up and fuse together?
- the amorphous liquid part, what is it velocity in Fig. 3 relative to icebergs?
The paper claims on page 16 “However, the reasonable....” I don’t think this claim is justified. The model only reproduces aspects, but that does not mean the model is correct.
Table 1 should contain the experimental data compared to.
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Reviewer 3 Report
Comments and Suggestions for AuthorsThis manuscript discussed the viscosity of liquids within the dual model. Compared to the situation with gases and solids, our understanding of transport properties of liquids remains rather limited. One of the reasons is the absence of a small parameter, as correctly pointed out by the author. The duality of liquid dynamics, where the molecules exhibit fast solid-like oscillations about temporary equilibrium positions in addition to slow diffusion of these equilibrium positions plays the essential role. Because the complete theory of liquid transport is not yet developed and it is very unlikely that it will be developed in future, new ideas and proposals are welcome. As such, this manuscript deserves publication. However, there are several issues which need to be clarified first:
1. A reference for the expression for the viscosity of the dilute gas of hard spheres, appearing at the bottom on p. 2, should be provided. A believe there is a misprint in the numerical coefficient. Within the Chapman-Enskog theory it should be $\eta = 5\sqrt{\pi m k_B T}/\pi d^2$. Here d is the molecular diameter, not the distance.
2. There is a logic flaw in the next paragraph on p. 3. The author writes “Firstly, unlike gas molecules, liquid molecules interact among them by means of intense forces, comparable to those among solid molecules, and working at distance”. In fact, forces between gas and liquid molecules (as well as solid) are THE SAME. Liquids are just much more compressed so that intermolecular distances are much smaller. Then, “the presence of an interaction potential prevents to deal liquid molecules as hard spheres”. In fact, liquid molecules are often treated as hard spheres. Hard sphere model is a very popular model in the context of liquids and solids (and glasses).
3. It should be mentioned that Eq. (2) cannot be truly universal since it fails to describe the viscosity of the hard sphere fluid, to give an example.
4. Regarding Section 3.1. Since both the diffusion coefficient and the shear viscosity can be estimated within the model, the natural question arises: What about Stokes-Einstein (SE) relation in dense fluids? It is known that the SE relation without the hydrodynamic diameter operates in dense simple and not so simple liquids: 10.1063/1.5080662, 10.1080/00268976.2019.1643045, 10.1103/PhysRevE.104.044110. This also includes water, and other molecular liquids, see 10.1063/5.0150871 and references therein.
5. When discussing different approaches to transport properties of liquids an influential paper by Zwanzig “On the relation between self-diffusion and viscosity of liquids” J. Chem. Phys. 79, 4507 (1983) should be mentioned. It naturally demonstrates why SE relation should work and serves as a basis for related approaches to liquid dynamics, e.g. the vibrational paradigm for transport properties of dense liquids 10.1016/j.physrep.2023.11.004
6. At the bottom of p. 22 a relation between the shear viscosity, thermal conductivity and specific heat is discussed. It is stated that it was early introduced for gases and was proven also in the case of liquids. More explanations are needed here. What exactly the specific heat in this case? For atomic gases the known relation is $\lambda/\eta=15/4m$, where $\lambda$ is the thermal conductivity, $\eta$ is the shear viscosity, and $m$ is the atomic mass. In liquids it breaks severely down, as demonstrated in Figs. 4 and 5 of Ref. 10.1103/PhysRevE.103.013207 to provide an example.
7. On p. 24 the author discusses the role of fundamental constants in the universal minima of viscosity. A classical point of view on this phenomena deserves to be mentioned as discussed in 10.1063/5.0082465
8. Units should be provided for the numbers presented in Table I.
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Round 2
Reviewer 1 Report
Comments and Suggestions for Authorspublish as is
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Reviewer 2 Report
Comments and Suggestions for AuthorsDear Editors,
the authors engaged well with my remarks and I support publication in the present form.
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Reviewer 3 Report
Comments and Suggestions for AuthorsThe paper has been revised by the author taking into account my previous comments. I am satisfied with the revisions and can now recommend its publication. There are few places in the manuscript where I see
Errore. L'origine
riferimento non è stata trovata.
This should be corrected before publication.
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