# Talk:Multicomponent Flow

Review of Scholarpedia article "Multicomponent Flow" by Vincent Giovangigli

This article introduces the reader to the broad and complex area of multicomponent flow, which pervades many areas of science and engineering. The article is well written and engaging, offering a variety of different examples to guide the reader through this are of fluid mechanics. The background given in the Introduction is a very good summary of the diverse types of scenarios in which multicomponent fluid dynamics is important. The Fundamental Equations section gives a concise treatment of the basic equations describing these flows: the sections on Chemistry and Transport Fluxes are very good. The Mathematical Structure sections seems a bit technical and needs a short introductory paragraph before "Vector equations", perhaps with some elementary references to classic computational fluid dynamics texts to further guide the reader (e.g., Anderson, Tannehill & Pletcher, Chung, Laney). The section on Extended Models is useful, as it provides a very concise introduction to other related areas in which multicomponent flows exist: many useful references are given. It would be good to have a slightly lengthier Numerical Simulation section, as CFD continues to be a major tool in understanding these (and other) flows. One aspect that seems missing is mention of Experiments. Are there some classical mixing experiments or other experiments involving 2 or more fluid species (other than combustion) that could be commented on?

The following is a list of other suggestions and corrections:

(1) first sentence of Introduction, "...flows consist of different..." (2) second sentence of Introduction, add one or two references after "immiscible" (3) first sentence of second paragraph, "Earth's" (4) first sentence of third paragraph, delete "percents" (5) first sentence of Fundamental Equations section, what are "finer" theories? Can "molecular finer theories" be replaced by "kinetic theories"? Also used in Transport fluxes. (6) Subsection on conservation equations, some of the notation seems nonstandard to me and might confuse readers: I would use "J" instead of "F" for diffusion flux, "F" instead of "b" for body force, "sigma" instead of "Pi" for viscous stress. If the notation used corresponds exactly or closely to a particular reference, please mention that reference. References are needed in general for these equations. Nothing is saved by using "\partial_t" in place of "\partial/\partial t". Last sentence of this subsection, "...equations (1)-(3)..." and add at the end of sentence "...defined in Eqs. (4)-(6).". (7) At the end of Thermodynamics, it would be helpful to briefly define "nonideal fluids" (8) In the Chemistry section, use large square brackets in the expression for \omega_k in the quantity multiplying (\nu_ki^b - \nu_ki^f) (9) In Transport fluxes, "...\kappa denotes the bulk viscosity..." and later in that paragraph, "...which is the analog of the Soret effect." (10) Third paragraph of Transport fluxes, "article" instead of "paper" (11) At the end of the Transport fluxes section, please add some simple expressions for mixture coefficients (e.g., those that are based on weightings of mass fractions and molecular weights in the case of binary mixing). Maybe the Chapman-Cowling approximation? (12) Maybe the Numerical Simulation section should be moved immediately after the Mathematical Structure section, with the Extended Models section at the end of the article? This seems to be better to me. (13) In the Turbulent flows subsection, last sentence of first paragraph "...or Reynolds-averaged Navier-Stokes (RANS) modeling." First sentence of second paragraph, "...by applying a filter or averaging operator, respectively..." Also, please reference the Scholarpedia articles for "Turbulence", "Subgrid-Scale Modeling", "Rayleigh-Taylor" and "Richtmyer-Meshkov" (the last two important multicomponent flow applications should be mentioned here). (14) Spelling: "Nonideal thermodynamics" (15) Third sentence in Plasmas section, "electric field" (16) In the Plasmas section, an important application to mention (and provide a few references such as Lindl and Meyer-ter-Vehn and Atzeni) is inertial confinement fusion (ICF), which involves multicomponent flow, plasmas etc. (17) First sentence of Numerical Simulation section, "Peric" has a \latex issue (18) Starting with the second sentence of the Multiple scales subsection, there are many "~" after numbers. Last sentence of this subsection, "...fastest time scales..." (19) Algorithms subsection, "Newton-Krylov" and delete extra ")" after Nonaka et al. 2012 (20) End of Algorithms subsection, add reference to EGLIB (21) Example 1, "x" is missing in a few places (22) Last paragraph of Example 1, "CVD" instead of "cvd", "...with the substrate...", no comma after "desorption", put "mainly present in the hot zone of the reactor" in parentheses, comma after "CVD systems". (23) Example 3, first sentence, "reentering" and "Earth's", "...reaction mechanism involves...", second paragraph comma after "0.8" (24) Reference need some clean up: "--" and {\bf}, Ern and Giovangigli 1994 "Physics", Ern and Giovangigli 1998 "Physica A", "Peric", "Tohoku", O'Rourke, "PhD thesis", Zeldovich and Raizer "Temperature" (25) Recommended Reading: please use capitals for first letter in titles for uniformity, also "Menlo Park"

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The author would first like to thank the referee for his careful reading of the article and his helpful suggestions. All the Referee's suggestions have been taken into account in the revised version on the article Multicomponent Flow. To answer the questions raised by the Referee in more details, the following changes have been made (the rerefee's text is italic fonts between lines).

*The Mathematical Structure sections seems a bit technical and needs a short introductory paragraph before "Vector equations", perhaps with some elementary references to classic computational fluid dynamics texts to further guide the reader (e.g., Anderson, Tannehill & Pletcher, Chung, Laney).
*

*It would be good to have a slightly lengthier Numerical Simulation section, as CFD continues to be a major tool in understanding these (and other) flows. *

A short introductory paragraph has been added and the Numerical Simulation section has been enlarged. The references suggested by the referee have been added to the bibliography and mentioned at the appropriate place. The Numerical Simulation section is now entitled Computational Reactive Flow Dynamics and has been merged with the mathematical section as also suggested by the referee.

* One aspect that seems missing is mention of Experiments. Are there some classical mixing
experiments or other experiments involving 2 or more fluid species (other than combustion) that could be commented on ? *

A new section about transport coefficients has been added. In the first version of the article, the evaluation of transport coefficients was only suggested. There is now more information about the transport linear systems, the algorithms and also empirical formulas. As an illustration, the Stefan-Maxwell equations for the diffusion velocities are also presented. An experiment by Duncan and Toor (1962) about three component gases is then mentioned and briefly commented. Other references to experiments (indeed to laser diagnostics) have also been added in the Computational Reactive Flow Dynamics section to illustrate the need to validate numerical simulations against experimental measurements.

(1) *first sentence of Introduction, "...flows consist of different..." *

This correction has been made.

(2) *second sentence of Introduction, add one or two references after "immiscible" *

A reference to Drew and Passman (1989) has been added.

(3) *first sentence of second paragraph, "Earth's"*

(4) *first sentence of third paragraph, delete "percents"*

These corrections have been made.

(5) *first sentence of Fundamental Equations section, what are "finer" theories?
Can "molecular finer theories" be replaced by "kinetic theories"? Also used in Transport fluxes.*

At the beginning of `Fundamental Equations’ Section, the `finer theories’ are detailed as `statistical mechanics’, `kinetic theory of dilute gases’, and `kinetic theory of dense gases’. They do not reduce to `Kinetic Theories’ since it is also possible to at least get the conservation equations and the fluxes form statistical mechanics (Bearman and Kirkwood 1958). In the `Transport Fluxes’ Section, the `finer theories’ are now explicited to avoid any confusion.

However, in the `Transport Coefficients’ new Section, it is now mentioned that only kinetic theories yields the transport coefficients.

(6) *Subsection on conservation equations, some of the notation seems nonstandard
to me and might confuse readers: I would use "J" instead of "F" for diffusion flux,
"F" instead of "b" for body force, "sigma" instead of "Pi" for viscous stress.
If the notation used corresponds exactly or closely to a particular reference,
please mention that reference.
References are needed in general for these equations.
Nothing is saved by using "\partial_t" in place of "\partial/\partial t".
Last sentence of this subsection, "...equations (1)-(3)..." and add at the
end of sentence "...defined in Eqs. (4)-(6).". *

Most of the notation suggested by the referee is now used. In particular, the diffusive mass fluxes are denoted by J, the specific forces by f, and \partial/\partial t is used instead of \partial_t. The viscous tensor is still denoted by \Pi since it differs from the viscous stress tensor (-\Pi). This point is now explained as well as the fact that the Cauchy stress tensor sigma is -(p I + \Pi). Using a Pressure tensor pI+\PI or a viscous tensor \Pi is somewhat natural since both are fluxes at variance with stress tensors. Many authors have used such tensors like for instance de Groot and Mazur, Landau and Lifchitz, Kee, Coltrin and Miller, Williams, and Oran and Boris.

The resulting notation is exactly that used by De Groot and Mazur and references to (de Groot and Mazur 1984; Williams 1985; Rosner 1986; Giovangigli 1999; Kee et al. 2003) have also been added.

(7) *At the end of Thermodynamics, it would be helpful to briefly define "nonideal fluids"*

It has been added that nonideal fluids are such that the compressibility factor z = p m/(rho R T) deviates from unity.

(8) *In the Chemistry section, use large square brackets in the expression
for \omega_k in the quantity multiplying (\nu_ki^b - \nu_ki^f)*

(9) *In Transport fluxes, "...\kappa denotes the bulk viscosity..."
and later in that paragraph, "...which is the analog of the Soret effect."*

(10) *Third paragraph of Transport fluxes, "article" instead of "paper"*

These modifications have been made but it is still indicated between parenthesis that the bulk viscosity is sometimes termed the volume viscosity.

(11) *At the end of the Transport fluxes section, please add some simple
expressions for mixture coefficients (e.g., those that are based on
weightings of mass fractions and molecular weights in the case of binary mixing).
Maybe the Chapman-Cowling approximation? *

As already discussed, in the first version of the article, the evaluation of transport coefficients was only suggested. There is now more information about the transport linear systems and the transport algorithms. The use of empirical formulas is also mentioned as suggested by the referee and such a formula is provided for the mixture viscosity. The Stefan-Maxwell equations for the diffusion velocities are also presented for illustration and reference is made to the Duncan and Toor experiment. It was not reasonably possible to include the Chapman-Enskog theory or a comprehensive discussion of the transport coefficients. Such an addition would be too long and `Brevity is the soul of wit’ as indicated in the Instructions to authors.

(12) *Maybe the Numerical Simulation section should be moved immediately
after the Mathematical Structure section, with the Extended Models section
at the end of the article? This seems to be better to me. *

The numerical section has been merged with the mathematical section as suggested by the referee. However, it was not possible to put the `Extended Models’ after the examples. Indeed, the high pressure flame uses a nonideal equation of state, and the CVD model and the reentry flow also use radiative losses at the solid boundaries so that they are also `extended models’.

(13) *In the Turbulent flows subsection, last sentence of first paragraph
"...or Reynolds-averaged Navier-Stokes (RANS) modeling."
First sentence of second paragraph, "...by applying a filter or averaging
operator, respectively..." Also, please reference the Scholarpedia articles
for "Turbulence", "Subgrid-Scale Modeling", "Rayleigh-Taylor" and
"Richtmyer- Meshkov" (the last two important multicomponent flow
applications should be mentioned here). *

(14) *Spelling: "Nonideal thermodynamics"*

(15) *Third sentence in Plasmas section, "electric field"*

All these corrections and additions have been done.

(16) *In the Plasmas section, an important application to mention (and provide
a few references such as Lindl and Meyer-ter-Vehn and Atzeni) is inertial
confinement fusion (ICF), which involves multicomponent flow, plasmas etc. *

A sentence about inertial confinenment has been added as well as the references suggested by the referee.

(17) *First sentence of Numerical Simulation section, "Peric" has a \latex issue *

(18) *Starting with the second sentence of the Multiple scales subsection,
there are many "~" after numbers. Last sentence of this subsection,
"...fastest time scales..." *

(19) *Algorithms subsection, "Newton-Krylov" and delete extra ")"
after Nonaka et al. 2012 *

(20) *End of Algorithms subsection, add reference to EGLIB*

All these corrections have been done.

(21) *Example 1, "x" is missing in a few places *

There were many x,y, and z missing and this has been corrected.

(22) *Last paragraph of Example 1, "CVD" instead of "cvd", "...with the substrate...",
no comma after "desorption", put "mainly present in the hot zone of the reactor"
in parentheses, comma after "CVD systems". *

(23) *Example 3, first sentence, "reentering" and "Earth's", "...reaction
mechanism involves...", second paragraph comma after "0.8" *

(24) *Reference need some clean up: "--" and {\bf},
Ern and Giovangigli 1994 "Physics", Ern and Giovangigli 1998 "Physica A",
"Peric", "Tohoku", O'Rourke, "PhD thesis", Zeldovich and Raizer "Temperature" *

(25) *Recommended Reading: please use capitals for first letter in titles for
uniformity, also "Menlo Park"*

All these corrections have been done in the article.