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The equations of motion of ordinary relativistic hydrodynamics are derived by considering conservation equations of the energy tensor and particle number current, where constitutive relations relate the energy tensor and number current to the pressure, energy density, four-velocity, particle number density etc. But suppose I want to describe a fluid consisting of multiple species of particles that can undergo chemical reactions with one another. Then the conservation of particle number of certain species no-longer holds.

Question: How do you derive the resulting equations of motion for chemically reacting fluids? I am most interested in the relativistic case, but might be able to make do with the non-relativistic version.

A quick derivation and sources would be appreciated!

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  • $\begingroup$ It is necessary to describe the problem in words. Then we can consider a suitable model. Relativistic streams are cosmic plasma or heavy ion collision products? If chemical reactions occur, then the flow is usually subsonic, or supersonic. There has been a lot of research into the problem of burning and detonation. There has also been a lot of research into the problem of reacting flows in chemical reactors and in the boundary layer. $\endgroup$
    – Alex Trounev
    Commented Jul 15, 2019 at 3:33
  • $\begingroup$ Do you understand how to derive the non-relativistic hydrodynamic equations, including chemical reaction? $\endgroup$
    – Chet Miller
    Commented Jul 15, 2019 at 20:44
  • $\begingroup$ @ChetMiller No, I don't know how to do any sort of hydrodynamics with chemical reactions. If you are familiar with the non-relativistic version, I would be very interested! $\endgroup$
    – user105620
    Commented Jul 15, 2019 at 23:47
  • $\begingroup$ Well, it takes some learning and time, but you can do it. You need to learn first how to analyze transport processes (viscous momentum, heat, and mass transfer), how to quantify chemical kinetics, and then how to combine the two. I suggest starting with a book on transport processes such as Transport Phenomena by Bird, Stewart, and Lightfoot and a book on chemical reaction engineering like that by Levenspiel. This will contain what you need. $\endgroup$
    – Chet Miller
    Commented Jul 16, 2019 at 0:24
  • $\begingroup$ The most general hydrodynamic model for a mixture that is undergoing nuclear or chemical reactions that is stable, causal and thermodynamically consistent is derived from general principles in Bulk viscosity in relativistic fluids: from thermodynamics to hydrodynamics (2020). See also this answer for more references and ideas: physics.stackexchange.com/a/747464/226902 $\endgroup$
    – Quillo
    Commented Nov 12, 2023 at 17:28

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