Chapman–Enskog derivation of multicomponent Navier–Stokes equations

There are several reasons to extend the presentation of Navier-Stokes equations multicomponent systems. Many technological applications based on physical phenomena that present neither in pure elements nor binary mixtures. Whereas Fourier's law must already be generalized binaries, it is only with more than two components Fick's breaks down its simple form. The emergence dissipative affects also inertial confinement fusion configurations, designed as prototypes for future nuclear plants hopefully replacing fission ones. This important topic can described much simpler terms many textbooks since publication formalism put forward recently by Snider \textit{Phys. Rev. E} \textbf{82}, 051201 (2010). In a very natural way, replaces linearly dependent atomic fractions independent set partial densities. Then, Chapman-Enskog procedure hardly complicated mixtures elements. Moreover, recent proposal convergent kinetic equation Baalrud and Daligault Plasmas} \textbf{26}, 082106 (2019) demonstrates Boltzmann potential mean force far better choice situations close equilibrium, equations, Landau or Lenard-Balescu equations. our comprehensive presentation, we emphasize arguments behind derivation keep mathematics possible. excludes technical non-essential aspect solution linearized through an expansion Hermite polynomials. We discuss link second principle Thermodynamics entropy increase, what learned from this exposition.