**Srboljub Simić**^{[1]}, **Milana Pavić-Čolić**^{[2]} and **Damir Madjarević**^{[1]}

*Non-equilibrium mixtures of gases: modelling and computation*

**Pages:** 135-214

**Received:** 4 February 2015

**Accepted in revised form:** 21 April 2015

**Mathematics Subject Classification (2010):** 76P05, 80A17, 76L05, 76R50.

**Keywords:** Mixtures of gases, extended thermodynamics, kinetic theory of mixtures, diffusion, shock waves.

**Author address:**

[1] : Department of Mechanics, University of Novi Sad, Trg Dositeja Obradovića 6, 21000 Novi Sad, Serbia

[2] : Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Serbia

This research was partially supported by by the Ministry of Education, Science and Technological Development, Republic of Serbia, through the project "Mechanics of nonlinear and dissipative systems -- contemporary models, analysis and applications", Project No. ON174016.}

**Abstract:**
These notes present the material about modelling of non-equilibrium processes in mixtures of gases.
It is mainly concerned with mixtures described within the context of extended thermodynamics, but also covers certain features of the kinetic theory of mixtures.
General introduction puts extended thermodynamics into proper position with respect to other approaches (TIP and kinetic theory of gases).
Extended thermodynamics of multi-temperature mixtures of Euler fluids is properly established and analyzed. Shock waves as particular non-equilibrium
problem are thoroughly discussed. Kinetic modeling of mixtures is also discussed and related to the results of extended thermodynamics.
The notes contain new results related to comparison of extended thermodynamic model of mixtures with Maxwell-Stefan diffusion model,
and shock structure analysis in viscous multi-temperature model.

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