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The goal of the course is to present several approaches to modelling of multi-component materials in the
framework of mechanics and thermodynamics of continua. The general theory will be presented together with
derivation of simplified models.
Last update: T_MUUK (05.05.2015)
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Credit for exercises based on the active participation at the seminars and on the successful solution of homeworks has to be assigned before the beginning of the exam. Last update: Málek Josef, prof. RNDr., CSc., DSc. (12.10.2017)
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K. Hutter, K. Johnk, Continuum methods of physical modelling, Springer-Verlag Berlin- Heidelberg, 2004. R.M. Bowen, Theory of mixtures in continuum physics III, ed. A.C. Eringen. Academic Press, New York, 1976. C.Truesdell, Rational thermodynamics, Springer-Verlag, New York, 1984. L.Schneider, K. Hutter, Solid-fluid mixtures of frictional materials in geophysical and geo-technical context, Springer-Verlag Berlin-Heidelberg, 2009. K.R. Rajagopal, L. Tao, Mechanics of mixtures, World scientific publishing, Co. Singapore, 1995. D.A. Drew, S.L. Passman, Theory of multicomponent fluids, Springer, 1998. I. Samohýl, Racionální termodynamika chemicky reagujících směsí, Academia, Praha 1982. I. Muller, A thermodynamic theory of mixtures of fluids, Arch. Rat. Mech. Anal., 28, 1-39, 1968. Last update: Šmíd Dalibor, Mgr., Ph.D. (05.05.2015)
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The exam is oral and consists of answering two questions from selected group of topics. More details is available at http://www.karlin.mff.cuni.cz/~malek/new/index.php?title=NMMO541_Theory_of_Mixtures , item Syllabus and general remarks. Last update: Málek Josef, prof. RNDr., CSc., DSc. (12.10.2017)
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1. Continuum theory of mixtures: Motivation, basic applications, assumption of co-occupancy, kinematics 2. Measures and relations between them, balance of mass, momentum, angular momentum, energy and entropy for the mixture components and for the mixture as a whole, definition of mixture velocity, mixture classes I,II,III,IV 3. Class I mixtures, derivation of Fick’s law and Fick-Navier-Stokes-Fourier (Fick-NSF) model 4. Fick-NSF model with boundary conditions 5. Quasi-incompressible approximations, quasi-incompressible variants of the Fick-NSF model 6. Derivation of the Cahn-Hilliard-NSF model 7. Chemical reactions - introduction, stoichiometry 8. Chemical reactions - mixture of ideal gasses, chemical potential, chemical equilibrium, mass action law, chemical kinetics 9. Derivation of the Allen-Cahn-NSF model 10. Mechanical interaction between the phases, basic mechanical analogues of the interaction mechanisms in mixtures, drag, lift, Magnus force, virtual mass effect 11. Class II mixtures, derivation of the Darcy law and other simplified models for flows through porous media (Forchheimer, Brinkman) 12. A thermodynamic framework for the mixture of two liquids 13. Balance equations at interfaces, generalized interface conditions 14. Multi-phase mixture theory: formalism, averaging, balance equations, structure of the interaction terms Last update: Šmíd Dalibor, Mgr., Ph.D. (05.05.2015)
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Recommended prerequisities: Single-component continuum mechanics and thermodynamics. Last update: Šmíd Dalibor, Mgr., Ph.D. (05.05.2015)
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