Description of non-Newtonian phenomena and explanation how to model these phenomena within the complete
thermomechanical framework using the concept as natural configuration, maximization of rate of entropy production, implicit constitutive theory. Basic mathematical insights on equations describing steady and unsteady
flows of Newtonian and non-Newtonian incompressible fluids will be also given.
Last update: T_MUUK (16.05.2008)
Popis základních charakteristik nenewtonských tekutin a jejich modelování v jednotném termomechanickém rámci.
Matematický pohled na rovnice popisující proudění newtonských a nenewtonských tekutin.
Aim of the course -
Last update: JOSEF/MFF.CUNI.CZ (06.05.2008)
The course aims to describe basic phenomena that cannot be captured by Newtonian (Navier-Stokes) fluids and then to provide a derivation of models that have the ability of capturing these phenomena.
Last update: JOSEF/MFF.CUNI.CZ (06.05.2008)
Cílem předmětu je poskytnout posluchači základní popis jevů, které nemohou newtonské (Navier-Stokesovy) tekutiny popsat a odvodit modely, které naopak jsou vhodné k jejich popisu.
Literature - Czech
Last update: Prof. PhDr. Alan Josef, CSc. (23.05.2006)
[1] W. R. Schowalter: Mechanics of Non-Newtonian Fluids, Pergamon Press (Oxford), 1978.
[2] R. R. Huilgol: Continuum mechnaics of viscoelastic liquids, Hindusthan Publishing Co. (Delhi), 1975.
[3] J. Malek, K. R. Rajagopal: Mathematical issues concerning the Navier-Stokes equations and some of its generalizations, Handbook of Differential Equations, Evolutionary Equations, Vol. 2 (eds. C. Dafermos and E. Feireisl),
Elsevier, 2005, 371-459.
Teaching methods -
Last update: JOSEF/MFF.CUNI.CZ (06.05.2008)
Lecture course
Last update: JOSEF/MFF.CUNI.CZ (06.05.2008)
přednáška
Syllabus -
Last update: Prof. PhDr. Alan Josef, CSc. (23.05.2006)
The lecture course, offerred only in the winter semesters, is scheduled for two years. In the even calendar year, we focus on modeling of the non-Newtonian phenomena in the full thermomechanical framework. In the odd year, we analyze selected models within the modern theories on nonlinear partial differential equations.
The key topics: foundation of continuum fluid mechanics and thermodynamics (what is a fluid, incompressibility, inhomogeneity, duitable description, balance equations); Newtonian (Navier-Stokes) fluids, description of non-Newtonian phenomena (shear-thinning/shear-thickenning, pressure-thichening, stress relaxation, nonlinear creep, normal stress differences, jump discontinuities in stress)accompanied by sample models that can capture these non-Newtonian features and by several important materials (biological fluids, granular materials, mixtures) that exhibit such non-Newtonian behavior; derivation of an hierarchy of models within an unified thermomechanical setting - from the Navier-Stokes equations upto the equations for viscoelastic materials; various types of boundary conditions; a link between the principle physical concepts and mathematical analysis of relevant models.
Last update: Prof. PhDr. Alan Josef, CSc. (25.05.2006)
Prednaska ma dvoulety cyklus a se svolenim prednasejiciho
lze prednasku zapsat opakovane. Semestr v sudem roce bude zameren na
modelovani jevu charakteristickych pro nenewtonske tekutiny
napeti, aj.) v ramci termomechaniky kontinua. Semestr v lichem roce bude
venovan matematicke analyze vybranych modelu (lze jej absolvovat
nezavisle na prvni casti).
Cilem prednasky je seznamit studenty s: (i) základy mechaniky a termodynamiky tekutin (co jsou tekutiny, nestlacitelnost, nehomogenita, moznosti popisu, bilancni vztahy); (ii) newtonskymi (Navier-Stokesovy) tekutinami;
(iii) zakladnimi charakteritikami nenewtonských tekutin (zeslabeni, zesileni smyku, nelinearni viskozita, pritomnost rozdilu normalovych napeti v jednoduchem smykovem poli, napetova relaxace, nelinearni creep, skokove singularity v tensoru napeti) a priklady modelu, ktere tyto jevy popsat mohou a které nikoliv, a priklady materialu (biologicke tekutiny, granulovane materialy, smesi), ktere tyto charakteristiky vykazuji. Bude prezentovana a odvozena cela hiearchie modelu v jednotnem termomechanickem popisu, od Navier-Stokesovych rovnic az k rovnicim pro viskoelasticke materialy. Pozornost bude venovana hranicnim podminkam. Duraz bude kladen na ty fyzikalni aspekty, ktere hraji dulezitou roli v matematicke analyze odvozenych modelu.