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Biochemical and mechanical processes in synovial fluid - modeling, analysis and computational simulations
Pustějovská, Petra ; Málek, Josef (advisor) ; Süli, Endré (referee) ; Jäger, Willi (referee) ; Maršík, František (referee)
vi Title: Biochemical and mechanical processes in synovial fluid - modeling, mathematical analysis and computational simulations Author: Petra Pustějovská (petra.pustejovska@karlin.mff.cuni.cz) Department: Matematický ústav UK, Univerzita Karlova v Praze Institut für Angewandte Mathematik, Universität Heidelberg Supervisors: prof. RNDr. Josef Málek CSc., DSc. (malek@karlin.mff.cuni.cz) Matematický ústav UK, Univerzita Karlova v Praze, Prof. Dr. Dr. h.c. mult. Willi Jäger (jaeger@iwr.uni-heidelberg.de) Institut für Angewandte Mathematik, Universität Heidelberg Abstract: Synovial fluid is a polymeric liquid which generally behaves as a viscoelastic fluid due to the presence of polysaccharide molecules called hyaluronan. In this thesis, we study the biological and biochemical properties of synovial fluid, its complex rheology and interaction with synovial membrane during filtration process. From the mathematical point of view, we model the synovial fluid as a viscous incompressible fluid for which we develop a novel generalized power-law fluid model wherein the power-law exponent depends on the concentration of the hyaluronan. Such a model is adequate to describe the flows of synovial fluid as long as it is not subjected to instantaneous stimuli. Moreover, we try to find a suitable linear viscoelastic model...
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Biochemical and mechanical processes in synovial fluid - modeling, analysis and computational simulations
Pustějovská, Petra ; Málek, Josef (advisor) ; Süli, Endré (referee) ; Jäger, Willi (referee) ; Maršík, František (referee)
vi Title: Biochemical and mechanical processes in synovial fluid - modeling, mathematical analysis and computational simulations Author: Petra Pustějovská (petra.pustejovska@karlin.mff.cuni.cz) Department: Matematický ústav UK, Univerzita Karlova v Praze Institut für Angewandte Mathematik, Universität Heidelberg Supervisors: prof. RNDr. Josef Málek CSc., DSc. (malek@karlin.mff.cuni.cz) Matematický ústav UK, Univerzita Karlova v Praze, Prof. Dr. Dr. h.c. mult. Willi Jäger (jaeger@iwr.uni-heidelberg.de) Institut für Angewandte Mathematik, Universität Heidelberg Abstract: Synovial fluid is a polymeric liquid which generally behaves as a viscoelastic fluid due to the presence of polysaccharide molecules called hyaluronan. In this thesis, we study the biological and biochemical properties of synovial fluid, its complex rheology and interaction with synovial membrane during filtration process. From the mathematical point of view, we model the synovial fluid as a viscous incompressible fluid for which we develop a novel generalized power-law fluid model wherein the power-law exponent depends on the concentration of the hyaluronan. Such a model is adequate to describe the flows of synovial fluid as long as it is not subjected to instantaneous stimuli. Moreover, we try to find a suitable linear viscoelastic model...
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Modeling multiphase flow in porous media with an application to permafrost soil
Heida, Martin ; Málek, Josef (advisor) ; Málek, Josef (referee) ; Jäger, Willi (referee)
3 Abstract This thesis contains the derivation of two-scale models for multi phase and multi con- stituent flow in porous media. It will be achieved by using phase field models for the porespace together with formal asymptotic expansion. The equations describing the processes in the porespace are obtained by using the assumption of maximal entropy production rate, which was first developed and used by Rajagopal and Srinivasa. This method is able to yield thermodynamically consitent models in the bulk starting from constitutive assumptions on energy and on the rate of entropy production. In partic- ular, the method will lead to a new point of view on phase field models and it will be possible to derive well known models like the Cahn-Hilliard-Navier-Stokes system, Korteweg's equation or the Allen-Cahn model of phase transition. In order to derive suitable boundary coditions, the assumption of maximum rate of entropy production is generalized to processes on the surface of a bounded domain and applied to phase field models. Finally, the same method is used to derive a thermodynamically consistent scaling of such multi phase and multi constituent systems. The resulting equations are homogenized via formal asymptotic expansion. This method will be applied to the air/water system in soil as well as to the active...
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