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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Modeling of porous metal oxide layer growth in the anodization process
 Habera, Michal ; Hron, Jaroslav (advisor) ; Pavelka, Michal (referee)
Under suitable conditions anodic metal oxidation leads to growth of complex porous structures. The initiation and growth of these structures is an interesting and challenging task for electrochemical modelling. One must identify chemical reactions in a multi-phase framework, derive a proper partial differential equations and solve them in time dependent domains. In this work, electrochemical model for the oxide growth in nano scales is presented. Physically motivated equations are formulated with precise mathematical meaning and existence of solutions is studied. Electrostatic potential fulfilling high-field conduction law and interfacial jump conditions is sought for. Numerical discretization is performed with the use of finite element method and free boundaries are tracked with characteristic level-set functions. Basic mechanism governing the growth of porous structures is given and numerical experiments are explained on it's basis. This thesis presents novel contributions to the electrochemical and mathematical picture of nanopores growth.
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Numerické simulace ferrotekutin
 Habera, Michal ; Hron, Jaroslav (advisor) ; Souček, Ondřej (referee)
The stress tensor of a ferrofluid exposed to an external magnetic field is subject to an additional magnetic terms. For a linearly magnetizable medium, such terms results in an interfacial magnetic force acting on the ferrofluid boundaries. This force changes the characteristics of many free-surface ferrofluid phenomena. The aim of this work is to implement this force into Navier-Stokes equations and propose a numerical method to solve them. The interface of ferrofluid is tracked with the use of level-set method and additional reinitialization step assures conservation of its volume. Incompressible Navier-Stokes equations are formulated for divergence free velocity fields while discrete interfacial forces are treated with continuous surface force model. Velocity-pressure coupling is given by projection method. To predict the magnetic force effect quantitatively, Maxwell's equations for magnetostatics are solved in each time step. Finite element method is utilized for the spatial discretization. At the end of the work, equilibrium droplet shape and dripping phenomenon are qualitatively compared to known experimental results. Powered by TCPDF (www.tcpdf.org)
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