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Identifier 000396461
Title Systems of spherical particles in stokes flow
Alternative Title Συστήματα σφαιρικών σωματιδίων σε ροή stokes
Author Λαζαρίδου, Χριστίνα Ν.
Thesis advisor Τζαβάρας, Αθανάσιος
Reviewer Ροζάκης, Φ
Χαρμανδάρης, Β.
Abstract In this thesis, we study the most demanding model for computing the kinetic equations of particles in a Stokes flow, namely stochastic model for N point particles. Our goal is to analyze this model using the perspective of Brownian motion and Ito Calculus. First of all, we propose the model of spherical Brownian particles. We derive the equations of motion for the particles provided that they are rigid and both transitional and rotational motion occurs. In the second part of thesis, the kinematics and dynamics of rigid bod¬ies indicates that many rigid particles interact with a viscous incompressible fluid whose motion is governed by the Navier - Stokes system of equations. Furthermore, the equations of motion and energy represent a classical for-mulation of the problem that possesses a global-in-time weak solution. In the third part of thesis, the diffusion of particles is described by the Brownian motion through a phenomenological equation which has two dif¬ferent but equivalent forms the Smoluchowski equation and the Langevin equation which establishes Brownian motion as a kind of stochastic process based on macroscopic laws. Finally, a collection of Brownian particles are supposed to be points, Ito-formula is applied to their stochastic differential equation and kinetic equation for friction theory, which is the Smoluchowski equation, is derived. To tackle this fundamental issue, Stokes equations should be solved in order to obtain the velocity and the Oseen tensor.
Language English
Issue date 2015-07-17
Collection   School/Department--School of Sciences and Engineering--Department of Mathematics and Applied Mathematics--Post-graduate theses
  Type of Work--Post-graduate theses
Permanent Link https://elocus.lib.uoc.gr//dlib/2/2/3/metadata-dlib-1444118486-836582-10016.tkl Bookmark and Share
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