title: Analysis and Numerical Approximation of Dielectrophoretic  Force Driven Flow Problems
creator: Gerstner, Philipp
subject: 510
subject: 510 Mathematics
description: Dielectric fluids under the influence of an external electric field and temperature variations experience a body force that is a combination of buoyancy and dielectrophoresis. The resulting motion can be described by the so-called Thermal-Electro-Hydrodynamic (TEHD) Boussinesq  equations. In this thesis, a variational formulation for these equations is proposed, with an emphasis on the mathematical modeling of the acting body force. Within this framework, existence and stability of steady and unsteady solutions is shown. Moreover, uniqueness of steady solutions under certain conditions is proven.   As second part of this thesis, a numerical method is roposed for approximately solving the TEHD Boussinesq equations in the stationary and instationary case. The spatial discretization is based on the conforming Finite Element Method (FEM) and temporal discretization is realized by  a variant of the Backward Differentiation Formula (BDF). In both cases, a priori error estimates are derived and validated by numerical experiments in a 2D test problem.  Finally, the 3D flow inside a vertical annulus with applied temperature and electric potential gradient is simulated. The formation of vortex structures is analyzed and the obtained results are compared with experimental data. By means of the corresponding adjoint problem, the sensitivity of solutions w.r.t. perturbations is investigated and it is numerically shown, that steady solutions are not unique in this scenario.
date: 2020
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/28828/1/ThesisPhilippGerstner.pdf
identifier: DOI:10.11588/heidok.00028828
identifier: urn:nbn:de:bsz:16-heidok-288287
identifier:   Gerstner, Philipp  (2020) Analysis and Numerical Approximation of Dielectrophoretic Force Driven Flow Problems.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/28828/
rights: info:eu-repo/semantics/openAccess
rights: Please see front page of the work (Sorry, Dublin Core plugin does not recognise license id)
language: eng