Izračun oblike proste površine magnetne tekočine v homogenem magnetnem polju : doktorska disertacija

slovenian

doktorska dela

2020

Differential Evolution (DE)   Energy Functional   Ferrofluid   Finite Element Methods (FEM)   hexagonal pattern   Ritz method   Rosensweig instability   Young-Laplace equation

Univerza v Mariboru, Fakulteta za elektrotehniko računalništvo in informatiko

The thesis deals with the computation of a magnetic liquid free surface deformation under the influence of a homogeneous magnetostatic field. When a magnetic liquid, which is a stable colloidal suspension of magnetic nanoparticles, is exposed to an external magnetic field exceeding a certain critical value, spike-like shapes appear on the surface of the liquid. The distribution and the height of the spikes depend on the magnetic field strength, as well as the properties of the magnetic liquid. Two case studies of free surface deformation are covered theoretically and numerically in the thesis. The first case study is devoted to a single spike, where the free surface is described as a polynomial function in cylindrical coordinates with applied cylindrical symmetry. To obtain the shape deformation, a system of nonlinear magnetic augmented Young-Laplace equations is solved iteratively. In the second case study, the research effort is focused on the free surface deformation of a central spike in a periodical hexagonal pattern placed in three-dimensional space (3D). Due to the periodical nature of the problem, the free surface is approximated by three planar waves, whose two-dimensional wave-vectors are mutually displaced by 2%/3 in the x-y plane. The surface deformation is achieved through the energy function, with the combination of Differential Evolution and the Ritz method. The computational strategy is divided into two stages. At the first stage, the magnetic field is computed by the Finite Element Method (FEM), while a free surface profile is obtained in the second stage. The numerical results of the magnetic liquid free surface deformation obtained by the proposed methods are compared by the numerical and experimental results published in the References. To support the theoretical predictions as well as numerically obtained results, measurements of the magnetic field were performed at a close distance above the spikes of the magnetic liquid, which show that the magnetic field is distributed in a similar way as a free surface.

07.08.2023