Linear stability of ferrofluids in a non-uniform magnetic field
File(s)
Author(s)
Ferguson Briggs, Sarah Helen
Type
Thesis
Abstract
The linear stability of Newtonian ferrofluids subject to non-uniform magnetic fields is consid- ered in different geometries. First, a ferrofluid column with constant magnetic susceptibility, centred on a current-carrying rigid wire and surrounded by another ferrofluid with a differ- ent susceptibility, is investigated. Ferrofluids with non-uniform susceptibilities are considered next. For a constant susceptibility the magnetic forcing is confined to the interface, but for a non-constant susceptibility the forcing is felt in the bulk of the fluid. It is postulated that a sta- tionary state of a ferrofluid with a non-uniform susceptibility in the presence of a non-uniform field, such that regions of highest susceptibility do not coincide with regions of highest field, may be unstable. An instability could be driven by the release of magnetic energy, since a minimum energy configuration may be reached when ferrofluid regions of high susceptibility and regions of high field coincide. This is explored for equilibria in a cylindrical domain, a planar domain and in a general three-dimensional domain. In a cylindrical domain, a stability condition is determined for a ferrofluid surrounding a current-carrying rigid wire, whose susceptibility varies radially. In a planar configuration, a stationary state of ferrofluid between two channel walls is found. The susceptibility and field vary normal to the wall, such that the regions of highest field and susceptibility do not coincide, and it is proven to be unstable. Methods of stabilising both systems are determined. For the cylindrical system, a constant axial field suffices, but for the planar domain it is shown that a rapidly rotating field is necessary to dampen unstable modes. Lastly, a stability condition is obtained for a general volume of ferrofluid, whose susceptibility varies slowly with position, subject to a non-uniform field.
Version
Open Access
Date Issued
2022-09
Date Awarded
2022-12
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Mestel, Jonathan
Papageorgiou, Demetrios
Sponsor
Engineering and Physical Sciences Research Council
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)