| Summary: | In this thesis, we discuss the use of a superconducting solenoid magnet to investigate radial interfacial instabilities between two rotating immiscible, incompressible fluids of differing density. The magnetic field produced by the solenoid magnet is used to induce a radial body force on diamagnetic and paramagnetic fluids, providing an effective acceleration in the radial direction that affect the instability growth rate at the interface. The applied rotation is then controlled to induce instability for various wavenumbers, analogous with horizontal gravitational instability. The investigation is focused on a circular Hele-Shaw cell containing two fluids of non-equal density that occupy a small gap between two solid flat plates.
An experimental study is carried out by varying the angular velocity on the two-fluid system at a vertical equilibrium point in the magnetic field. The magnetic force creates an initial condition in which the more dense fluid occupies an inner circular region of a rotating circular cell, centred on the axis, while the less dense fluid occupies the outer region. Under rotation, both fluid layers experience a centripetal acceleration directed towards the axis, causing Rayleigh-Taylor instability to develop.
We were able to extract and analyse the interface between the fluid layers to determine the growth rates for increasing wavenumbers and determine the fastest growth rate. We then derived a linear growth model by approximating a highly viscous three-dimensional Stokes flow to a two-dimensional potential flow problem by taking a depth-averaged velocity over the vertical distance of our experimental cell. The model also allowed us to determine a critical angular velocity for which instability occurs. Comparisons of the fastest growing wavenumber between the model and our experimental results showed a qualitative agreement between the two. The dynamic viscosity of the fluid layers in our experiments caused a quantitative difference in our results, leading us to investigate different viscosity values. By setting the viscosity as an unknown parameter and employing non-linear curve fitting, the viscosity of both fluids layers were found to be greater than anticipated. However, we were able to show experimentally that the excitation of wavenumbers can be influenced by the angular velocity of the system.
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