Determining surface tension using DC magnetic levitation

The values of material physical properties are vital for the successful use of numerical simulations for electromagnetic processing of materials. The surface tension of materials can be determined from the experimental measurement of the surface oscillation frequency of liquid droplets. In order for this technique to be used, a positioning field is required that results in a modification to the oscillation frequency. A number of previous analytical models have been developed that mainly focus on electrically conducting droplets positioned using an A.C. electromagnetic field, but due to the turbulent flow resulting from the high electromagnetic fields required to balance gravity, reliable measurements have largely been limited to microgravity. In this work axisymmetric analytical and numerical models are developed, which allow the surface tension of a diamagnetic droplet positioned in a high DC magnetic field to be determined from the surface oscillations. In the case of D.C. levitation there is no internal electric currents with resulting Joule heating, Marangoni flow and other effects that introduce additional physics that complicates the measurement process. The analytical solution uses the linearised Navier-Stokes equations in the inviscid case. The body force from a DC field is potential, in contrast to the AC case, and it can be derived from Maxwell equations giving a solution for the magnetic field in the form of a series expansion of Legendre polynomials. The first few terms in this expansion represent a constant and gradient magnetic field valid close to the origin, which can be used to position the droplet. Initially the mathematical model is verified in microgravity conditions using a numerical model developed to solve the transient electromagnetics, fluid flow and thermodynamic equations. In the numerical model (as in experiment) the magnetic field is obtained using electrical current carrying coils, which provides the confinement force for a liquid droplet. The model incorporates free surface deformation to accurately model the oscillations that result from the interaction between the droplet and the non-uniform external magnetic field. A comparison is made between the analytical perturbation theory and the numerical pseudo spectral approximation solutions for small amplitude oscillations.

Applications of DNP-NMR for the measurement of heteronuclear T1 relaxation times

Measurement of heteronuclear spin-lattice relaxation times is hampered by both low natural abundance and low detection sensitivity. Combined with typically long relaxation times, this results in extended acquisition times which often renders the experiment impractical. Recently a variant of dynamic nuclear polarisation has been demonstrated in which enhanced nuclear spin polarisation, generated in the cryo-solid state, is transferred to the liquid state for detection. Combining this approach with small flip angle pulse trains, similar to the FLASH-T(1) imaging sequence, allows the rapid determination of spin-lattice relaxation times. In this paper we explore this method and its application to the measurement of T(1) for both carbon-13 and nitrogen-15 at natural abundance. The effects of RF inhomogeneity and the influence of proton decoupling in the context of this experiment are also investigated.