Experimental investigation of creep and the recovery behaviours of magnetorheological fluids

Abstract

This paper presents an analytical study on the transient electrodynamic and fluid flow phenomena in a magnetically-levitated liquid sphere. Using the method of separation of variables, analytical solutions are derived for the transient electromagnetic field inside and outside the sphere in the form of the magnetic vector potential, and the fluid flow field in terms of the stream function, respectively. Both asymptotic and detailed analyses are described. It is found that the decay of a levitation system is characterized by three quite different time scales: one for the electromagnetic field, one for the fluid flow field, and one for the thermal field. The electromagnetic field decays several orders of magnitude faster than either the fluid flow field or the temperature field, and therefore its effect can be well ignored when the flow and/or thermal fields are considered. The ratios of these time scales may be related to the nondimensional system numbers that characterize the system. Detailed calculations show that when started from a symmetric velocity field, the decay results in a reduction of the velocity level but the flow pattern remains unchanged, whereas the evolution from an asymmetric flow field involves both a diminution in the velocity level and a change in the flow pattern. The two decaying processes are also characterized by different time scales, with the one for the asymmetric case being larger. Application of the analyses to design and control the experiments of undercooling and/or free surface oscillations under microgravity is also discussed. It is found that an undercooling of a desired degree may be obtained free from the internal flow influence if an appropriate starting temperature is chosen for the experiment. It is also possible to carry out the experiments of free surface oscillation without the interference from the internal flow; however, careful control is needed to maintain the liquid at a relatively constant temperature.