Forces acting on a permanent magnet placed in a rectangular cavity with a magnetic fluid

A boundary value problem of forces acting on a permanent magnet placed in a rectangular cavity with concentrated magnetic fluid is solved by the control-volume method. The solutions available in the current literature have been obtained for dilute solutions, in which the inter-particle interactions (steric, magnetodipole and hydrodynamic) and magnetic fields generated by the magnetic fluid are inessential. Moreover, these studies neglect the magnetophoresis of colloidal particles and diffusion processes, which strongly restrict the applicability range of the obtained results. The inter-particle interactions can significantly increase the intensity of the fluid magnetization, and disregard of the magnetophoresis and particle diffusion implies that the known solutions are valid only over a limited time interval, which is short compared to the time of the onset of equilibrium particle distribution in the cavity. The main objective of this study is to estimate quantitatively the contributions of all these factors. The selected problem geometry corresponds to a simple uniaxial magnetofluidic accelerometer. The solution is searched for a two-dimensional problem using the dynamic equation of mass transfer recently introduced in J. Chem. Phys., 2011, vol. 134, 184508. The calculations have been performed to evaluate the magnetic field generated by the fluid and the field of colloidal particle concentration. The plots of the resultant force acting on the magnet versus its displacement from the equilibrium, the energy of magnetodipole interactions and volume-averaged particle concentration are presented. The basic finding of this work is the establishment of a very strong dependence of the computation results on the selection of an adequate theoretical model. In particular, it has been shown that disregard of inter-particle interactions in the fluid can lead to a computational error exceeding hundred percents.