Effective and Practical Methods to Calculate the Second-Order Buoyancy in Magnetic Fluid Acceleration Sensor

This paper concerns the nature of the peculiar second-order buoyancy experienced by a magnet in magnetic fluid acceleration sensor. The equilibrium differential equation of magnetic fluid under the action of magnetic field and gravity field is established and the expression for calculating the second-order buoyancy is derived. Three practical and effective methods to calculate the second-order buoyancy called surface integral method, magnetic force method, and equivalent magnetic force method are proposed. Besides, the second-order buoyancy is calculated by the three methods mentioned above and measured experimentally. The calculation results are in very good agreement with the experimental results, for all the three methods, the calculation error is less than 7% compared with the numerical range of second-order buoyancy. Both calculation and experimental results show that the second-order buoyancy increases rapidly with the decrease of the axial distance between the bottom of the magnet and the container, and the trend can be fitted well by an exponential function.