Free-Surface Vibrations of a Magnetic Liquid

A theory of magnetic fluid sloshing in a solenoidal magnetic field is developed herein. It shows that (a) the free-surface waves on a magnetic fluid are dynamically similar to the waves on an ordinary liquid in a reduced gravity field, and (b) the apparent reduction in gravity depends on the strength of the applied magnetic field. But, a deviation from true low-gravity behavior occurs whenever the Bond number (ratio of effective gravitational force to surface tension force) is much smaller than 1.0. The deviation is caused by a magnetic interaction that induces a jump in pressure across the free surface. To verify the conclusions of the theory and to evaluate the usefulness of magnetic sloshing as a low-gravity sloshing simulation, an exploratory series of tests was conducted using a magnetic-colloid liquid and a large solenoidal electromagnet. Measured slosh natural frequencies agreed well with theory, but the measured slosh damping was larger than predicted by existing correlation equations.