Deformation of Ferrofluid Marbles in the Presence of a Permanent Magnet

Abstract

This paper investigates the deformation of ferrofluid marbles in the presence of a permanent magnet. Ferrofluid marbles are formed using a water-based ferrofluid and 1 μm hydrophobic polytetrafluoride particles. A marble placed on a Teflon coated glass plate deforms under gravity. In the presence of a permanent magnet, the marble is further deformed with a larger contact area. The geometric parameters are normalized by the radius of an undistorted spherical marble. The paper first discusses a scaling relationship between the dimensionless radius of the contact area as well as the dimensionless height and the magnetic Bond number. The dimensionless contact radius is proportional to the fourth root of the magnetic bond number. The dimensionless height scales with the inverse square root of the magnetic Bond number. In the case of a moving marble dragged by a permanent magnet, the deformation is evaluated as the difference between advancing and receding curvatures of the top view. The dimensionless height and the contact diameter of the marble do not significantly depend on the speed or the capillary number. The scaling analysis and experimental data show that the deformation is proportional to the capillary number.