Self-Organized Structures in Magnetic Liquids

Amazing patterns occur when a droplet of an oily suspension of finely divided magnetic particles, a magnetic liquid is confined within a Hele-Shaw cell and is subject to a magnetic field perpendicular to the surface of the cell. The pattern is macroscopic and the typical linear dimension of the pattern is about six orders of magnitude bigger than the particles in the magnetic liquid.

In a series of experiments we have investigated the effect on the pattern of varying the height of the cell between 0.5 mm and 2 mm The height of the cell was shown to drastically influence both the characteristic sizes and the nature of the pattern The pattern changes character from being chaotic to become labyrinthine and finally droplet-like as the height is increased.

The effect of varying the amount of magnetic liquid in the Hele-Shaw cell while maintaining the total volume of the cell was also studied In this case, the typical pattern consists mainly of columns; we have investigated how the size distribution of the columns, viewed from above, change as the fraction of ferrofluid in the cell is increased When increasing the fraction of ferrofluid, the number of columns remains approximately the same, but the bigger ones grow on the expense of the smaller.

From the center of mass of the columns a 2D-Veronoi pattern is constructed in the plane of the cell, and the edge statistics are found as a function of the fraction of magnetic liquid in the Hele-Shaw cell. The average number of edges in the Veronoi cells is always between 5 and 6, and this number is approaching 6 as the fraction of ferrofluid is increased.

The edge statistics give information about the spatial arrangement of the droplets. Finally, experiments have been carried out in which we focused on how the pattern depends on the applied magnetic field.