2-DIMENSIONAL PATTERNS OF MAGNETIC PARTICLES AT AIR-WATER OR GLASS-WATER INTERFACES INDUCED BY AN EXTERNAL MAGNETIC-FIELD - THEORY AND SIMULATION OF THE FORMATION PROCESS

We describe theoretically the formation process of two-dimensional pat terns of magnetic particles at an interface under the action of an ext ernal magnetic field. First, we developed a theoretical model for the forces acting on the particles, which are the magnetic attraction towa rd the axis of symmetry, magnetic repulsion due to the induced dipoles , electrostatic repulsion due to the surface net charge and electric d ipoles of the particles, and lateral capillary forces in the case of a liquid interface. Then, we developed a Brownian dynamics algorithm an d simulated the pattern formation. Our simulations reproduced the hexa gonally aligned two-dimensional patterns, which were experimentally ob served and reported in the complementary experimental work, that is, t hey reproduced the distance between the particles and the time of patt ern formation. Irregular patterns such as square and pentagonal ones t hat were experimentally observed were also simulated, We calculated th at when the distance between particles is larger than 20 mu m (i.e., i n case or a weak magnetic field), the magnetic force is sufficient to explain the pattern formation. But, when the distance is smaller than 20 mu m, the electrostatic repulsive force may play an essential role in determining the interparticle distance. Our calculations showed tha t the lateral capillary forces and the electrostatic dipolar repulsive forces were negligible for the pattern formation process. Finally, ou r method for simulating the pattern formation may be applied for under standing these processes and predicting the patterns that might be for med at liquid or solid interfaces.