Magnetic colloid pattern formation at magnetic-field induced phase separation

Magnetic-field induced phase separation of the magnetic colloid in the Hele-Shaw cell is considered. The phase diagram of the magnetic colloid in dependence on the thickness of the Hele-Shaw cell and the deviation from the critical point is derived, which shows that in the transition to the ordered phase, the periodic system of stripes is continuous for magnetic Bond number greater than critical. Equations that describe the kinetics of the phase separation under the action of a magnetic field of different orientation with respect to the cell, among which it is possible to mention normal, tangential, and rotating in the plane normal to the boundaries of the cell, oblique and conical, are derived. By numerical simulation, different pattern formation phenomena are studied and the main points to be mentioned are the following: under the action of the normal field in dependence on the deviation from the critical point, labyrinthine or hexagonal patterns are formed; under the action of the tangential field a system of parallel stripes is formed; under the action of the magnetic field rotating in the plane normal to the boundaries of the Hele-Shaw cell a periodic system of the parallel stripes is formed. Different structure transformation processes are observed with change of the magnetic field orientation and its value: under the action of the normal magnetic field with the magnetic Bond number greater than the magnetic Bond number of the rotating field on the system of parallel stripes formed under the action of the rotating field, the development of chevrons is observed; the chevron pattern under the action of a magnetic field with a greater value of the magnetic Bond number undergoes secondary instability leading to the formation of hairpins. Under the action of the oblique field on the hexagonal pattern, the formation of a system of parallel stripes if the inclination angle of the field is large enough is observed. During this process of structure transformation, the formation of dislocations and their migration is observed.