Instabilities of concentration stripe patterns in ferrocolloids

Equations describing the kinetics of the phase separation in ferrocolloids in a Hele-Shaw cell under the action of a rotating magnetic field are proposed. Numerical simulation on the basis of a pseudospectral technique demonstrates that upon the action of a rotating field on a magnetic colloid which undergoes the phase separation a periodical system of stripes parallel to the plane of a rotating magnetic field stripes is created. The period of a structure found numerically satisfactorily corresponds to the one calculated on the basis of the energy minimum. Thus, the undulation instability leading to the formation of chevron structures takes place if the tangential component of a rotating magnetic field is eliminated, whereas the normal component is increased at the same time. If during the development of the undulation deformations of a concentration pattern the magnetic Bond number is large enough the secondary instabilities may occur leading to the fingering of stripes to bring about merging and break-up of stripes. It is shown that an increase in the magnetic Bond number leads to the onset of the instability at the boundaries between the regions with homogeneous orientation of stripes as well as to formation of the characteristic hairpin patterns.