Structural transformations in ferrofluids.
We present results of theoretical study of internal structural transformations in magnetic liquids consisting of identical spherical magnetic particles suspended in a carrier liquid. As the results show, when the dimensionless characteristic energy of magnetic interaction epsilon between particles is less than a certain critical value epsilon('), the system of particles is in spatially homogeneous state with linear chainlike aggregates. When epsilon exceeds epsilon('), bulk droplike aggregates, consisting of large number of particles, can occur in this system. The critical parameter epsilon(') decreases when external magnetic field increases. This means that, in accordance with all known experiments, magnetic field stimulates the phase separation. Our estimates of epsilon(') are in agreement with magnitudes of the parameter of interaction between particles in typical ferrofluids where these phase transitions have been observed experimentally. Analysis shows that the bulk dense structures can occur provided that the total number N of particles in the system exceeds a threshold value N', which is about a thousand by order of magnitude. We think that this result explains why the bulk dense clusters, observed in many real experiments, have never been observed in three-dimensional computer simulations of ferrofluids-the total number of particles in these simulations was too small to provide the formation of bulk structures.