Structure induced in suspensions by a magnetic field

Magnetorheological as well as electrorheological fluids exhibit a phase separation when a field is applied to the suspension. We observe the formation of aggregates elongated in the direction of the field and whose length L is fixed by the thickness of the cell. The average radius b of these aggregates has been measured for L between 100 µm and 700 µm for two volume fractions F=5%F=5% and F=10%F=10%. In this range we find for a magnetorheological fluid composed of micronic superparamagnetic particles an experimental law b ?a(L/a)n with an exponent n ˜0.67 ±0.04. We can recover this experimental law and predict the characteristic size of the aggregates from the knowledge of the magnetic permeability of the particles with a model based on the hypothesis of close packed aggregates. The agreement with the experiments is good especially at the lower volume fraction. Actually on a larger range of thicknesses our model predicts a continuous increase of this exponent towards a final value of one for large values of L/a.