Scaling in the aggregation dynamics of a magnetorheological fluid

We present experimental results on the aggregation dynamics of a magnetorheological fluid, namely, an aqueous suspension of micrometer-sized superparamagnetic particles, under the action of a constant uniaxial magnetic field using video microscopy and image analysis. We find a scaling behavior in several variables describing the aggregation kinetics. The data agree well with the Family-Vicsek scaling ansatz for diffusion-limited cluster-cluster aggregation. The kinetic exponents z and z(') are obtained from the temporal evolution of the mean cluster size S(t) and the number of clusters N(t), respectively. The crossover exponent Delta is calculated in two ways: first, from the initial slope of the scaling function; second, from the evolution of the nonaggregated particles, n(1)(t). We report on results of Brownian two-dimensional dynamics simulations and compare the results with the experiments. Finally, we discuss the differences obtained between the kinetic exponents in terms of the variation in the crossover exponent and relate this behavior to the physical interpretation of the crossover exponent.