Cluster morphology in magneto-rheological fluids: fractal dimensions during anisotropic aggregation and disaggregation processes

Details Cluster morphology in magneto-rheological fluids: fractal dimensions during anisotropic aggregation and disaggregation processes Cluster morphology in magneto-rheological fluids: fractal dimensions during anisotropic aggregation and disaggregation processes

2007-01-11

arxiv.org/abs/cond-mat/0701239v1

Physics

Condensed Matter

Materials Science

Submitted to Physical Review E

Scientific paper

We study the evolution of the fractal dimensions during anisotropic aggregation and disaggregation (i.e., when the applied field is switched off) processes, in a magneto-rheological fluid composed by super-paramagnetic particles with a diameter of 1 micron, suspended in water under the action of a constant uniaxial magnetic field. We use video-microscopy and image analysis to retrieve the form of the aggregates and calculate the following fractal dimensions: one-dimensional $D_1$, two-dimensional $D_2$, perimeter-based fractal dimension $D_p$ and two-dimensional capacity dimension or box-counting dimension $D_B(2D)$. We apply this methodology for different values of the magnetic field amplitude and particle concentration. During aggregation, we can calculate an average value $\left\sim 1.84$ for the rod-like chains and we find a linear dependence of the capacity dimension with the ratio of two characteristic length scales. By means of a quantification of the roughness, we interpret $D_p$ as a measure of the clusters border roughness, while the capacity dimension represents how the chains fill the space. We also show how the quadratic deviation of the cluster contour height follows power-law behaviours in the initial stages of aggregation and disaggregation. We compare our results on projected fractal dimensions with previous theoretical and experimental studies about aggregation of magnetic particles. As a result, we check some recently proposed theoretical relation between $D_p$ and the three-dimensional fractal dimension $D_f$.

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