Fractal patterns, cluster dynamics, and elastic properties of magnetorheological suspensions

Abstract

We study pattern formation and the aggregation processes in magnetorheological suspensions in the presence of a static magnetic field, and some of their associated physical properties. In particular, we analyze the elastic modes as a function of the intensity of the applied field and for several particle concentrations. We observe that the clusters formed in these systems have multifractal characteristics, which are the result of three well defined stages of the aggregation process. In these stages three generations of clusters are produced sequentially. The structure of the suspension can be well characterized by its mass fractal dimensions and the mass radial distribution. The size distribution of the second-generation clusters written in terms of their mass fractal dimension allows us to calculate the sound speed of the longitudinal modes in the large wavelength regime. This multifractal analysis applied to several kinds of aggregates reveals that the occurrence of at least three stages of aggregation is a common feature to several physical aggregation processes.

Multi-fractal imaging and structural investigation of silica hydrogels and aerogels

“…By SAXS experiments, we can analyze the first-generation clusters [21], by AFM the secondgeneration ones, and finally SEM reveals a third stage of these aggregation patterns. The fiber-like first generation clusters aggregate to form spherical secondgeneration ones, and in the third-aggregation process, second-generation clusters, at a large scale, aggregate and rearrange to form more complex structures.…”

Hierarchical Structures in Granular Matter

“…Blair and Kudrolli [5] found that for small values of parameter Γ, T g depends linearly with Γ. The concentration, φ, is defined as the ratio between the number of paramagnetic particles n 1 and the total number of the particles n 2 .…”

“…In this analysis, the mass fractal dimension and the radial distribution function of the cluster structure were measured on digital pictures. The method used in this paper to measure the mass fractal dimension is a variation of the standard box counting method, adapted to explore radial and angular correlations in systems affected by potentials with radial or axial symmetries [5,6]. In this method, the mass fractal dimension is defined by the power law: M ∝ r D where M is the average mass contained in a circle of gyration radius r. This mass is measured in an ensemble to properly extract the information of the correlations.…”

“…In those dispersions there occurs some well defined sequential stages in the aggregation processes that generate multifractal clusters. In these stages the viscosity of the liquid matrix has also a sequentially increasing influence [5,6]. This paper analyzes experimentally the effects of the granular temperature on the characteristics of the structures generated by aggregation of magnetic particles due to the application of an external static magnetic field.…”

Mass-distribution scaling and pattern formation in magneto-rheological suspensions

“…We have studied pattern formation in MRS formed by micrometric iron oxide particles dispersed in silicone oil, in the presence of an external field. We have found that the resulting structure exhibits three aggregation stages, which can be well characterized by the behaviour of their measured mass fractal dimension [2]. In this work, we calculate and discuss the mass radial distribution, this function shows another aspect of the different regimes of mass scaling, and could provide additional elements to describe the hierarchical structure of the MRS.…”