Fractal aggregates evolution of methyl red in liquid crystal

Abstract

The spontaneous formation of dendritic aggregates is observed in a two-dimensional confined layered system consisting of a film composed of liquid crystal, dye and solvent cast above a polymer substrate. The observed aggregates are promoted by phase separation processes induced by dye diffusion and solvent evaporation. The growth properties of the aggregates are studied through the temporal evolution of their topological properties (surface, perimeter, fractal dimension). The fractal dimension of the completely formed structures, when they are coexistent with different types of structures, is consistent with theoretical and experimental values obtained for Diffusion-Limited Aggregates. Under different experimental conditions (temperature and local dye concentration) the structure forms without interactions with other kinds of structures, and its equilibrium fractal dimension is smaller. The fractal dimension is thus not a universal property of the observed structures, but rather depends on the experimental conditions.

Nanoparticle Aggregation and Fractal Growth in Fluid Smectic Membranes

“…Few measurements have, however, been performed in 2D. DLA has been observed in systems of polystyrene latex particles confined to two dimensions at an airwater interface [15,16] a dye molecule that is weakly soluble in liquid crystal, was observed to precipitate out of a thin film over the course of several hours [18], forming aggregates with a fractal dimension of 1.61. Liquid crystals, well known for their electrooptic properties and widespread application in displays, exhibit phases with varying degrees of orientational and positional order, making them attractive tools for controlling self-assembly at the nanoscale [19,20].…”

Multifractal Analysis of a Wake for a Single Wind Turbine

“…The similar methodology in the velocity field carried out in the centerline and in the section on the end of the blade has shown small differences in the maximum fractal spectra. [29,30]. The typical shape of an equilibrium turbulence spectra is parabolic [28].…”

Simulation of turbulence mixing in the atmosphere boundary layer and analysis of fractal dimension

“…If we want to estimate diffusion in a fractal environment, we may substitute the first order structure function scaling exponent ( =1) as (34):…”

“…The ImaCalc program was used to study the fractal parameter, structure function for different geophysical objects [33][34][35]. We calculated the The same approach was used in the single wind turbine wake study [36].…”