FRACTAL RESERVOIRS

Since the 1980s, when the study of fractal structures quickly began to move forward, there are many unexplored aspects about how a fractal object interacts with certain types of environments. In some of these problems extensively studied in the area of out-of-equilibrium growth models, there is an interaction of a fractal surface with external fields, especially a diffusive field [1, 2, 3]. In another area, the study of the interaction of molecules with enzymes, proteins, or biological tissues is modeled by fractals, in catalytic processes or adsorption, an area known as chemistry between 2 and 3 dimensions [4]. More recently, Balankin and coworkers studied the kinetics of the water escape from aluminum crumpled surfaces [5]. This process occurs until the mass of water absorbed by the surface reaches the threshold of the water retained in the structure by surface tension forces. In the present work, we are interested to study experimentally the process of absorption and retention of water by crumpled wire balls, a much more effective system for the retention of water than the aluminum wrinkled surfaces. These balls were made with wire with 1.5 mm in diameter and had radii varying from 0.40 to 5.15 cm. Such structures are obtained in approximately spherical shapes by the use of nearly isotropic external compressing forces and have a high porosity and behave as fractals. The experiment consists of (1) generation and characterization of the balls, (2) immersion of the samples in water by following a fixed protocol, (3) evaluation of the retained water as a function of the size of the balls, the volume of pores, and the surface roughness, and (4) comparison of the experimental results with a simple mean-field model.

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[3] M. A. F. Gomes, G. L. Vasconcelos, G. C. Nascimento, J. Phys. A: Math. Gen. \textbf{20}, L1167 (1987).

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[5] A. S. Balankin et alli, Phys. Rev. E \textbf{83}, 036310 (2011).