Scaling in complex systems: a link between the dynamics of networks and growing interfaces.

We consider growing interfaces as dynamical networks whose nodes are the discrete points of the interface and the edges the physical interactions among them. We map the points of the interface formed at each time into a graph by means of a visibility algorithm. As the corresponding interfaces grow, their visibility graphs change over time. We show that the visibility graphs are all scale free for each time. We use the variance of the node degrees as a measure of the dynamical properties of these graphs. This magnitude reveals an unexpected scaling behaviour of these graphs in both the number of nodes and time. This enables to define three robust exponents that characterize any type of dynamics with more detail than the classical scaling analysis applied directly to the physical interfaces. To check the feasibility of this approach we study and classify six different dynamical processes and estimate their critical exponents. We conclude that the dynamics of physical systems far from equilibrium can be determined by its corresponding visibility network. Indeed, this methodology is able to discern among dynamical processes that hitherto have been classified in the same universality class according to the scaling analysis of their interfaces.

Using iron-loaded sepiolite obtained by adsorption as a catalyst in the electro-Fenton oxidation of Reactive Black 5.

This study explores the possibility of using iron-loaded sepiolite, obtained by recovering iron from polluted water, as a catalyst in the electro-Fenton oxidation of organic pollutants in textile effluents. The removal of iron ions from aqueous solution by adsorption on sepiolite was studied in batch tests at iron concentrations between 100 and 1,000 ppm. Electro-Fenton experiments were carried out in an electrochemical cell with a working volume of 0.15 L, an air flow of 1 L/min, and 3 g of iron-loaded sepiolite. An electric field was applied using a boron-doped diamond anode and a graphite sheet cathode connected to a direct current power supply with a constant potential drop. Reactive Black 5 (100 mg/L) was selected as the model dye. The adsorption isotherms proved the ability of the used adsorbent. The removal of the iron ion by adsorption on sepiolite was in the range of 80-100 % for the studied concentration range. The Langmuir and Freundlich isotherms were found to be applicable in terms of the relatively high regression values. Iron-loaded sepiolite could be used as an effective heterogeneous catalyst for the degradation of organic dyes in the electro-Fenton process. Successive batch processes were performed at optimal working conditions (5 V and pH 2). The results indicate the suitability of the proposed combined process, adsorption to iron remediation followed by the application of the obtained iron-loaded sepiolite to the electro-Fenton technique, to oxidize polluted effluents.

Optimisation of decolourisation and degradation of Reactive Black 5 dye under electro-Fenton process using Fe alginate gel beads.

The aim of this work was to improve the ability of the electro-Fenton process using Fe alginate gel beads for the remediation of wastewater contaminated with synthetic dyes and using a model diazo dye such as Reactive Black 5 (RB5). Batch experiments were conducted to study the effects of main parameters, such as voltage, pH and iron concentration. Dye decolourisation, reduction of chemical oxygen demand (COD) and energy consumption were studied. Central composite face-centred experimental design matrix and response surface methodology were applied to design the experiments and to evaluate the interactive effects of the three studied parameters. A total of 20 experimental runs were set, and the kinetic data were analysed using first-order and second-order models. In all cases, the experimental data were fitted to the empirical second-order model with a suitable degree for the maximum decolourisation of RB5, COD reduction and energy consumption by electro-Fenton-Fe alginate gel beads treatment. Working with the obtained empirical model, the optimisation of the process was carried out. The second-order polynomial regression model suggests that the optimum conditions for attaining maximum decolourisation, COD reduction and energy consumption are voltage, 5.69 V; pH 2.24 and iron concentration, 2.68 mM. Moreover, the fixation of iron on alginate beads suggests that the degradation process can be developed under this electro-Fenton process in repeated batches and in a continuous mode.