Chaos-driven detection of methylene blue in wastewater using fractional calculus and laser systems

Abstract Methylene blue (MB) concentrations in residual water were detected using fractional calculus, the Rössler chaotic attractor and laser systems. A Nd:YVO4 nanosecond pulsed laser at 532 nm, with pulse energies ranging from 2 µJ to 7 µJ, was applied to irradiate different water samples containing MB concentrations from 20 µl to 100 µl. Fractional calculus was employed with the purpose of modeling the temperature distribution in the samples, with the Caputo fractional derivative describing photothermal effects induced by laser irradiation. Different MB concentrations were detected by using the Rössler chaotic attractor, it monitored variation on concentrations, associating attractor shapes with MB concentrations. Lower concentrations showed a weaker attractor response, whereas higher concentrations manifest stronger attractor shapes in magnitude. Raman spectroscopy confirmed the detection of MB in residual water from the Requena dam, located in Tepeji del Río de Ocampo, Hidalgo, Mexico. The application of fractional calculus improved the prediction of heat distribution in the samples, by incorporating numerical simulation. The results suggest that this approach is suitable for real-time monitoring, as it associates MB concentrations with distinct chaotic attractor shapes. This technique shows promise for the detection of other contaminants as well. Future research should focus on refining this method and expanding its application to develop innovative monitoring solutions.