Singularly perturbed dynamics of the tippedisk

The tippedisk is a mathematical-mechanical archetype for a peculiar friction-induced instability phenomenon leading to the inversion of an unbalanced spinning disc, being reminiscent of (but different from) the well-known inversion of the tippetop. A reduced model of the tippedisk, in the form of a three-dimensional ordinary differential equation, has been derived recently, followed by a preliminary local stability analysis of stationary spinning solutions. In the current paper, a global analysis of the reduced system is pursued using the framework of singular perturbation theory. It is shown how the presence of friction leads to slow–fast dynamics and the creation of a two-dimensional slow manifold. Furthermore, it is revealed that a bifurcation scenario involving a homoclinic bifurcation and a Hopf bifurcation leads to an explanation of the inversion phenomenon. In particular, a closed-form condition for the critical spinning speed for the inversion phenomenon is derived. Hence, the tippedisk forms an excellent mathematical-mechanical problem for the analysis of global bifurcations in singularly perturbed dynamics.

Textile Wastewater Treatment in a Spinning Disc Reactor: Improved Performances—Experimental, Modeling and SVM Optimization

The paper presents an experimental study regarding the treatment of a real textile wastewater using the spinning disc (SD) technology, either individually or associated with an advanced Fenton oxidation step. The SD efficiency was investigated by studying the color, suspended solids, or turbidity removals, at distinctive feeding flowrates (10–30 L/h) and disc rotating speeds (100–1500 rpm). The data revealed increasing removal trends and allowed to establish the highest removal values. Based on obtained experimental results, the wastewater treatment efficiency by SD technology was reasonably good and thus, the WW indicators can be improved within relatively short periods of time. Additionally, based on supervised learning algorithms, the study includes treatment modeling for turbidity and color removal, followed by turbidity removal optimization relying on the best learned models. Satisfactory results obtained with the modeling and optimization procedures provide useful predictions for the approached treatment processes. Furthermore, within this study, a Fenton oxidation process was applied to SD technology to minimize the color and solids content. The influence of pH, hydrogen peroxide and ferrous ions concentrations was also investigated in order to establish the highest removal efficiencies. Overall, the SD technology applied in textile effluents treatment proved to be an appropriate and efficient alternative to classical mechanical step applied within the primary treatment step and, when associated with an advanced oxidative process in the secondary step, rendered good improvement, namely of 62.84% and 69.46% for color and respectively, suspended solids removal.

Numerical Approximation of Microorganisms Hybrid Nanofluid Flow Induced by a Wavy Fluctuating Spinning Disc

The analysis explored a numerical simulation of microorganisms, carbon nanotubes (CNTs) and ferric oxide water-based hybrid nanofluid flow induced by a wavy fluctuating spinning disc with energy propagation. In the presence of CNTs and magnetic nanoparticulates, the nanofluid is synthesized. The exceptional tensile strength, flexibility, and electrical and thermal conductivity of carbon nanotubes and iron nanoparticles have been extensively reported. The motive of the proposed analysis is to optimize thermal energy conveyance efficiency for a spectrum of industrial and biomedical applications. The phenomena have been expressed as a system of partial differential equations (PDEs) which contain the momentum, energy, concentration, and motile microorganism equations. The modeled equations have been diminished to the dimensionless system of nonlinear ODEs through a similarity framework. The Matlab built-in package boundary value solver has been utilized to solve the obtained system of ODEs. The findings are compared to the PCM technique for validity purposes. The results are illustrated graphically and discussed. The layout of a rotating disc has a positive effect on energy transition and velocity profile. The irregular rotating surface increases energy progression up to 15% relative to a smooth surface. The accumulation of nanocomposites (CNTs and magnetic nanoparticles) significantly enhanced the thermal capabilities of the liquid medium. When operating with a low distribution, it is more impactful.