Representation of Kinetics Models in Batch Flotation as Distributed First-Order Reactions

Four kinetic models are studied as first-order reactions with flotation rate distribution f(k): (i) deterministic nth-order reaction, (ii) second-order with Rectangular f(k), (iii) Rosin–Rammler, and (iv) Fractional kinetics. These models are studied because they are considered as alternatives to the first-order reactions. The first-order representation leads to the same recovery R(t) as in the original domain. The first-order R∞-f(k) are obtained by inspection of the R(t) formulae or by inverse Laplace Transforms. The reaction orders of model (i) are related to the shape parameters of first-order Gamma f(k)s. Higher reaction orders imply rate concentrations at k ≈ 0 in the first-order domain. Model (ii) shows reverse J-shaped first-order f(k)s. Model (iii) under stretched exponentials presents mounded first-order f(k)s, whereas model (iv) with derivative orders lower than 1 shows from reverse J-shaped to mounded first-order f(k)s. Kinetic descriptions that lead to the same R(t) cannot be differentiated between each other. However, the first-order f(k)s can be studied in a comparable domain.

Analysis of Memreactance with Fractional Kinetics

In this work, the analysis of the memreactance, i.e., meminductor and memcapacitor, with fractional-order kinetics has been proposed. The meminductances, memcapacitances, and related parameters due to both DC and periodic input waveforms have been derived. The behavioral analysis has been thoroughly performed with the aid of numerical simulation. The effects of fractional-order kinetics have been explored where both linear and nonlinear dopant drift scenarios have been considered. Moreover, the emulation of memreactance with fractional-order kinetics by using the memristor and the effect of the fractional-order kinetics on the memreactance-based circuits have also been mentioned along with the extension of our results to the fractional-order memreactance.

Fractional kinetics of photocatalytic degradation

In this paper, photocatalytic degradation processes of different materials are fitted to the first-order kinetic model, second-order kinetic model and fractional first-order kinetic model. Deterministic coefficients are calculated for the evaluation of the validity of these models. The fitting results show clearly that the degradation process can fit the fractional first-order kinetic model in a very good manner. In this way, two material parameters can be well defined. One is the degradation time, which can be used to describe the photocatalytic degradation process quantitatively. Another is the order of the derivative, which could be related to the material’s microstructure.