DYNAMICS OF COOPERATIVE REACTIONS BASED ON CHEMICAL KINETICS WITH REACTION SPEED: A COMPARATIVE ANALYSIS WITH SINGULAR AND NONSINGULAR KERNELS

Chemical processes are constantly occurring in all existing creatures, and most of them contain proteins that are enzymes and perform as catalysts. To understand the dynamics of such phenomena, mathematical modeling is a powerful tool of study. This study is carried out for the dynamics of cooperative phenomenon based on chemical kinetics. Observations indicate that fractional models are more practical to describe complex systems’ dynamics, such as recording the memory in partial and full domains of particular operations. Therefore, this model is modeled in terms of classical-order-coupled nonlinear ODEs. Then the classical model is generalized with two different fractional operators of Caputo and Atangana–Baleanu in a Caputo sense. Some fundamental theoretical analysis for both the fractional models is also made. Reaction speeds for the extreme cases of positive/negative and no cooperation are also calculated. The graphical solutions are achieved via numerical schemes, and the simulations for both the models are carried out through the computational software MATLAB. It is observed that both the fractional models of Caputo and Atangana–Baleanu give identical results for integer order, i.e. [Formula: see text]. By decreasing the fractional parameters, the concentration profile of the substrate [Formula: see text] takes more time to vanish. Moreover, binding of first substrate increases the reaction rate at another binding site in the case of extreme positive cooperation, while the opposite effect is noticed for the case of negative cooperativity. Furthermore, the effects of other parameters on concentration profiles of different species are shown graphically and discussed physically.

An approach to the assessment of dimethyl carbonate and ethanol effect as gasoline oxygenating agents under engine conditions via a Computational Fluid Dynamics model

An ASTM-CFR engine was modeled through Computational Fluid Dynamics (CFD) coupled with chemical kinetics to evaluate the effect on combustion characteristics and engine emissions of dimethyl carbonate (DMC) and ethanol as gasoline components, the latter as reference oxygenating agent. Validation against experimental in-cylinder pressure data indicated adequate reproduction of these fuels combustion, all blends showing higher and earlier pressure peaks than neat gasoline (ca. 0.2 MPa and 2 CAD). Simulated temperatures were close for all fuels, though slightly advanced for the oxygenated blends (ca. 2 CAD). Similar behavior of the oxygenates was predicted regarding HC, CO and soot emissions: ca. 90% reduction in HC, CO, and soot emissions were observed, but ethanol displayed up to 3.5% CO2 reduction and 17% NOx increase, while DMC showed up to 7% decrease in CO2 and 6% increase in NOx. Considering the advantage of using chemical kinetics for combustion calculations in the CFD model, i.e., quantification of any species present in the reaction mechanism, including those difficult to observe/measure experimentally, concentrations of non-regulated emissions (e.g., formaldehyde) were studied. In particular, a minor increase in formaldehyde emissions was found with both oxygenated fuels. Albeit a first approach to assessing oxygenating compounds effects on gasoline combustion and emissions under engine conditions through a CFD + detailed chemistry model, the results underline the potential of DMC as gasoline oxygenating agent, and are a starting point for studying non-measured/non-regulated species and parametric engine analysis in future models.