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Multiscale Modeling of Heterophase Polymerization
Published in Hugo Hernandez, Klaus Tauer, Heterophase Polymerization, 2021
The use of kinetic expressions is an example of this bottom-up model order reduction. The rate of a chemical reaction depends on factors such as molecular kinetic energy, molecular orientation, and electronic configuration [248], relevant at the atomistic and molecular scales. However, at the macroscopic scale, the rate of reaction is expressed for a component Ci as ri=vik(T)∏jCjaj where Vi is a stoichiometric coefficient, k(T) is a temperature-dependent rate coefficient, [Cj] denotes the concentration of all components involved in the reaction, and aj are empirical coefficients. Equation 3.69 incorporates all dynamical effects involved at the lower scale, into a macroscopic term.
Reaction Kinetics in Food Systems
Published in Dennis R. Heldman, Daryl B. Lund, Cristina M. Sabliov, Handbook of Food Engineering, 2018
Ricardo Villota, James G. Hawkes
Chemical kinetics encompasses the study of the rates at which chemical reactions proceed. The area of kinetics in food systems has received a great deal of attention in past years, primarily due to efforts to optimize or at least maximize the quality of food products during processing and storage. Moreover, a good understanding of reaction kinetics can provide a better idea of how to formulate or fortify food products in order to preserve the existing nutrients or components in a food system or, on the other hand, minimize the appearance of undesirable breakdown products. Unfortunately, limited kinetic information is available at present for food systems or ingredients that would facilitate the development of food products with improved stability or the optimization of processing conditions. A major consideration, however, is that indirectly some of the information available may be used to predict kinetic trends and thus establish major guidelines in formulation, storage, and process conditions. Thus, it is within the scope of this chapter to (a) present a general discussion on general kinetics, outlining some of the fundamental principles, (b) provide information on a variety of food systems, indicating their reactivity and reported kinetic behavior, and (c) provide an understanding of current changes resulting from external influences, including updated analytical methodologies and technological advances. It is considered that a better understanding of kinetics in food systems will facilitate the development of a more complete and sound database.
Reaction kinetics
Published in A. W. Jayawardena, Environmental and Hydrological Systems Modelling, 2013
An important concept in reaction kinetics is the time required to halve the concentration from an initial state, which is referred to as the half-life. In each of the above three cases, the half-lives (t1/2) are c02k,ln(2)k, and 1kc0. It can be seen that the second half-life is twice as long as the first. Half-lives for some typical radioactive elements are as follows: 238uranium = 4.5 billion years; 234uranium = 240,000 years; 14carbon = 5730 years; 220lead = 22 years; 222radon = 3.8 days; 214polonium = 160 ms.
Photodegradation and Box-Behnken design optimization for methomyl using Fenton process based on synthesized CuO nanocrystals via facile wet chemical technique
Published in Chemical Engineering Communications, 2021
Maha A. Tony, Patrick J. Purcell, Shehab A. Mansour
The reaction kinetics most appropriate to methomyl removal were examined by plotting Equations (16)–(18) for the experimental data. The kinetic parameters, as well as the regression coefficients (R2), for each reaction order are shown in Table 4. Examination of Table 4 shows that the reaction is best modeled by a second-order reaction. Additionally, the second-order reaction constant, k2, is significantly affected by reaction temperature, decreasing with increasing temperature, from 0.045 to 0.003 L mg−1 min−1 over the temperature range investigated. These results suggest that, at lower temperature, the concentration of species, which are the product of the reaction between the Cu2+ and H2O2, increases that means the reaction rate (Buxton et al. 1988). Another kinetics parameter of importance is half-life of a reaction, t1/2, which is defined as the time required for the reactant concentration to decrease to half of its initial concentration, Co (Najjar et al. 2001). Examination of Table 4 shows that the calculated t1/2 is a function of reaction temperature; t1/2 increases with increasing the temperature. In summary, it has been found that methomyl removal by copper nanoparticles in a photo-Fenton-like reagent follows a second-order reaction model for the temperature range investigated. A second-order kinetic model for the treatment of methomyl accords with that obtained by Samet et al. (2012) for the treatment of insecticide contaminated wastewater, as well as El Haddad et al. (2014) and Youssef et al. (2016) for the treatment of dyed wastewater using Fenton’s reagent. In contrast, Bounab et al. (2015) found that a first-order kinetic model better represented the treatment of m-cresol using an iron-loaded activated carbon, electro-Fenton treatment process.