Search results for "Rate equation"
showing 8 items of 38 documents
Guidelines for the assessment of the rate law of slurry photocatalytic reactions
2017
Abstract The assessment of the rate law of slurry photocatalytic reactions appears to be a hard task, mainly because in this type of reactions the average rate of reaction, which is experimentally observed in a real reactor, could be very different from the “true” (intrinsic) rate of reaction, which cannot be measured directly. In the present work, it is shown how a proper mathematical model allows the utilization of the differential and/or the integral methods of kinetic analysis. The mathematical model must take into account not only the momentum and the mass balances, but also the radiative transfer equation. However, the discrimination among different proposed kinetic laws remains diffi…
A reaction engineering approach to kinetic analysis of photocatalytic reactions in slurry systems
2016
Abstract The knowledge of the rate equation is fundamental for the assessment of the activity of the photocatalytic material and for the study, design and optimization of photocatalytic reactors. In the case of photocatalytic reactions, the local volumetric rate of photon absorption (LVRPA) affects the reaction rate and its inherently uneven distribution within a “slurry” reactor makes complex a correct kinetic analysis. In the present work it is shown which are the critical aspects of the kinetic analysis in slurry reactors and how to carry out photocatalytic experiments to minimize the misinterpretations of the experimental results. In particular, the influence of the type of illumination…
Heterogeneous kinetics: from solid–gas reaction to solid–liquid dissolution
2002
Abstract The extension of the formal kinetics of solid–gas reactions to solid–liquid dissolution is investigated theoretically. The work is based on modelling the dissolution of a solid in a closed system by a stoichiometrically simple chemical reaction A solid ⇄A liquid proceeding up to either an equilibrium state if the solid phase is initially in excess or exhaustion in the reverse situation. The initial amount of solid compared to the capacity of the liquid phase appears as a major factor of complexity. First, the rate equation is formulated in terms of the intensive variables without any assumption about the mechanism and the rate-limiting step. The resulting equations are compared to …
Impact of buffer gas quenching on the $^1S_0$ $\to$ $^1P_1$ ground-state atomic transition in nobelium
2017
International audience; Using the sensitive Radiation Detected Resonance Ionization Spectroscopy (RADRIS) techniquean optical transition in neutral nobelium (No, Z = 102) was identified. A remnant signal when delaying the ionizing laser indicated the influence of a strong buffer gas induced de-excitation of the optically populated level. A subsequent investigation of the chemical homologue, ytterbium (Yb, Z = 70), enabled a detailed study of the atomic levels involved in this process, leading to the development of a rate equation model. This paves the way for characterizing resonance ionization spectroscopy (RIS) schemes used in the studyof nobelium and beyond, where atomic properties are c…
Growth kinetics of racemic heptahelicene-2-carboxylic acid nanowires on calcite (104).
2016
Molecular self-assembly of racemic heptahelicene-2-carboxylic acid on a dielectric substrate at room temperature can be used to generate wire-like organic nanostructures consisting of single and double molecular rows. By means of non-contact atomic force microscopy, we investigate the growth of the wire-like pattern after deposition by experimental and theoretical means. From analyzing the time dependence of the mean row length, two distinct regimes were found. At the early post-deposition stage, the mean length grows in time. Subsequently, a crossover to a second regime is observed, where the mean row length remains nearly constant. We explain these findings by a mean-field rate equation a…
Experimental organic matter maturation at 2kbar: Heat-up effect to low temperatures on vitrinite reflectance
2012
Abstract An experimental study was performed to evaluate the effect of heat-up to various low temperatures on vitrinite reflectance ( VR ) at 2 kbar employing the same previously used heat-up procedures, starting material and apparatus. Heat-up is the isobaric experimental procedure consisting of the increase in temperature of the laboratory vitrinite maturation from room temperature to the desired run temperature T end of heat-up at which the isobaric-isothermal maturation starts. Experiments employed cold-seal pressure vessels with classical heat-up devices and were carried out on wet (water added) xylite of swamp cypress. Confined system maturation experiments were conducted at 2 kbar an…
Collisional Relaxation Processes Studied by Coherent Raman Spectroscopy for Major Species Present in Combustions
1992
The effects of collisional relaxation processes on the Q-branch profile of major species present in combustions have been studied by high resolution stimulated Raman spectroscopy. Particular interest has focused on the following collisional systems: N2-N2, O2-O2, CO2-CO2, O2-N2, N2-CO2 and N2-H2O. For each colliding pair, starting from accurate determinations of line broadening coefficients over a wide temperature range, state-to-state rates for rotational energy transfers have been deduced by using various fitting laws. Among these rate laws, special attention has been paid to the temperature dependence of the energy corrected scaling (ECS) law combined with a hybrid exponential-power law …
Remarks on regularity for p-Laplacian type equations in non-divergence form
2018
We study a singular or degenerate equation in non-divergence form modeled by the $p$-Laplacian, $$-|Du|^\gamma\left(\Delta u+(p-2)\Delta_\infty^N u\right)=f\ \ \ \ \text{in}\ \ \ \Omega.$$ We investigate local $C^{1,\alpha}$ regularity of viscosity solutions in the full range $\gamma>-1$ and $p>1$, and provide local $W^{2,2}$ estimates in the restricted cases where $p$ is close to 2 and $\gamma$ is close to 0.